case study on rational choice theory

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• Published: 01 October 2020

Deviations of rational choice: an integrative explanation of the endowment and several context effects

• Joost Kruis   ORCID: orcid.org/0000-0001-8700-0326 1 ,
• Gunter Maris 2 ,
• Maarten Marsman   ORCID: orcid.org/0000-0001-5309-7502 1 ,
• Maria Bolsinova 3 &
• Han L. J. van der Maas   ORCID: orcid.org/0000-0001-8278-319X 1  

Scientific Reports volume  10 , Article number:  16226 ( 2020 ) Cite this article

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• Human behaviour
• Statistical physics

People’s choices are often found to be inconsistent with the assumptions of rational choice theory. Over time, several probabilistic models have been proposed that account for such deviations from rationality. However, these models have become increasingly complex and are often limited to particular choice phenomena. Here we introduce a network approach that explains a broad set of choice phenomena. We demonstrate that this approach can be used to compare different choice theories and integrates several choice mechanisms from established models. A basic setup implements bounded rationality, loss aversion, and inhibition in a natural fashion, which allows us to predict the occurrence of well-known choice phenomena, such as the endowment effect and the similarity, attraction, compromise, and phantom context effects. Our results show that this network approach provides a simple representation of complex choice behaviour, and can be used to gain a better understanding of how the many choice phenomena and key theoretical principles from different types of decision-making are connected.

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Introduction.

The response behaviour of humans on (discrete) choice problems has been extensively studied in many fields of science, such as economics 1 , 2 , 3 , 4 , psychology 5 , 6 , 7 , 8 , psychometrics 9 , 10 , cognitive science 11 , 12 , 13 , 14 , neuroscience 15 , 16 , and engineering 17 , 18 . Traditional theories of choice assume the decision-maker as a homo economicus 19 , 20 , i.e., rational 1 , 5 , 21 . For choices to be rational all choice alternatives must be comparable and have transitive preference relations, so they can be ordered by the decision-maker. A second feature, and a central principle of rational choice theory, is that a rational decision-maker consistently chooses the outcome that maximises utility, or expected utility for risky or uncertain choices 5 , 22 , 23 , 24 . These assumptions clearly fail the scrutiny of everyday experience. To account for the observed inconsistencies, most models nowadays characterise choice as a probabilistic process 6 , 9 , 21 , 24 , 25 , 26 , 27 , 28 , 29 .

A prominent group of probabilistic choice models, such as Luce’s strict utility model 6 , 24 and the multinomial logit model 21 for preference, and Bock’s nominal categories model 30 for aptitude, are characterised by the following distribution for the choices:

in which \(p_S(x) \in [0,1]\) represents the probably of choosing alternative x from the set of possible alternatives S as a function of the utility of alternative x , \(\exp (\pi _x)\) , where \(\pi _x \in \mathbb {R}\) . This distribution is also known as the Boltzmann distribution 31 , 32 from statistical mechanics. For binary choice problems \((S = \{x,y\})\) Eq. ( 1 ) takes a form known as the Bradley–Terry–Luce model in the decision-making literature 33 , 34 , or as the Rasch model 9 in psychometrics:

Models with this form have the property of simple scalability, which implies that the probability of choosing option x over option y is strictly increasing in the utility of x and strictly decreasing in the utility of y . Several properties with respect to independence from irrelevant alternatives (IIA) and transitivity follow from simple scalability. The degree to which choices are considered rational from a probabilistic perspective, is often described by the extent to which the choice probabilities for a set of choice alternatives possess these properties 6 , 24 , 35 , 36 , 37 .

For example, the weakest form of IIA is regularity, which implies that the probability of choosing an alternative can never increase by adding more alternatives. A set of preference probabilities is regular if \(x \in A \subseteq S\) and \(p_{\scriptscriptstyle {A}}(x) \ge p_{\scriptscriptstyle {S}}(x)\) . The strongest form of IIA is the choice axiom that is satisfied when \(x \in A \subseteq S\) and \(p_{\scriptscriptstyle {S}}(x) = p_{\scriptscriptstyle {A}}(x) \sum _{y \in {\scriptscriptstyle {A}}}p_{\scriptscriptstyle {S}}(y)\) . Meaning that the probability of choosing an alternative from a particular set is equal to the probability of choosing the alternative from a subset times the probability of selecting any alternative in this subset from the original set. Models are characterised as either strict, strong, or weak binary utility models depending on the expression that can be used to obtain the binary choice probabilities. If the positive real number \(v_i\) denotes the utility of alternative i , then a model is strict if \(p_{x,y}(x) = v_x/(v_x + v_y)\) , strong if \(\phi\) is a cumulative distribution function with \(p_{x,y}(x) = \phi [v_x - v_y]\) and \(\phi [v_x - v_x] = {}^{1}\!/_{2}\) , and weak if \(p_{x,y}(x) \ge {}^{1}\!/_{2}\) when \(v_x \ge v_y\) . Rationality is also assessed by considering different observable properties of pairwise probabilities, such as the product rule, quadruple condition, strong, moderate, and weak stochastic transitivity, and the multiplicative and triangle conditions, each describing a different degree of strictness in the ordering of the choice probabilities. We refer the reader to Luce and Suppes 24 for a comprehensive treatment of these properties.

Although models with simple scalability have statistically desirable properties, their assumptions are often violated in reality. In the preferential choice literature for example, violations of IIA known as the similarity, attraction, compromise, and phantom context effects describe different situations in which the preference relation between two choice alternatives changes when a third alternative is introduced 7 , 24 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 . Another example is the endowment effect that describes the tendency of people to perceive an alternative as having increased in value after they have chosen it 3 . We will discuss these violations and phenomena in more detail later.

Over time, theories and models have been adapted or extended to account for these deviations. Bounded rationality 53 , for example, is the theory that instead of searching for the alternative with maximum utility, we search until we find the first alternative with satisfactory utility. Loss aversion, which postulates that the perceived utility of not losing something is greater than the perceived utility of gaining that exact same thing, was offered as an explanation for the endowment effect 3 , 54 , 55 . Whereas the elimination by aspects model 42 provided a first account for the similarity effect only, multi-attribute multi-alternative sequential sampling models, such as multi-alternative decision field theory 14 , 56 , 57 , 58 , 59 , 60 , the leaky competing accumulator model 61 , 62 , 63 , 64 , the multi-attribute linear ballistic accumulator model 65 , 66 , 67 , the \(2N-\) ary choice tree model 68 , 69 , and the associations and accumulation model 70 , also account for the attraction and compromise context effect using a range of different mechanisms. The interested reader is referred to three recent papers that offer a comprehensive comparison between the different models 37 , 71 , 72 .

Although these approaches are capable of modelling context effects, one drawback is that they are fairly complex. With increasing complexity generalisability often takes a hit, and models that are tuned to account for one type of choice effect fail to account for other choice effects, hence drawing inferences beyond the task-setting becomes challenging. Developing a simple choice model that is capable of connecting a broader spectrum of choice phenomena would thus be a worthwhile effort. For one, unifying distinct phenomena in a collective framework puts them on equal footing and hence can stimulate the development of formal theories that can account for all of them. Also, formalising our theories requires us to be precise and concrete, this in contrast to verbally formulated theories which are easily misinterpreted, often hold hidden assumptions, claim predictions that are not clearly derived from the theory, as well as hide consequences from the model that are not desired. Moreover, formal theories may lead to interesting predictions and new insights, and hence new possibilities to falsify the theory, that might not have been discovered if the phenomena are investigated independently. In this paper we propose such a probabilistic model for choices that conceptualises choice problems as a combination of a choice structure, an alternative evaluation process, and a choice trigger condition.

In the remainder of this paper, we start by introducing the choice structure, represented by a network in which the nodes are the cues and alternatives, and the edges describe the relationships between them. We demonstrate a basic setup of our choice model, in which the binary node states follow a distribution known as the quadratic exponential binary distribution, or Ising model, and alternatives are evaluated with single spin-flip dynamics. Sampling choices from the invariant distribution of the configurations in which only one alternative is active, the choice conditions, gives us choice probabilities with the same form as the Boltzmann distribution from Eq. ( 1 ). Triggering a choice as soon as the condition holds for the first time, implements bounded rationality and predicts the occurrence of context effects. We then discuss how our approach compares to multi-attribute multi-alternative models and implements, or might be extended with, the mechanics used by those models. Finally, we discuss some challenges and future directions for the model.

Here we introduce the different components of the choice model and derive predictions for choice probabilities and response times.

Choice model

The choice model consists of a structure, a process, and a trigger. The choice structure describes the alternatives available for a choice and the origin of their utilities. The choice process describes how the alternatives are evaluated. The choice trigger describes the condition that stops the evaluation process and prompts a decision.

The specific form of these three components allows for some variation depending on the specific setting. For example, in this paper we let the state of cues and alternatives in the choice structure be either active or inactive. While this is reasonable in the case of preferential choice, in the case of modelling an opinion we might want to use three possible states, namely pro, neutral, or against. These types of variations are also possible in the case of the process and trigger elements of the choice model, and we discuss several of them throughout the paper.

In their simplest form choices can be structured as a combination of cues and alternatives and the relationships between them. Cues represent the conditions of the choice, e.g., ‘buy a book’, ‘select a present’, or ‘solve for x ’, and alternatives describe the possible choices. An appropriate representation of such a structure is a network in which the nodes correspond to the alternatives and the cues, and the edge between two nodes describes their relation. Figure 1 shows how the structure of a particular choice problem can be seen as a subset from a larger collection of related concepts.

Graph of (related) concepts and subsets of concepts as possible choice problems. Nodes represent concepts and edges represent a relationship between concepts. Nodes surrounded by a dashed box, represent concepts that can form a potential choice problem. For example, ( a ) If you have to choose between taxes ( TAX ), migration ( MIG ), or universal health care ( UHC ), which policy ( POL ) is most important for you? ( b ) Do you prefer Candidate 1 \((C_1)\) , Candidate 2 \((C_2)\) or Candidate 3 \((C_3)\) , as the Presidential Nominee ( PN )? ( c ) Is Washington DC ( WDC ) or Paris ( PAR ) the capital ( CAP ) of France ( FRA )? ( d ) Do you want a sandwich ( SDW ), a baguette ( BAG ), or a croissant ( CRO ) for breakfast ( BRF )? Concepts present in the graph but not part of a subset are respectively, age ( AGE ), United States of America ( USA ), Congress ( CON ), and Eiffel Tower ( EIF ).

To arrive at predictions about choice behaviour we assume that both the type and strength of a relationship between two nodes can vary, and that nodes outside of the choice subset can also influence a decision through their relationship with nodes that are in the choice subset. In Fig. 2 possible relationships between a cue and the alternatives are illustrated for the choice structure from Fig. 1 b.

Choice structure with a single cue ( PN ) and three alternatives \((C_1, C_2, C_3)\) . Cues are represented as dark grey nodes with white text and alternatives are represented as light grey nodes with black text. Edges represent a positive (solid) or negative (dashed) relationship between nodes, and a ring around a node represents whether the nodes is generally appealing (solid) or unappealing (dashed). The thickness of both the edges and rings around the nodes corresponds to intensity of the relationship/appeal.

We refer to the experienced magnitude and direction of an alternative’s utility in terms of an alternative’s appeal. Figure 2 shows that an alternative’s appeal is a function of its general appeal and relationship with the cue and the other alternatives. The general appeal of an alternative captures the relation between the alternative and nodes that are not in the choice structure. For example, in Fig. 1 we see that the general appeal of a candidate is a function of policy and age. The relation with a cue can positively or negatively affect the appeal of an alternative. For example, asking Do you want a nice and fresh croissant, yesterdays leftover sandwich, or a somewhat dry baguette, for breakfast? enhances the appeal of the croissant through the suggestive phrasing of the cue. A relation between two alternatives signals that the appeal of one is related to that of the other alternative. The next step is formalising the choice structure as a probability distribution.

For a choice structure with n nodes, let \(\mathbf {x} = [x_1, x_2, \dots , x_n]\) be a vector representing the configuration of the node states in which \(x_i \in \{0,1\}\) denotes whether node i is active \((x_i = 1)\) or inactive \((x_i = 0)\) . Let \(\mathbf {A}\) be a symmetric \(n \times n\) matrix in which \(a_{ij} \in \mathbb {R}\) describes the relation between the node i and node j in the choice structure. Let \(\mathbf {b} = [b_1, b_2, \dots , b_n]\) be a vector of length n in which \(b_i \in \mathbb {R}\) describes the general appeal of node i . A valid probability distribution over the states is obtained by endowing them with the following distribution:

in which \(\beta\) , a non-negative real number, and \(\mu \in \mathbb {R}\) are scaling constants, \(\sum _{\langle i,j \rangle }\) denotes the summation over all distinct pairs of i and j , and Z is the normalising constant that sums over all the \(2^n\) possible configurations of \(\mathbf {x}\) such that the probabilities of the possible states sum to one. We can multiply \(\beta\) by some constant and divide \(\mathbf {A}\) and \(\mathbf {b}\) by the same constant without affecting the probabilities of the states, the same holds for \(\mu\) and \(\mathbf {b}\) . As such, we set both \(\beta\) and \(\mu\) to one for now, making them drop out of the equation, and discuss later how they might be used to model choice setting variations, such as time-pressure and/or individual differences.

The distribution in Eq. ( 3 ) can be recognised as the Ising model 73 , 74 , a highly popular and one of the most studied models in modern statistical physics 75 , or as the quadratic exponential binary distribution as it is known in the statistics literature 76 , 77 . Capable of capturing complex phenomena by modelling the joint distribution of binary variables as a function of main effects and pairwise interactions 78 , it has been used in fields such as genetics 79 , educational measurement 80 , and psychology 78 , 81 , 82 , 83 . In the context of choice it has been applied in sociology in Galam’s work on group decisions in binary choice problems 84 , 85 . In this application each node represents the choice of one person on a specific problem, and the pairwise interactions describe the influence of all people in the group on the individuals choice. Another application is the Ising Decision Maker from Verdonck and Tuerlinckx 86 , a sequential sampling model for speeded two-choice decision-making. In this model each of the two alternatives is represented by a pool of nodes, inside a pool nodes excite each other, between pools nodes inhibit each other. A stimulus is represented by a change in the external field, after which the node states are sequentially updated. The response process monitors the mean activity per pool, and chooses the first alternative for which this activity crosses a threshold. Both these models use this distribution in a substantially different way compared to the current application, and have not been applied to explain deviations from rationality. As such we will not discuss them in more detail for this paper.

A connection between Eq. ( 3 ) and probabilistic choice models is found by realising that the distribution of \(\mathbf {x}\) is a function of the Hamiltonian:

and that the probability of each configuration is given by plugging \(H_{\mathbf {x}}\) in the Boltzmann distribution from Eq. ( 1 ). That is, if S is the set of all configurations that a particular system can take and \(\mathbf {x}\) is one possible configuration of this system, then the probability of the system being in this state is given by:

We assume that until a person is faced with a choice, the internal state of the decision-maker (the resting configuration) is distributed according to Eq. ( 3 ). An advantage of this assumption is that well defined stochastic processes for these systems exist and can be used in the next component of the choice model that describes how alternatives are evaluated until a choice is triggered. When a person is confronted with a choice all cue nodes are activated and remain so during the choice process. The alternatives will, in most cases, be distributed according to the resting state distribution. Exceptions to this are discussed later on.

Although many configurations for the choice process are possible, to illustrate our approach we use a simple stochastic process for interacting particle systems to model the process of alternative evaluation. Specifically, a Metropolis algorithm with single spin-flip dynamics 87 in which a proposal configuration is generated at each iteration by sampling one alternative and flipping its state:

Let \(\mathbf {x}\) denote the current configuration of the system with \(H_{\mathbf {x}}\)

Select one node i at random and flip its value \(x^*_i = 1 - x_i\)

Calculate \(H_{\mathbf {x}^*}\) for the configuration with the flipped node.

If \(H_{\mathbf {x}^*} < H_{\mathbf {x}}\) , keep the configuration with the flipped node.

If \(H_{\mathbf {x}^*} \ge H_{\mathbf {x}}\) , keep the configuration with flipped node with probability \(\exp {\left( H_{\mathbf {x}} - H_{\mathbf {x}^*}\right) }\) .

For a choice with m alternatives the evaluation process will thus transition between \(2^m\) possible configurations of the alternative states.

From Eq. ( 4 ) it can be derived that in a choice structure in which both the general appeal and the relationships are positive, the most likely configuration is the one with all alternatives active. This is reasonable as it implies that the most preferred state for a decision-maker is to posses all alternatives. In most applications a person is forced to choose only one of the alternatives, however. We impose this by defining potential choice conditions as configurations in which only a single alternative is active and discuss two possibilities for making decisions.

The first is that the alternative evaluation process is terminated when the single-spin flip algorithm has converged and a choice is sampled from the invariant distribution of the potential choice configurations:

in which \(M = [x_1, x_2, \dots , x_m]\) denotes the subset of m alternative nodes and \(K = [x_{m + 1}, x_{m + 2}, \dots , x_{m+k}]\) denotes the subset of k cue nodes. If we let the Markov chain run until convergence, the effect of any interactions between choice alternatives will have worn out and the property of simple scalability will hold for the choice probabilities, guaranteeing that choices are in accordance with the choice axiom. The choice axiom is known to be violated in particular choice problems, however, which leads us to the second choice trigger possibility.

At some moment during the process a potential choice condition is met for the first time. One could say that a choice has effectively been made and there is no need for a decision-maker to continue. This choice trigger implements the idea of bounded rationality and explains various types of irrational choices as we explain after we discuss the consequences of our model setup for rational choices.

Rational choice

Although our setup implements bounded rationality, it does not preclude rational choices. However, while choice structures can be made for which even the strongest gradation of rationality holds, finding clear cut rules for when a structure adheres to which gradations of rationality is a different kettle of fish. In the methods section we show that a very simple expression exists for the expected choice probabilities in the single spin-flip algorithm as a function of the transition matrix for the possible configurations of the alternatives. Deriving general rules for the adherence to different types of rationality requires one to express these probabilities as a function of the parameters \(\mathbf {A}\) and \(\mathbf {b}\) . As this expression is already of a gargantuan size for \(n=3\) , and there is no reasonable way to derive general algebraic properties from it, we only work out the binary case in the methods section and show that even then determining when choices are guaranteed to be at least weakly rational is not necessarily straightforward.

For \(n>2\) the expectation of rational behaviour for a particular choice structure has to be derived on a case by case basis. As for n alternatives there are \(2^n - n - 1\) possible subsets of at least two variables, investigating the assumption of independence of irrelevant alternatives will be more time consuming compared to determining properties of the pairwise probabilities of a choice set. A statistical program such as R 88 can calculate these expected pairwise choice probabilities in reasonable time for choice situations with up to 15 alternatives using the expression from the methods section. For larger numbers of alternatives numerical solutions can be obtained with a simulation approach. Additionally, assumptions that simplify the analytical expression for the expected choice probabilities can also be used to derive rational choice properties.

Irrational choice

We define irrational decision-making as those choice situations in which the odds of choosing one alternative over the other, as established by their pairwise choice probabilities, changes as a function of adding other alternatives to the set. We realise that for readers well versed within the choice literature this definition may seem both rather vague, because our definition creates a dividing line somewhere between the choice axiom and regularity, as well as strict, as violating the choice axiom means that the strictest rules and conditions for rationality can still hold for the binary choice probabilities. However, although we touched upon the different gradations of rationality in the previous paragraphs, we think that a more conceptual approach is more appropriate here. We will discuss examples in which it is immediately clear that the choice probabilities as predicted by rational choice theory are conceptually counter intuitive.

Context effects are perhaps the most well known and studied violations of IIA and are often described by a situation in which a preference relation between two alternatives, a target and a rival, is established. Then a third alternative is introduced, the decoy, and it is demonstrated that adding the decoy changes the choice probabilities in favour of the target. These effects can range from only increasing the probability for the target while keeping the original order of the preference relations between the alternatives intact, to a full reversal of the preference relation. In our model these effects can be explained by the presence of a relationship between two choice alternatives and its influence on the resting state distribution and the alternative evaluation process.

For several types of context effects we provide an example and show how it can be explained in our model. As our explanation of the context effect does not require bias in the presentation of the choice, we assume the relationship between all pairs of a cue and an alternative to be the same across the board \((a_{mk} = 1)\) . In the Supplementary Materials we work out the specific steps to calculate the choice probabilities for our example of the attraction effect, as well as provide the parameter values for the other examples.

The similarity effect 38 , 39 describes the situation in which adding a decoy that is highly similar to the rival results in an increased preference for a dissimilar target alternative. The classic example for this effect was given as a thought experiment that provides the choice probabilities, expected under rational choice theory for a choice between three recordings:

“Let the set U have the following three elements: \(D_C\) , a recording of the Debussy quartet by the C quartet. \(B_F\) , a recording of the eighth symphony of Beethoven by the B orchestra conducted by F . \(B_K\) , a recording of the eighth symphony of Beethoven by the B orchestra conducted by K . The subject will be presented with a subset of U , will be asked to choose an element in that subset, and will listen to the recording he has chosen. When presented with \(\{D_C, B_F\}\) he chooses \(D_C\) with probability \({}^{3}\!/_{5}\) . When presented with \(\{B_F, B_K\}\) he chooses \(B_F\) with probability \({}^{1}\!/_{2}\) . When presented with \(\{D_C, B_K\}\) he chooses \(D_C\) with probability \({}^{3}\!/_{5}\) . What happens if he is presented with \(\{D_C, B_F, B_K\}\) ? ...He must choose \(D_C\) with probability \({}^{3}\!/_{7}\) . Thus if he can choose between \(D_C\) and \(B_F\) , he would rather have Debussy. However, if he can choose between \(D_C\) , \(B_F\) , and \(B_K\) , while being indifferent between \(B_F\) and \(B_K\) , he would rather have Beethoven.”    Debreu, 1960 38 .

It is clear that these expected choice probabilities are highly implausible. Specifically, in this case one would expect that when presented with \(\{D_C, B_F, B_K\}\) , \(D_C\) would be chosen with probability \({}^{3}\!/_{5}\) and the remaining \({}^{2}\!/_{5}\) would be split evenly among \(B_F\) and \(B_K\) . Such intuition has been proven correct in studies with a similar format as the thought experiment 7 , 41 , 42 .

One choice structure that explains the similarity effect does this by introducing a negative association between the two Beethoven recordings, as in shown in Fig. 3 . The negative relation between \(B_F\) and \(B_K\) has no influence on choice probabilities for any of the possible two-element subsets, as such the slightly larger base appeal of \(D_C\) will result in choosing \(D_C\) with probability \({}^{3}\!/_{5}\) when presented with \(\{D_C, B_F\}\) or \(\{D_C, B_K\}\) . When presented with \(\{B_F, B_K\}\) , the negative relation works in both ways and \(B_F\) and \(B_K\) are chosen with equal probability. While the conditional distribution of the model from Eq. ( 6 ) predicts that \(D_C\) will be chosen with probability \({}^{3}\!/_{7}\) when a choice has to be made from all three alternatives together, the rule that one stops as soon as the choice conditions hold for the first time will actually predict that when presented with \(\{D_C, B_F, B_K\}\) , \(D_C\) is chosen with probability \({}^{3}\!/_{5}\) and \(B_F\) and \(B_K\) are both chosen with probability \({}^{1}\!/_{5}\) . Our explanation of the ‘irrational’ (yet intuitive) choice behaviour in this example of the similarity effect rests on the presence of a negative relation between the Beethoven recordings.

Choice structure for Debreu’s example of the similarity effect. With cue ‘choose a recording’ ( R ), and alternatives, ‘Beethoven conducted by F ’ \((B_F)\) , ‘Beethoven conducted by K ’ \((B_K)\) , and ‘Debussy by the C quartet’ \((D_C)\) .

One could argue that the ability to reverse engineer a network structure until the desired choice probabilities are obtained is a weakness of our approach. We believe that this is actually an advantage as, for one, it is possible to check if adaptations of the choice structure will still result in plausible choice behaviour. For example, imagine that you chose \(B_K\) from the set \(\{D_C, B_F, B_K\}\) and are asked to choose once more from the remaining recordings \(\{D_C, B_F\}\) . Taking into account that you already have \(B_K\) \((x_{B_K} = 1)\) , the negative relation between \(B_K\) and \(B_F\) in our choice structure results in a prediction that you will choose \(D_C\) with near certainty. This demonstrates that the choice structure does not only explain observed behaviour, but also predicts new, and in this case plausible, behaviour for adaptations of the choice problem. Furthermore, as we will discuss in the next example, it also allows one to come up with theoretically distinct choice structures for a single choice phenomenon and compare them. While the initially expected choice probabilities might be the same, manipulations that result in distinct predictions for each choice structure can be tested.

The attraction, or asymmetric dominance, effect 44 , 45 describes the situation in which the addition of a decoy alternative that is a substandard version of the target increases the preference for the target. Simonson and Tversky 46 investigated this effect by offering two groups a choice between (a subset of) 6 dollar \(({\$})\) , a nice pen \((P_+)\) , and a (less attractive) plain pen \((P_-)\) . In the first group, choosing from the subset \(\{{\$}, P_+\}\) , more people chose the money (64%) compared to the nice pen (36%). In the second group, choosing from the set \(\{{\$}, P_+, P_-\}\) , as expected, almost no one chose the plain pen (2%), however, the money was now only chosen 52% of the time, while the proportion of people choosing the nice pen rose to 46%.

Figure 4 shows two possible choice structures that predict expected choice frequencies similar to those found in the experiment, however, each of these explain the attraction effect in a different way. In Fig. 4 a the explanation of the attraction effect rests on the presence of a negative association between the money and the plain pen, while in Fig. 4 b the effect is explained by a positive association between both of the pens. Our model thus provides two theoretically distinct choice structures that both explain how the mere addition of a less appealing decoy can boost the choice probabilities for the otherwise less frequently chosen target alternative.

Choice structure for Simonson & Tversky’s example of the attraction effect. With cue ‘choose an Reward’ ( R ), and alternatives, ‘money’ \(({\$})\) , ‘nice pen’ \((P_+)\) , and ‘plain pen’ \((P_-)\) . The attraction effect can be explained with a negative relationship between the money and the plain pen ( a ), or a positive relationship between the two pens ( b ).

Obtaining the same results from different structures allows us to compare the different theories and predictions that characterise each structure. For example, someone who chose \(P_+\) as reward from the set \(\{{\$}, P_+, P_-\}\) is asked to choose once more from the remaining rewards \(\{{\$}, P_-\}\) . Taking into account that this person already possesses \(P_+\) \((x_{P_+} = 1)\) , the negative relation between \({\$}\) and \(P_-\) , in choice structure a , results in a prediction of choosing \({\$}\) in more than 90% of the cases, whereas the positive relation between \(P_+\) and \(P_-\) , in choice structure b , results in a prediction of still choosing \(P_-\) in 33% of the cases. While the initially expected probability distribution for choice structures a and b are thus the same, from the different prediction they make about a new situation, we can clearly distinguish which structure seems more plausible. The fact that our approach allows for these kinds of comparisons, and provides testable predictions, makes the theories captured in the model falsifiable.

In some cases the addition of a substandard version of the target alternative actually decreases the probability of selecting the target 89 , 90 , 91 , 92 . This reversed attraction effect, called the negative attraction or repulsion effect, although not consistently demonstrated, is mostly observed when choices are framed such that the decoy highlights the shortcomings of the more similar target alternative. For example, adding a smaller clementine to the choice between a fruit flavoured candy bar and an orange, might boost the probability of choosing the orange, as the clementine highlights the freshness and health aspects of citrus fruits. However, if the clementine shows some signs of a reduced freshness, e.g. crumpled skin or beginning to mould, it highlights the fleeting freshness of citrus fruit, and might instead boost the probability for the sugar filled candy bars and their long shelf life.

Just as the repulsion effect is the opposite of the attraction effect, so is its explanation, i.e., a positive relation between the rival and decoy alternatives. In the pen example from Fig. 4 , switching the sign of the relation between the money \(({\$})\) and the plain pen \((P_-)\) so it becomes positive, while keeping all other parameters the same, predicts a boost in the probability of choosing of the money \(({\$})\) with respect to the nice pen \((P_+)\) . Interestingly, whereas the negative relation in the attraction effect can result in a relatively large gain in choice probability for the target \((+ 10\%)\) , the same structure but with a positive relation results in only a modest gain in the predicted choice probability for the rival \((+ 2\%)\) . To increase the magnitude of the repulsion effect one has to decrease the general appeal of the added decoy. Finally, adding both an attracting and a repulsing decoy results in the context effects cancelling each other out when choosing between all four options.

The compromise effect 45 describes the situation in which a decoy is added for which the distance to the target mirrors that of the distance between the rival and the target, but in the opposite direction. This boosts the preference for the target alternative by making it seem like the compromise. Distance should in this context be interpreted as the relative position of the alternatives on particular attributes, such as prize and quality in the next example.

Tversky and Simonson 47 investigated the compromise by offering two groups a choice between (a subset of) cameras of either low ( L ), medium ( M ), or high ( H ), prize and quality. While in the first group, choosing from the subset \(\{L, M\}\) , people chose both cameras with approximately equal probability, in the second group, choosing from the set \(\{L, M, H\}\) , people now chose both cameras L and H each with a probability of approximately \({}^{1}\!/_{4}\) , while camera M was still chosen with a probability of approximately \({}^{1}\!/_{2}\) . Based on the seemingly equal appeal of the L and M camera in group one, one would expect that both would be also be chosen with an approximately equal probability in group two. Or conversely based on the lower appeal of camera L in group 2, one would expect that in group one camera L would be chosen with a probability of approximately \({}^{1}\!/_{3}\) and hence camera M with a probability of approximately \({}^{2}\!/_{3}\) .

A possible explanation for why this is not the case might be that the (dis)advantages between the cameras H and L camera are much more evident than those between the cameras M and L or M and H . Therefore, the weakness of camera L gets highlighted when camera H is part of the choice set, this in turn frames the camera M as the compromise that is of higher quality compared to camera L , but not as expensive as camera H . Once again, as is shown in Fig. 5 , our explanation of the compromise effect can be captured by introducing a negative relation between the rival camera L and the decoy camera H .

Choice structure for Tversky & Simonson’s example of the compromise effect. With cue ‘buy a Camera’ ( C ), and alternatives with respective quality and prize levels, ‘Low’ ( L ), ‘Medium’ ( M ), and ‘High’ ( H ).

So far the similarity, attraction, and compromise effect are each explained in our model by a negative interaction between the decoy and the rival. Whereas in the similarity effect, this relation is assumed to exist because of the large similarities between the rival and decoy alternatives, in the attraction and compromise effects, however, this relation is a function of the large dissimilarities between the two.

One explanation for this could be that only when (dis)similarities go into the extreme they are highlighted and start influencing the choice process. Another explanation comes from observed correlations between context effects, i.e., one study found that people who show the attraction effect also show the compromise effect, but not the similarity effect 60 . This could suggest that people either focus on similarities or dissimilarities, and hence the choice structure of a person only contains negative relations for one of those types. Whereas the attraction and compromise effect occur when a choice structure contains only negative relations as a function of dissimilarity, a choice structure in which negative relations are the result of similarity will only elicit the similarity effect. Not all context effects can be explained by a (negative) relation between the rival and decoy alternatives alone. In some cases it also manifests itself through the influence of the choice structure on the initial alternative configuration.

The phantom decoy effect 52 describes the situation in which the added decoy alternative is superior to both the target and rival alternatives, yet more similar to the target compared to the rival, but most importantly, unavailable. When it is communicated that the decoy cannot be chosen it subsequently boosts the preference for the target alternative.

Pratkanis and Farquhar 52 studied the phantom decoy effect by offering two groups a choice between (a subset of) paperclips each with varying degrees of friction and flexibility. The target paperclip ( T ) and the rival paperclip ( R ), although different in these properties, were of comparable quality. The decoy paperclip ( D ) had a quality superior to both T and R but was in terms of friction and flexibility more alike to paperclip T . In the first group, choosing from the subset \(\{T, R\}\) , people chose each paperclip with approximately equal probability. People in the second group, however, who thought they where choosing from the set \(\{T, R, D\}\) , chose the paperclip of type T with a probability of approximately \({}^{4}\!/_{5}\) , after the decoy D was revealed to be unavailable and hence the choice had to made again from the subset \(\{T, R\}\) .

As is shown in Fig. 6 , our explanation of the phantom decoy effect, at this point perhaps unsurprisingly, partially rests on the presence of a negative relation between the rival and the decoy. It depends however, on when the unavailability of the decoy is communicated how the phantom effect is elicited. If this is communicated before the choice is offered the first time, the choice process is still updated to still sample and flip, but not terminate at, paperclip D . As shown in Fig. 6 a, the combination of a negative relation between the D and R paperclips, together with the larger general appeal of paperclip D , reduces the probability for choosing paperclip R . If the unavailability of paperclip D is not communicated before the first choice and all three paperclips appear to be available, the choice structure from Fig. 6 a without the previously introduced constrained will be evaluated and paperclip D is most likely to be chosen. At this point, the configuration of the choice structure is known, as only the cue and the node for paperclip D will be active. If at this point one is informed that paperclip D is unavailable, the choice process starts again from the known configuration. Given that node D is active, we can from this moment regard it as an additional cue, as is shown in Fig. 6 b. Consequently, due to the negative interaction between paperclip D and paperclip R , flipping the R node and hence choosing it become less likely compared to paperclip T .

Choice structure for Pratkanis & Farquhar’s example of the phantom decoy effect. With cue ‘choose a Paper Clip’ ( PC ), and the decoy ( D ), rival ( R ), and target ( T ) paperclip alternatives. Depending on when the unavailability of the decoy is communicated, the phantom decoy effect is explained by a constrained version of the regular choice process ( a ), or an additional choice process in which the decoy is an extra cue ( b ).

As shown in the Supplementary Materials , eliciting the phantom effect requires a much stronger negative relation between the decoy and rival when the unavailability of the decoy is known upfront, compared to when the unavailability is communicated after a choice is made for the first time. While it is easily argued that this is a rather intuitive hypothesis, it once again shows that our approach allows for making diverging predictions based on variations in the model setup.

The endowment effect 3 describes the situation in which people value an object higher if they possess it compared to when they do not. To illustrate this effect we consider a variation on the Debreu example in which you are given a Beethoven recording ( B ) and are immediately asked if you want to exchange it for an equally appealing Debussy recording ( D ). While the choice axiom predicts that you would exchange Beethoven for Debussy about half the time, the endowment effect says that people are unlikely to switch, a prediction that has been experimentally verified 93 . The endowment effect has been explained with choice-supportive bias 94 and loss aversion 54 .

In our model both explanations would translate to an increase in base appeal of an alternative as soon as it has been chosen. With our setup we obtain a new explanation that does not depend on changes in the values of the choice problem but ties into the choice process itself. Having been given the Beethoven makes the choice conditions satisfied, and hence the initial configuration of the alternatives is known when offered to exchange it for the Debussy. Exchanging them requires a sequence of events in the choice process that, due to the equal appeal of both alternatives, has a lower probability compared to keeping the Beethoven. Specifically, the only way that switching becomes an option is when the initial state, the choice condition for the Beethoven, is left in the first iteration by sampling and accepting the flip of either node B or node D . From the resulting configurations both choices are then equally likely. Let \(u_R = a_{RB} + b_B = a_{RD} + b_D\) denote the appeal for both the Beethoven and Debussy recordings. The probability of exchanging B for D is then given by:

Equation ( 7 ) shows that only when someone is indifferent about both alternatives \((u_R = 0)\) , i.e., they are neither appealing nor unappealing, the probability of exchanging is a half. In all other cases the endowment effect rears its head and the probability of exchanging will be less a half. Having demonstrated how several choice phenomena are explained in this setup, we turn to another property of our model, response times.

Response times

Response time predictions can be very informative when comparing different choice structures, evaluation processes and trigger conditions. As shown in the methods section, the single spin-flip algorithm provides the expected number of iterations until a choice condition is reached as a proxy for time. This can be used to investigate expected ordering of response times for a particular choice structure. For example, in a simple structure with no relationship existing between alternatives the expected number of iterations before a choice is triggered increases in the number and appeal of the alternatives. Or, assuming that longer response times are indicative of more deliberate decision-making, i.e., requiring more visits to a choice condition before a choice is triggered, we expect that context effects diminish and choices get increasingly rational. With increasing the required number of visits to a choice condition, choice probabilities go to Eq. ( 6 ) if a choice is sampled proportional to the number of visits of each condition. If the first alternative for which the choice condition has been visited the required number times is chosen, choice probabilities go to one for the alternative with the highest general appeal.

The model also allows incorporating response time phenomena such as the speed-accuracy trade-off 95 , which predicts that under time-pressure choices are faster but less accurate, through \(\beta\) . In an application of the Ising model to attitudes 96 , 97 , the attention to an attitude object is represented by \(\beta\) . This interpretation fits well within the choice model, as such an inverse relation can also be assumed between time-pressure and attention. As \(\beta\) scales the magnitude of the entire choice structure, lower values will not only reduce the expected number of iterations before a choice is made, but also the effect of \(\mathbf {A}\) and \(\mathbf {b}\) , and with that the magnitude of the context effects. This is also in line with research that showed that context effects tend to be smaller under time-pressure 66 , 98 . Choice expectations under time-pressure can be even more fine-tuned by using \(\mu\) . For example, the assumption that people under time-pressure only focus on the general appeal of the alternative can be modelled by letting \(\mu = {}^{1}\!/_{\beta }\) . In the methods section we show how different forms of time-pressure, modelled as variations in the relation between \(\beta\) and \(\mu\) , influence the expected choice probabilities for the attraction effect.

In this article we proposed a model for choices in which the choice structure is represented by a network, for which the node states have a distribution known as the quadratic exponential binary distribution or Ising model. Single spin-flip dynamics describe the alternative evaluation process in our basic setup, and potential choice conditions are states in which only one alternative is active. The invariant distribution of this choice process is the same as that of several classic choice models with the property of simple scalability, which guarantees choices to be rational. Stopping when the choice conditions hold for the first time predicts a series of well known violations of rationality known as context effects and several other choice phenomena. This approach allows one to represent choice situations in an accessible way, and can be used to compare different choice structures, alternative evaluation process assumptions, and trigger variations with respect to the choice behaviour they predict. Furthermore, as we show next, it implements or can be extended with features and mechanics used in more complex choice models. We first review the relation between our model and the elimination by aspects (EBA) model, multi-alternative decision field theory (MDFT), the leaky competing accumulator model (LCA), and (simple) 2N-ary Choice Tree (2NCTs), and end with discussing some limitations and prospects of our approach.

One of the first models to offer an explanation for the similarity effect was Tversky’s EBA model 42 . In the EBA model an alternative is characterised by a collection of attributes. At each step in the choice process one attribute is selected proportional to an attention weight, and alternatives without this attribute are eliminated until only one alternative remains. Although the utility of an alternative in the EBA model is a function of unique attributes and those shared between pairs of alternatives, choice probabilities can be calculated independently of the specific attributes. The EBA model can only explain the similarity effect, which occurs when a subset of the alternatives share some attributes that are not shared with the other alternatives. For example, the two Beethoven recordings share attributes that are not shared by the Debussy recording. As such the probability of selecting an attribute that is unique to a Beethoven is smaller when both recordings are in the choice set with the Debussy, compared to when only one is.

MDFT, the LCA, and 2NCTs, are capable of explaining more context effects. They are sequential sampling models, which entails that (noisy) information about the alternatives is integrated in an accumulator for each alternative throughout the choice process. Whereas MDFT and the LCA each assume one accumulator per alternative, in the 2NCTs each alternative has two accumulators, one for positive information and one for negative information. For all models the process stops when either a time limit is reached or one of the (positive) accumulators crosses a threshold, triggering in both cases a choice for the alternative for which the most (positive) information is accumulated. In the 2NCTs the process can also terminate when for all but one of the alternatives the threshold of the negative accumulator is crossed and these alternatives are eliminated.

As in the EBA model, an alternative’s appeal is a function of its attributes and attention switches between these attributes over time. The explanation of the context effects in MDFT, the LCA, and 2NCTs rest primarily on some form of asymmetry between, or particular positioning of, the alternatives on attributes and must therefore be specified for all alternative-attribute combinations. In our model we do not need to specify different attributes or assume switching between attributes to predict context effects, as the influence of attributes is captured in the general appeal of the alternative. The influence of different attributes can be made explicit by adding an additional layer of attribute nodes , in which the position of the alternative on the attribute is encoded in the edge between them. During the process one can assume that attributes are always active and function as cues, or let their activity vary over time to incorporate the assumption that attention stochastically switches between attributes.

The models require several other mechanisms to explain context effects. Lateral inhibition 99 , a neural concept in which an exited neuron inhibits its neighbours, is applied with the same magnitude for all alternative pairs in the LCA, and decreasing with the distance between alternatives in MDFT. The LCA and 2NCTs (also) rely on an implementation of loss aversion. In the LCA accumulators can only take non-negative values and the influence of negative differences between attribute values relative to positive differences is reduced. In the 2NCTs the evaluation process decreases the probability of updating a negative accumulator relative to that of a positive accumulator.

Both inhibition and loss aversion are part of our model. Loss aversion is implemented within the process of single spin-flip dynamics, i.e., the probability of activating an appealing alternative is always one, whereas the probability of eliminating an appealing alternative is decreasing in the appeal. Inhibition comes in the form of the negative interactions between the alternatives and plays a vital role in the prediction of context effects. Global inhibition as found in the LCA can be implemented by lowering the interaction between each pair of alternatives with a constant. Otherwise independent alternatives then become negatively related and the evaluation process will move faster to a potential choice condition 100 .

Although our approach has several advantages with respect to the more complex multi-attribute multi-alternative models, it does not provide the same insight in choices times distributions. That being said, our predictions with respect to the ordering of response times are often the same as these models, and the model even provides novel explanations for some response time phenomena. For example, the prediction that context effects strengthen with longer decision times can, in addition to time-pressure, also be explained by the format of the experiment. The study manipulated time-pressure by letting a participants evaluate the characteristics of novel stimuli for 2, 4, 6, or 8 s, after which a choice had to be made immediately. Participants who could look to the stimuli for less than 8 s made choices less consistent with the context effects compared to participants that could look for 8 s 98 .

Whenever a choice is presented the available alternatives must be encoded to determine their appeal, a process that takes time. For daily choices alternatives are recurring and embedded within a stable choice structure such that decoding takes almost no time. New alternatives must be placed within the global structure and connected to the relevant concepts before their perceived appeal stabilises. As multi-attribute multi-alternative models must specify all alternatives-attribute combinations, studies often use fictional products defined on small numbers of attributes only. Fictional alternatives are new to the participant and time is required to derive the general appeal of, and establish the appropriate relationships between, alternatives. This explanation is consistent with a transition from \(\beta = 0\) , a choice structure with no relationships and no general appeal, to \(\beta = 1\) , a fully formed structure, during this transition the magnitude of the context effects increases. In contrast to the other models, however, our model predicts that context effects diminish when time-pressure is reduced even further and more deliberation can take place before a choice is triggered.

We discussed our model assuming that all alternatives are known and everyone has the same choice structure. It is clear that choice situations exist in which the alternatives are not necessarily provided, or in such large numbers that evaluating them all might be infeasible. Furthermore, while it is a common assumption that the behaviour of individuals can be described by a set of parameters for the group, it is often rather unrealistic. Future research should focus on extending the model for these situations. For example by introducing initial selection probabilities for alternatives to be included in the choice structure, or interpreting \(\beta\) and \(\mu\) as parameters that are different for each person, or extend the model for individual choice structures 101 .

We also recognise that data and findings in psychology from a few decades ago are sometimes questionable with respect to the current standards of research. For example, papers that used alternative methods to analyse data from a study by Tversky on within-person transitivity 102 , find that for several (but not all) persons for whom Tversky asserted that they showed intransitive behaviour, the results are no longer significant 103 , 104 , 105 . Although we believe that there is general consensus, based on a large body of research, that humans do not always make rational decisions, some experiments about irrational choice behaviour remain disputed. We therefore want to stress the importance of replicating these studies, or setting up new experiments that investigate the same phenomenon.

Another point, discussed in the paper by Regenwetter et al. 104 , is that often behaviour that may seem intransitive is actually rational when previously unobserved variables are taken into account. As an example they take a student that assumes that their supervisor’s perceived utility of meeting locations is stable over time, but that this is not the case as the varying teaching location of the supervisor actually determines this utility. As such, while the student judges the choices for meeting locations of the supervisor to be intransitive, this is in reality not the case. This example shows that, particularly for within-person choice effects, it is important to take context variables into account. In our model this could be accounted for by introducing nodes for these context variables, in case of the example a node for each of the teaching locations, that has a positive relation with the closest meeting locations, and which is active if the day of the meeting the supervisor has to teach in that location.

Even though very precise quantitative predictions are generally out of reach with behavioural data, there is merit in the prediction of qualitative phenomena, such as the ordering of probabilities, interaction effects, shapes of distributions, and even phenomena such as phase transitions. Formalising our theories about behaviour allows us to obtain these predictions. While we already propose multiple extensions to our model, ideally, it will be formal theories that dictate the assumptions, mechanisms, and structural characteristics to be used in a particular setup. By taking the opportunities to extend, refine, and improve the elements of the choice model, we can hopefully create a broad understanding of how the many phenomena and key theoretical principles from different types of decision-making are connected.

We derive the expression for the expected choice probabilities for the single spin-flip algorithm, demonstrate these steps for the attraction effect, and provide the parameter values for all examples used in the main text. We then visualise how variations of \(\beta\) and \(\mu\) influence the choice probabilities for the attraction effect. We end by showing the parameter based expression for the binary case and discuss some properties with respect to rational choice.

Single spin-flip dynamics

For a choice structure with k cues and m alternatives there are \(2^m\) possible configurations of \(\mathbf {x}\) . We use \(\mathbf {x}_i\) to denote the i th of these \(2^m\) possible states. Let \(\mathbf {P}\) be a square matrix of order \(2^m\) in which element \(P_{ij}\) contains the probability of transitioning from \(\mathbf {x}_i\) to \(\mathbf {x}_j\) in one step of the single spin-flip algorithm, and \(P_{ii}\) contains the probability staying in the current state. As the algorithm changes at most one alternative at each iteration \(\mathbf {P}\) will be highly sparse with at most m non-zero elements in each row. From \(\mathbf {P}\) we obtain the expected rational choice probabilities, contained in the stationary distribution, as they are proportional to the elements of the first eigenvector of \(\mathbf {P}\) that correspond to states in which the choice conditions are met (i.e., \(\sum _{i=1}^n x_i = k + 1)\) . We will not go into this approach at length as these probabilities can simply be obtained from the conditional distribution presented in Eq. ( 6 ).

The expected choice probabilities for stopping as soon as the choice conditions are met for the first time are obtained by reformulating the Markov chain with transition matrix \(\mathbf {P}\) as an absorbing chain. To that end we make a distinction between the m absorbing states, i.e., those states in which only one alternative is active, and \(2^m - m\) transient states, i.e., those states in which more than one alternative or no alternatives are active. The transition matrix for the absorbing chain \(\mathbf {P}^{*}\) has the canonical form:

in which \(\mathbf {Q}\) contains the transition probabilities between transient states, \(\mathbf {R}\) contains the transition probabilities from transient states to absorbing states, \(\mathbf {1}\) contains the transition probabilities between absorbing states, i.e., an identity matrix of order n , and \(\mathbf {0}\) contains the transition probabilities from absorbing states to transient states, i.e., a matrix with zeros. Rearranging \(\mathbf {P}\) in its canonical form allows us to derive the expected progression of the Markov chain more easily 106 .

Let \(y \in \{1,2,\dots , m\}\) denote the chosen alternative, let \(\mathbf {z} = [z_1, z_2, \dots , z_{{\scriptscriptstyle {2}}^m}]\) denote the resting state probabilities in which \(z_i \in [0,1]\) denotes the probability for the choice process to start in alternative configuration \(\mathbf {x}_i\) . We divide \(\mathbf {z}\) into the probabilities for starting in an absorbing state \((\mathbf {z}_a)\) , and for starting in a transient state \((\mathbf {z}_t)\) . Lastly, let t denote the number of iterations of the Metropolis algorithm.

The (marginal) probability that alternative y is chosen from the set of alternatives S is:

in which \(\mathbf {1}_y\) and \(\mathbf {R}_y\) represent the y th column of the matrices \(\mathbf {1}\) and \(\mathbf {R}\) respectively. Using the property of geometric series to rewrite the infinite sum over \(\mathbf {Q}^t\) this expression simplifies to:

The expected number of Metropolis iterations before alternative y is chosen is:

Once again we can rewrite the infinite sum over \(t \, \mathbf {Q}^{t-1}\) and simplify the expression to:

\(\varvec{\beta }\) and \(\varvec{\mu }\)

Influence of \(\beta\) and \(\mu\) on the choice probabilities ( a ) and response times ( b ) for the attraction effect example. The axes for both plots show \(\beta\) and \(\mu\) on a log-scale. ( a ) 6 different response phases are identified as a function of changes in \(\beta\) and \(\mu\) . ( b ) Response times are approximated with the log of the expected number of iterations before termination, averaged over all three choices.

Figure 7 visualises the effect of \(\beta\) and \(\mu\) on the expected choice probabilities and response times for the attraction effect example from Fig. 4 a. In Fig. 7 a we have identified 6 different response phases for this example.

Random phase (RND) The choice probabilities for choosing the money \(({\$})\) , the nice pen \((P_+)\) , or the not so nice pen pen \((P_+)\) , differ at most \(10\%\) from one another.

Strong attraction effect phase (AE+) The probability of choosing \(P_+\) is greater than the probability of choosing \({\$}\)

Normal attraction effect phase (AE) The probability of choosing \({\$}\) is smaller than \(62\%\)

Choice axiom phase (CA) The choice probabilities for all options differs only a marginally from those expected under Eq. ( 6 ) if \(\beta\) and \(\mu\) would both be one.

Increasingly rational phase (RA) The probability of choosing \({\$}\) is larger than \(66\%\)

Rational phase (RA+) The probability of choosing \({\$}\) is larger than \(90\%\)

The distribution of the different phases as a function of \(\log (\beta )\) and \(\log (\mu )\) in Fig. 7 a shows that the random phase primarily takes place when both \(\beta\) and \(\mu\) are small. When \(\mu\) is small and \(\beta\) goes up the attraction effect is at its strongest, which makes sense as the influence of relationships between alternatives becomes stronger, while keeping the influence of the general appeal small. When both \(\beta\) and \(\mu\) increase we find that choices become increasingly rational, i.e., eventually the money is chosen almost with near certainty. At this point we run into the limit of our computational precision, as is shown by the white area in the upper right corner of both plots. Specifically, as the initial condition will go to one for all alternatives active, and the probability of transitioning out of this state becomes increasingly close to zero, calculating the inverse of the transitions matrix can no longer be done accurately.

This is also what we see when looking to the distribution of the log mean response times as a function of \(\log (\beta )\) and \(\log (\mu )\) in Fig. 7 b, which shows clearly that these are increasing in both \(\beta\) and \(\mu\) . While in most cases the expected number of iterations is thus small, the median of the plot range is approximately 38 iterations before a response is selected, at some point the mean expected number of iterations before a choice is made goes up to 54419290677, or fifty-four billion four hundred nineteen million two hundred ninety thousand six hundred seventy-seven. This tells us that for those corresponding values of \(\beta\) and \(\mu\) , the probability of getting out of a transitive state is extremely small. Of course, the number of iterations is only a proxy for response times and therefore does not tell us how long the choice process will actually take. For example, if the log number of iterations would be the number of seconds a choice process takes, 54419290677 iterations would amount to less than 25 s.

Looking to both Fig. 7 a,b we find that our model predicts random behaviour for very short response times, and with increasing these the context effects become visible. When response times go up even further, eventually the context effects diminish again and choices become increasingly rational. In the limit, choice probabilities go to one for the alternative with the largest general appeal and the expected number of iterations goes to infinite.

Rational choices

Expressing the expected choice probabilities as a function of the parameters \(\mathbf {A}\) and \(\mathbf {b}\) for a choice with n alternatives, requires one to write out all the possible paths to the n choice conditions from all \(2^n - n - 1\) configurations in which at least two alternatives are active. As this expression becomes already incomprehensible for \(n=3\) , we will limit ourselves to the simplest case of a binary choice problem. If we define \(u_i = \sum _{k \in {\scriptscriptstyle {K}}} a_{ik} + b_i\) , the probability of choosing alternative x over y in a binary choice problem is given by:

in which \(p_x\) denotes the probability to start in the configuration in which \(x=1\) and \(y=0\) , as such meeting the choice conditions and directly triggering a choice for alternative x . \(p_{\scriptscriptstyle {0}}\) and \(p_{\scriptscriptstyle {1}}\) denote the probabilities to start in a configuration in which all alternatives are inactive \((p_{\scriptscriptstyle {0}})\) or active \((p_{\scriptscriptstyle {1}})\) . Although this seems like a straightforward expression, even when assuming that there is no relation between the alternatives \((a_{xy} = 0)\) , we already obtain the four possible formulations depending on the values for \(u_x\) and \(u_y\) :

From Eqs. ( 13 ) and ( 14 ) it becomes clear that if no relationships exist between alternatives, the probability of choosing alternative x is purely a function of the difference between \(u_x\) and \(u_y\) if we started in either \(p_{\scriptscriptstyle {0}}\) or \(p_{\scriptscriptstyle {1}}\) . While it might seem a plausible assumption that choices will be at least weakly rational, i.e., \(p_{x,y}(x) \ge {}^{1}\!/_{2} \iff u_x \ge u_y\) , if there is no interaction between the alternatives, this is not necessarily the case.

For example, if the relation between cue k and alternative x is positive ( \(a_{kx} = 10\) ), but the general appeal of x is negative ( \(b_x = -5\) ), and the relation between cue k and alternative y is negative ( \(a_{ky} = 10\) ), but the general appeal of y is positive ( \(b_y = 5\) ). We find that \(u_x = 5\) and \(u_y = -5\) , and as \(u_x > u_y\) we would expect \(p_{x,y}(x) \ge {}^{1}\!/_{2}\) . Using Eq. ( 14 ) we can calculate that when starting in a non-absorbing configuration both transition probabilities are almost one, such that \(p_{x,y}(x) \approx p_x + p_{\scriptscriptstyle {0}} + p_{\scriptscriptstyle {1}}\) and the probability of choosing x over y is the sum of all starting configurations except \(p_y\) , i.e., \(p_{x,y}(x) \approx 1 - p_y\) . However, whereas the transition probabilities are only a function of the difference between \(u_x\) and \(u_y\) , the starting probabilities are not. In the resting state distribution the cue would almost always be inactive if \(b_k<< 0\) , and the probabilities \(p_{\scriptscriptstyle {0}}, p_x, p_y\) and \(p_{\scriptscriptstyle {1}}\) become primarily a function of \(b_x\) and \(b_y\) . As \(b_y>> b_x\) , we find that \(p_y \approx .99\) , which implies that 99% of the time we will start in the configuration that will immediately trigger the choice for alternative y . Although this situation might not necessarily be encountered in real life, it shows that determining when choices are guaranteed to be even weakly rational is not straightforward.

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Acknowledgements

This research was supported by NWO (The Dutch organisation for scientific research); No. 022.005.0 (J.K.), No. CI1-12-S037 (G.M.), No. 451-17-017 (M.M.), No. 314-99-107 (H.M.). During the preparation of the manuscript M.B. was working at ACTNext by ACT (Iowa City, USA). We thank Andrew Cantine (ACT) for proof-reading the manuscript.

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Kruis, J., Maris, G., Marsman, M. et al. Deviations of rational choice: an integrative explanation of the endowment and several context effects. Sci Rep 10 , 16226 (2020). https://doi.org/10.1038/s41598-020-73181-2

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Rational Choice Theory: What It Is in Economics, With Examples

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On This Page:

• According to rational choice theory, people calculate the costs and benefits of choices in making decisions. The perceived costs, risks, and benefits of certain actions can be dependent on one’s own personal preferences.
• The underlying notion of rational choice theory dates back to classical economists such as Adam Smith, but the theory was not adopted into sociology officially until the 1950s and 1960s.
• Rational choice theory uses axioms to understand human behavior. The most important of these is that people make choices due to a consideration of costs and rewards. People will only carry out an action when the benefit of an action outweighs its cost and will stop doing an action when the cost outweighs the benefit and individuals use the resources at their disposal to optimize rewards.
• Rational choice theory has both fanatical followers and harsh critics, creating justifications and endangering arguments against phenomena seemingly paradoxical to rational choice theory.
• Rational choice theory is used today in domains as diverse as political science, economics, and sociology.

Origin and Premises

Rational Choice Theory states that people use rational calculations to make rational choices and achieve outcomes that are aligned with their own, personal objectives.

Everyone makes choices by first considering the costs, risks, and benefits of making certain choices. Choices that seem irrational to one person can make sense to another based on the individual’s desire, as these choices are based on personal preferences.

At its core, rational choice theory assumes that people are in control of their own decisions. Rational choice theory can be helpful in understanding the behavior of individuals and groups and can help to determine why people, groups, and society move toward certain choices based on specific costs and rewards.

Rational choice theory conflicts with some other theories in sociology. For example, the psychodynamic theory states that people seek gratification due to unconscious properties.

Meanwhile, rational choice theory holds that there is always a rational justification for behaviors, and people try to maximize rewards because they are worth the cost.

Self-Interest and the Invisible Hand

The ideas behind rational choice theory are said to originate in Philosopher and economist Adam Smith’s essay, An Inquiry into the Nature and Causes of the Wealth of Nations (Smith, 1776).

In short, this essay proposed that human nature has a tendency toward self-interest, and this self-interest resulted in prosperity through the control of the so-called “invisible hand” — the collective actions of the self-interested human race.

Adam Smith’s ideas about the invisible hand were inspired by the work of Thomas Hobbes in “Leviathan” (1651), who stated that political institutions function as a result of individual choices.

Further Iterations

Although rational choice theory stemmed from neoclassical economists such as Smith, the theory moved into the social sciences in the 1950s and 1960s when George C. Homans, Peter Blau, and James Coleman related rational choice theory to social exchange.

Appropriating its economic origins, these social theorists stated that social behavior is driven by a rational calculation of costs and rewards.

Homan’s (1958) essay on social behavior as exchange, for example, argued that social interactions and small group processes could be explained by principles from microeconomic theory.

Meanwhile, Blau’s (1964) book on social exchange theory uses rational choice to describe the interactions between those in a bureaucracy (Oberschall, 1979).

Lastly, Harsanyi related ideas from game theory to social systems, particularly social exchange situations. Coleman (1964) created another branch of social exchange theory.

Coleman modeled social behavior mathematically as rational action and saw systems of collective decisions as like economic markets.

Characteristics

There are multiple rational choice theories, and the benefits that people are said to receive from their choices vary from one rational choice theory to the next.

Sometimes, rational choice theories say that individuals seek money or re-election, and others contend that the ends that people pursue are not necessarily self-serving in nature (Becker, 1976; Downs, 1957; Olson, 1965; Schelling, 1960; Green and Fox, 2007).

Nonetheless, rational choice theories make a few assumptions:

• All actions are rational and are made due to consideration of costs and rewards.
• The reward of a relationship or action must outweigh the cost of the action being completed.
• When the value of the reward diminishes below the value of the costs incurred, the person will stop the action or end the relationship.
• Individuals use the resources at their disposal to optimize their rewards.

At its core, Rational Choice Theory is a system of axioms that give a basis for predicting how individuals will make decisions. These axioms say that decisions happen between pairs of alternatives and that these alternative choices are consistent, transitive, independent, continuous, and monotonic.

By consistency, rational choice theorists demand that it is possible for a decision maker to rank all of their options according to how desirable they are. This is also called the assumption of connectedness. Preferences must be either equal or unequal, and unequal preferences can be ordered for comparison across the decision maker’s whole list of preferences.

Transitivity, meanwhile, is the assumption that if choice A is preferred to choice B, and choice B is preferred to choice C, then consistency requires that choice A be preferred to choice C (Green and Shapiro, 1994).

The distance between preferences or the magnitude of preferences does not need to be known to the person analyzing this ranking of choices.

Independence assumes that all preferences are completely independent of other preferences.

For example, the preferability of choice A does not depend on the preferability of choices B or C. Moreover, continuity assumes that preferences hold across time and space. Given the same conditions, the decision-maker will still prefer choice A in, say, a decade if they preferred it today.

Lastly, rational choice theorists assume monotonicity. This means that all decision rules and preferences are the same across individuals and times.

This assumption is in place because allowing for the assumption that there will be major variations in individual preferences dependent on individual characteristics creates major mathematical problems (Storm, 1990).

Rational Choice vs. Organizational Theories

Rational Choice Theory and Organizational Theory are two different but closely related theories.

Economic theorists use Rational Choice Theory as a means of aggregation. In essence, this means that Rational Choice Theory is useful when there is a need to link how individuals change their actions to how the characteristics of organizational change.

However, economic theorists tend to take a broad view where organizational context, organizational structure, and individual actions interact to change organizational functioning.

In this view, there is no assumption that the sum of individuals’ choices explains organizational behavior. Indeed, many organizational theories do away with individual actions altogether, preferring to examine the relationships between and among organizational and contextual characteristics.

Rational choice theory is premised on the assumption that people will carry out actions to maximize utility. Meanwhile, Organizational theory is based on the premise that organizations tend to be organized in a rational way, so as to make the means to completing ends efficiently.

A school of thought known as Organizational economic theory links Rational Choice Theory and Organizational Theory.

Advantages and Disadvantages

Rational choice theory has been tested severely on an empirical level (Quah and Sales, year).

Rational choice theory assumes that a good sociological theory is one that interprets any social phenomenon as the culmination of rational, individual actions.

This assumption allows sociological theories to cut out vague forces — such as, say, cognitive bias or evolution — as the cause of human behavior.

Although this grants rational choice theory a great deal of power, scholars such as Boudon (2003) have criticized it in describing many social phenomena.

This combination of success and failure in rational choice theory has created polarization in the social sciences community (Hoffman, 2000).

For instance, consider what Boudon (2003) calls the voting paradox. According to rational choice theory, the effect of a single vote on turnout for any election is so small that rational actors should always refrain from voting, as the costs of voting are always higher than the benefits.

Yet, millions of people vote in national elections each year.

Scholars have proposed many solutions to this voting paradox. One explanation is that people would feel strong regret if their ballot would have made a difference in an election’s outcome despite knowing that the probability of this event occurring is infinitesimally small (Frejohn and Fiorina, 1974).

Another explanation states that, by not voting, people run the risk of losing their reputation (Overbye, 1995). Boudon (2003) argues that all of these explanations do not eliminate the paradox of voting.

Psychologists have also devised a number of experiments, such as the “ultimatum game,” that resist rational choice theory (Wilson, 1993; Hoffman and Spitzer, 1985).

In the ultimatum game, there are two players. One player must decide how much money he and the other get from a shared pool, and the other can decide to accept or reject the offer.

If the second player accepts, everyone gets the amount offered; if he rejects, nobody gets the money. In the frame of rational choice theory, a rational first player would always try to offer as little as possible to the second player, and a rational second player would always accept.

However, studies have shown that second players rarely accept when offered less than about a third of the pool; in fact, a number of offering players split the money evenly.

On the other hand, people can frequently take actions where the benefit to the actor is zero or even negative. C.W. Mills (1951) identified what he called the “overreaction paradox.”

Mills studied female clerks working in a firm where they sat in a large room doing the same tasks at the same kind of desk in the same work environment. Frequently, conflicts broke out over minor issues, such as being seated closer to a heat or light source.

These paradoxes, Boudon argues, can be interpreted satisfactorily by either irrationality or rational choice theory — and these are just a few of the numerous observations that psychologists, sociologists, and economists have made where the theory fails.

Boudon (2003) offers three types of phenomena that tend to fall outside of rational choice theory’s explanatory jurisdiction.

The first of these involves a phenomenon where people base their choices on beliefs that are not commonplace.

For instance, someone may refuse to go to the doctor’s office because they believe that the doctor will harm them.

Rational choice theory is also ineffective when faced with phenomena characterized by normative common-place beliefs that do not have an effect on consequence (Boudon, 2001).

A citizen may strongly disapprove of corruption even if they are not affected by it.

Finally, Boudon argues that rational choice theory is ineffective when considering behavior by individuals for whom it cannot be assumed their behavior is dictated by self-interest.

For example, members of an audience may side fiercely with one character while watching a play despite the fact that the events of the play are of no consequence whatsoever to them. This can also happen in real-world situations.

For example, people can have strong opinions on issues such as capital punishment despite never having been implicated in the death penalty nor knowing anyone who has (Boudon, 2003).

There have also been strong advocates favoring rational choice theory, such as Riker (1995).

Riker criticizes experiments showing evidence against rational choice theory, claiming that most of the tests involve cases where there are no real stakes for participants that would necessitate careful calculation (for example, a lack of experiments where participants have been required to put up their own money for bets).

Additionally, Riker argues that the “naive” participants of rational choice theory experiments are not reflective of, say, highly-trained policymakers in political and economic voting.

• Criminology : Rational choice theory sees criminal behavior as the outcome of decisions and choices made by an offender. Cornish and Clarke (1987) use the theory as a framework for understanding crime control policies. According to Cornish and Clarke, individuals who commit crimes choose between criminal and non-criminal alternatives when seeking to achieve their goals.
• For example, someone who is drunk may choose to drive (criminal behavior), call a taxi, use public transportation, walk, or persuade a sober friend to drive them home. Usually, rational choice theory posits that non-criminal alternatives tend to be considered before criminal ones are, as criminal alternatives tend to come at a greater cost.
• Cornish and Clarke use “choice structures” to categorize crimes into different categories under rational choice theory. These choice structures represent the various factors that an individual must weigh when deciding whether or not to commit a crime.
• For example, factors that actors may consider when committing theft involving cash may involve the severity of punishment, the likely cash yield per crime, the planning necessary, and whether or not there is an identifiable victim.
• Meanwhile, someone deciding whether or not to use a substance illegally may take into account the extent to which it interferes with everyday tasks, the length and intensity of the “high” from the drug, and the method through which the drug is administered (1987).
• The researchers argue that a rational choice perspective on crime can suggest lines of inquiry that account for stability and change and criminal behavior and that people will generally choose to commit the crimes that provide the lowest cost-to-benefit ratio.
• In this view, strategies that attempt to attack the “root” cause of crime should focus on the difficulty of committing crimes over using non-criminal means (Cornish and Clarke, 1987).
• Political Sociology : Rational choice theory has been used extensively in political science. One advocate of the theory was William H. Riker.
• In his article, “The Political Psychology of Rational Choice Theory,” Riker (1995) presents a model of expected utility — a mathematical approximation of how much benefit people ought to derive from a situation — in considering why people vote.
• Countering the criticisms of people such as Boudon (2003), Riker accounts for factors unrelated to the outcome of an election pertinent to voting — such as pride in citizenship and satisfaction in taking sides (Riker, 1995).

Becker, G. S. 1976. The Economic Approach to Human Behaviour. Chicago: University of Chicago Press.

Blau, P. M. (1964). Social exchange theory. Retrieved September, 3(2007), 62.

Boudon R. 2001b. Sociology. International Encyclopedia of the Social and Behavioral Sciences. Amsterdam: Elsevier

Boudon, R. (2003). Beyond rational choice theory. Annual review of sociology, 29(1), 1-21.

Coleman, J. S. (1964). Introduction to mathematical sociology. Introduction to mathematical sociology.

Cornish, D. B., & Clarke, R. V. (1987). Understanding crime displacement: An application of rational choice theory. Criminology, 25(4), 933-948.

Downs, A. 1957. An Economic Theory of Democracy. New York: Harper and Brothers.

Ferejohn, J. A., & Fiorina, M. P. (1974). The paradox of not voting: A decision theoretic analysis. American political science review, 68(2), 525-536.

Green, D. P., & Fox, J. (2007). Rational choice theory. Social Science Methodology. L.: Sage Publications, 269-281.

Green, D., & Shapiro, I. (1994). Pathologies of rational choice theory: A critique of applications in political science. Yale University Press.

Hobbes, T (1651/1939). Leviathan. New York: Modern Library

Hoffman, E., & Spitzer, M. L. (1985). Entitlements, rights, and fairness: An experimental examination of subjects” concepts of distributive justice. The Journal of Legal Studies, 14(2), 259-297.

Homans, G. C. (1958). Social behavior as exchange. American journal of sociology, 63(6), 597-606.

Mills CW. 1951. White Collar. The American Middle Classes. New York: Oxford Univ.Press

Oberschall, A. (1979). 13. SOCIAL EXCHANGE AND CHOICE. Qualitative and Quantitative Social Research: Papers in Honor of Paul F. Lazarsfeld, 158.

Olson, M. (1965). The logic of collective action: Public goods and the theory of groups. Cambridge, MA: Harvard University Press

Overbye, E. (1995). Making a case for the rational, self‐regarding, ‘ethical’ voter… and solving the ‘Paradox of not voting’ in the process.

European Journal of Political Research, 27(3), 369-396.

Riker, W. H. (1995). The political psychology of rational choice theory. Political Psychology, 23-44.

Schelling, T. C. (1960). The Strategy of Conflict, 15. Auflage, Cambridge, MA.

Smith, A. (1776). An inquiry into the nature and causes of the wealth of nations: Volume One. London: printed for W. Strahan; and T. Cadell, 1776.

Wilson JQ. 1993. The Moral Sense. New York: Free Press

Further Information

Introduction to Choice Theory

Lovett, F. (2006). Rational choice theory and explanation. Rationality and Society, 18(2), 237-272.

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Rational Choice Theory: What It Is in Economics, With Examples

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What Is Rational Choice Theory?

Rational choice theory states that individuals use rational calculations to make choices and achieve outcomes that are aligned with their own personal objectives. These results are also associated with maximizing an individual's self-interest . Using rational choice theory is expected to result in outcomes that provide people with the greatest benefit and satisfaction, given the limited options they have available.

Key Takeaways

• Rational choice theory states that individuals rely on rational calculations to make choices that result in outcomes aligned with their own best interests.
• Rational choice theory is often associated with the concepts of rational actors, self-interest, and the invisible hand.
• Many economists believe that the factors associated with rational choice theory are beneficial to the economy as a whole.
• Adam Smith was one of the first economists to develop the underlying principles of the rational choice theory.
• There are many economists who dispute the veracity of the rational choice theory and the invisible hand theory.

Understanding Rational Choice Theory

Many mainstream economic assumptions and theories are based on rational choice theory. Rational choice theory is associated with the concepts of rational actors, self-interest, and the invisible hand.

Rational choice theory is based on the assumption of involvement from rational actors. Rational actors are the individuals in an economy who make rational choices based on calculations and the information that is available to them. Rational actors form the basis of rational choice theory. Rational choice theory assumes that individuals, or rational actors, try to actively maximize their advantage in any situation and, therefore, consistently try to minimize their losses.

Economists may use this assumption of rationality as part of broader studies seeking to understand certain behaviors of society as a whole.

Self-Interest and the Invisible Hand

Adam Smith was one of the first economists to develop the underlying principles of the rational choice theory. Smith elaborated on his studies of self-interest and the invisible hand theory in his book “An Inquiry Into the Nature and Causes of the Wealth of Nations,” which was published in 1776.

The invisible hand itself is a metaphor for the unseen forces that influence a free market economy. First and foremost, the invisible hand theory assumes self-interest. Both this theory and further developments in the rational choice theory refute any negative misconceptions associated with self-interest. Instead, these concepts suggest that rational actors acting with their own self-interest in mind can actually create benefits for the economy at large.

According to the invisible hand theory, individuals driven by self-interest and rationality will make decisions that lead to positive benefits for the whole economy. Through the freedom of production, as well as consumption, the best interests of society are fulfilled. The constant interplay of individual pressures on market supply and demand causes the natural movement of prices and the flow of trade. Economists who believe in the invisible hand theory lobby for less government intervention and more free-market exchange opportunities.

Advantages and Disadvantages of Rational Choice Theory

There are many economists who dispute the veracity of the rational choice theory and the invisible hand theory. Dissenters have pointed out that individuals do not always make rational, utility-maximizing decisions. The field of  behavioral economics is a more recent intervention into the problem of explaining the economic decision-making processes of individuals and institutions.

Behavioral economics attempts to explain—from a psychological perspective—why individual actors sometimes make irrational decisions, and why and how their behavior does not always follow the predictions of economic models. Critics of rational choice theory say that, of course, in an ideal world people would always make optimal decisions that provide them with the greatest benefit and satisfaction. However, we don't live in a perfect world; in reality, people are often moved by emotions and external factors.

The Nobel laureate Herbert Simon, who rejected the assumption of perfect rationality in mainstream economics, proposed the theory of bounded rationality instead. This theory says that people are not always able to obtain all the information they would need to make the best possible decision. Simon argued that knowledge of all alternatives, or all consequences that follow from each alternative, is realistically impossible for most decisions that humans make.

Similarly, the economist Richard Thaler pointed out further limitations of the assumption that humans operate as rational actors. Thaler's idea of mental accounting shows how people place greater value on some dollars than others, even though all dollars have the same value. They might drive to another store to save $10 on a $20 purchase but they would not drive to another store to save $10 on a $1,000 purchase.

Like all theories, one of the benefits of rational choice theory is that it can be helpful in explaining individual and collective behaviors. All theories attempt to give meaning to the things we observe in the world. Rational choice theory can explain why people, groups, and society as a whole make certain choices, based on specific costs and rewards.

Rational choice theory also helps to explain behavior that seems irrational. Because a central premise of rational choice theory is that all behavior is rational, any action can be scrutinized for its underlying rational motivations.

Helpful in explaining individual and collective behaviors

All theories attempt to give meaning to the things we observe in the world.

Can help to explain behavior that seems irrational

Individuals do not always make rational decisions.

In reality, people are often moved by external factors that are not rational, such as emotions.

Individuals do not have perfect access to the information they would need to make the most rational decision every time.

People value some dollars more than others.

Examples of Rational Choice Theory

According to rational choice theory, rational investors are those investors that will quickly buy any stocks that are priced too low and short-sell any stocks that are priced too high.

An example of a rational consumer would be a person choosing between two cars. Car B is cheaper than Car A, so the consumer purchases Car B.

While rational choice theory is logical and easy to understand, it is often contradicted in the real world. For example, political factions that were in favor of the Brexit vote, held on June 23, 2016, used promotional campaigns that were based on emotion rather than rational analysis. These campaigns led to the semi-shocking and unexpected result of the vote—the United Kingdom officially decided to leave the European Union. The financial markets then responded in kind with shock, wildly increasing short-term volatility, as measured by the  Cboe Volatility Index  (VIX).

Rational behavior may not involve receiving the most monetary or material benefit; the benefit of a particular choice could be purely emotional or non-monetary. For example, while it is likely more financially beneficial for an executive to stay on at a company rather than take time off to care for their new newborn child, it is still considered rational behavior for them to take time off if they feel that the benefits of the time spent with their child outweigh the utility from the paycheck they receive.

The key premise of rational choice theory is that people don’t randomly select products off the shelf. Rather, they use a logical decision-making process that takes into account the costs and benefits of various options, weighing the options against each other. 

Who Founded Rational Choice Theory?

Adam Smith, who proposed the idea of an "invisible hand" moving free-market economies in the mid-1770s, is usually credited as the father of rational choice theory. Smith discusses the invisible hand theory in his book “An Inquiry Into the Nature and Causes of the Wealth of Nations,” which was published in 1776.

What Are the Main Goals of Rational Choice Theory?

The main goal of rational choice theory is to explain why individuals and larger groups make certain choices, based on specific costs and rewards. According to rational choice theory, individuals use their self-interests to make choices  that will provide them with the greatest benefit. People weigh their options and make the choice they think will serve them best.

What Is Rational Choice Theory in International Relations?

States, intergovernmental organizations, nongovernmental organizations, and multinational corporations are all made up of human beings. In order to understand the actions of these entities, we must understand the behavior of the humans running them. Rational choice theory helps to explain how leaders and other important decision-makers of organizations and institutions make decisions. Rational choice theory can also attempt to predict the future actions of these actors.

What Are the Strengths of Rational Choice Theory?

One of the strengths of rational choice theory is the versatility of its application. It can be applied to many different disciplines and areas of study. It also makes reasonable assumptions and compelling logic. The theory also encourages individuals to make sound economic decisions. By making sound economic decisions, it is possible for an individual to acquire more tools that will allow them to further maximize their preferences in the future.

The Bottom Line

The majority of classical economic theories are based on the assumptions of rational choice theory: individuals make choices that result in the optimal level of benefit or  utility  for them. Further, people would rather take actions that benefit them versus actions that are neutral or harm them. Although many criticisms of rational choice theory exist—because people are emotional and easily distracted, and therefore, their behavior does not always follow the predictions of economic models—it is still widely applied across different academic disciplines and fields of study.

Adam Smith. “ An Inquiry Into the Nature and Causes of the Wealth of Nations .” Strahan, 1776.

Ann Kordas et al. (Eds.). “ World History, Volume 2: From 1400: 6.3 Capitalism and the First Industrial Revolution .” OpenStax, 2022.

The Nobel Prize. " Studies of Decision-Making Lead to Prize in Economics ."

The Nobel Prize. " Richard H. Thaler: Integrating Economic With Psychology ." Pages 2-3.

Gov.UK. " EU Referendum ."

Cboe. “ VIX Index Data for 2004 to Present (Updated Daily) .” Download CSV file.

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Rational Choice Theory: Why Irrationality Makes More Sense for Comparative Politics

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Rational Choice Theory (RCT) has emerged as one of the leading methodologies in political science. RCT studies have permeated the field since the 1950s. With the increasing quantification of the social sciences, RCT provided the way in which economic models and approaches were transferred to political science in an attempt to improve consistency and analysis. Economic theories prior to this were generally applied to the economic policies and behaviors of countries related to trade and commerce.

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Nakaska, J.D.J. (2010). Rational Choice Theory: Why Irrationality Makes More Sense for Comparative Politics. In: Wiarda, H.J. (eds) Grand Theories and Ideologies in the Social Sciences. Palgrave Macmillan, New York. https://doi.org/10.1057/9780230112612_8

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What is Rational Choice Theory?

Rational Choice Theory is one of several other theories social workers use to evaluate client behavior and choose therapeutic interventions. Rational choice theory assumes the rational process individuals use to make decisions to maximize the benefit for the individual, group, or society.

Researchers and professionals such as qualified psychology teachers use Rational Choice Theory to understand decision-making. Fields that use it include marketing, free market economy, economics, organizational psychology, criminology, psychology, psychiatry, and social work.

Origins of Rational Choice Theory

The rational choice theory has its roots in the classical political theory of the eighteenth century. According to McCarthy and Choudhary (2018) “the conceptual foundations” of what they call the rational choice approach (RCA) “originate[s] in Cesare Beccaria’s1764 essay On Crimes and Punishments and Jeremy Bentham’s 1789 work (in table of contents), An Introduction to the Principles of Morals and Legislation .

Rational choice theory is closely related to Exchange Theory. Rational choice theory is another theory developed by sociologist George Homans in the early 1960s. Social exchange theory says that rational actors make decisions and interact in society to maximize their benefits and minimize their costs. Using the lens of exchange theory, decisions by individuals, groups, organizations, and even countries are transactional and aim to maximize profit and reduce costs.

How Rational Choice Theory in used the Behavioral Sciences and Clinical Work?

RCT understands individuals’ and clients’ decision-making processes and underlying rational motivations in the behavioral sciences and clinical work. Many rational actors believe RCT is used to argue that individuals make decisions based on selfish or self-serving interests like an invisible hand and irrational behavior. But this is not always the case.

Elster (2001) explained that rational decision-making could involve entirely altruistic motivations and self interests. Often, individual choices are with the benefit of others in mind.

Of course, altruism can circle back to the individual in the form of positive rewards, and this may be part of a conscious plan in making a decision or choice. Still, highly altruistic motivations are entirely rational for some people.

What are the Disadvantages of Decision-Making?

Rational thoughts can be highly irrational as well. In the case of irrational decision-making, therapists need to understand what motivates a client to make the decisions they make.

Someone who holds a view of the world as dangerous and unforgiving, for example, may make choices that help them avoid pain and punishment; this kind of decision-making is entirely rational for them. Understanding how clients view what is rational can help a therapist choose an approach that either seeks to adjust their thinking about what actions are helping or harming them.

Therapeutic Applications of Rational Choice Theory

According to Özdemir, Tanhan, and Özdemir (2018), therapies using rational choice theory “exert their effect either by disrupting patients’ ability to preserve unawareness, increasing the cost of the symptom, decreasing the patient’s emotional distress, or eliminating the stressor.” Disorders treated using a rational choice frame include obsessive-compulsive disorder, addiction, neurotic, and repressive behaviors.

How Rational Choice Theory Is Applied?

Rational Choice Theory states it is an economic principle that assumes that individuals can make logical decisions based on personal preferences and that their behavior can be explained by their self-interest and rational behavior.

Rational choice theory conflicts suggest that when making decisions, individuals prefer the choice that offers the most benefit to them in terms of achieving their desired goals. This principle is applied to many different areas such as economic decisions such as purchasing goods, public policy decisions such as voting, and even criminal decisions such as what type of crime to commit helps in situational crime prevention before you commit a crime.

The theory can be applied in each of these cases to explain the choices individuals make. For example, when deciding whether or not to purchase a good, we weigh the benefits versus the costs of the good and make the rational decision (based on our goals) to purchase or not purchase. When considering public policy decisions, the same rational choice is applied in terms of which policy offer the most benefit to the individual, either in terms of financial benefit, convenience, or desire.

Even criminal decisions can be explained using rational choice theory fails as criminals weigh the possible costs and benefits of different types of criminal activity to determine which offers the most benefit. In summary, Rational Choice Theory is applied to explain the decisions human beings make in many different areas, costs, and rewards, which may be driven by self-interest, convenience, or desire.

Further and higher education in rational calculation, rational decisions, rational justification, rational considerations, rational action theory, rational choice perspective, sociological theory, rational thought, psychodynamic theory, social sciences, other theories, human decision making, social behavior, and understanding crime displacement, and situational crime prevention.

Rational choice theory definition and rational choice theory applies to individual and collective behaviors in human behavior and human rationality.

How Does Rational Choice Theory Explain Human Behavior?

The rational choice theory argues that human behavior is the result of conscious and rational choices made to maximize individual utility. Rational choice theory states that people are driven by self-interests and that these interests are based on obtaining the highest rewards with the lowest associated costs and risks, interest, and the invisible hand.

According to this theory, behavioral decisions are based on a cost-benefit analysis and a weighing of the potential rewards and costs associated with different courses of action. Consequently, people act in a manner that will bring them the most benefit, or the least amount of harm. This theory is often applied to criminal behavior, with the argument that offenders consider the consequences of their actions before engaging in certain activities.

For example, an offender might consider the risks of being caught and the associated punishments and thus may decide to not engage in the criminal behavior. This theory also explains why individuals might choose to comply with the law when breaking the law might be in their interest due to their evaluations of potential outcomes.

Additionally, rational choice theory can explain why people make decisions in their personal and professional lives, such as why they choose certain career paths or why they may invest their savings in certain products or activities. Ultimately, the rational choice theory is based on the idea that people make conscious, calculated decisions to maximize their utility.

What are the Applications of Rational Choice Theory?

Political science:.

Rational choice theory is often used in political science to understand how public policy is chosen and to explain how voters make decisions. This theory posits that individuals act rationally by taking into account all costs and benefits associated with a given option before making a decision.

Rational choice theory is a cornerstone of modern economics. Rational choice theory is used to explain why people make certain decisions in certain economic contexts. For example, rational choice theory can explain why a consumer may choose to purchase a certain product over another, or why an investor may choose to invest in a particular company’s stock.

Rational choice theory is also used in sociology to explain things like network formation, social interactions, or game theory. This theory is used to provide a better understanding of why people make certain choices or behave in certain ways.

Management:

The theory can be applied to management decisions as well. Managers often need to weigh the costs and benefits of different options before deciding on a course of action. Rational choice theory can be used to help evaluate these different options and to decide on a course of action that will maximize the benefit of the outcome.

Rational-Choice Theory of Neurosis

For example, Özdemir and others ( 2018) conceptualized the Rational-Choice Theory of Neurosis. They argue that repressive or neurotic behaviors are rational in that they can distract an individual from highly stressful or upsetting life events.

According to the authors, disorders that may constitute a coping mechanism and logical response to extreme stress include panic disorder, agoraphobia, anorexia, and obsessive-compulsive disorder (OCD). However, they point out that while symptoms distract from distressing thoughts, the individual may not be aware of why their behavior has changed.

Applications for Cognitive-Behavioral Therapy

Cognitive-behavioral seeks to disrupt and change the way people think about various issues, challenges, or events in their lives. Cognitive-behavioral therapy may involve examining whether an individual’s choices are rational. A therapist looks at the chain of thinking for an individual’s particular situation and disrupts that chain of thinking.

Then, a new way of thinking can emerge. Acceptance and Commitment Therapy is a form of cognitive-behavioral therapy. Rational choice theory helps clients accept what they cannot change and make achievable goals for the future. This is another example of treatment trying to help a client make rational choices for the future.

Strengths and Weakness

A strength of rational choice theory is it helps us to understand the motives behind individual and even collective behaviors. For example, why would an individual, group, or society choose a particular decision?

What is the calculus, and what are the expected rewards? RCT provides a framework for therapists to analyze and understand their clients’ behaviors and situational crime prevention. Then, therapists may use it to change these behaviors.

Also, several disciplines use rational choice theory to understand behaviors at the individual and group levels. Furthermore, rational choice theory helps practitioners understand behavior that is not so rational on its face. Then, it prompts them to know why it is rational for their client.

Rational Choice and Ethics in Decision-Making

Some also believe RCT does not consider the contribution of values and ethics to decision-making. For example, according to Crossman (2019), RCT “does not explain why some people seem to accept and follow social norms of behavior that lead them to act in selfless ways or to feel a sense of obligation that overrides their self-interest. “

Is Rational Choice too Induvalistic?

Another critique of RCT, according to Crossman , is that it is too individualistic. Some prefer not to use individualistic theories to understand human behavior and decision-making because they believe “ they fail to explain and take proper account of the existence of larger social structures. That is, there must be social structures that cannot be reduced to the actions of individuals and therefore have to be explained in different terms .”

Rational Choice and Social Work

Rational choice theory is just one of several theories that social workers use to guide their thinking about client behavior. Additionally, it helps them choose therapeutic interventions to help their clients.

For example, cognitive-behavioral therapies are a popular choice of intervention for clinical social workers . These therapies help clients recognize the rational purpose behind behaviors. They are also used by those who want to help their clients change behaviors that serve a rational purpose but are destructive or harmful.

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Rational Choice Theory in Political Decision Making

Rational choice theory builds from a very simple foundation. To wit: individuals are presumed to pursue goal-oriented behavior stemming from rational preferences. Rational choice theory benefits from the very precise formulations of its assumptions. Individual-level rationality is generally defined as having complete and transitive preferences. Both completeness and transitivity have precise, formal definitions. From complete and transitive preferences, one can develop utility function presentations reflecting those preferences. Utility functions have the advantage of establishing a measure and allowing one to assess attitudes toward risk. That is, utility functions can reflect risk acceptance, risk neutrality, or risk aversion. Although some rational choice theorists focus on individual-level decision making, most rational choice theorists consider the ways in which individuals’ decisions are aggregated into some sort of social outcome or social preference order. The aggregation of individuals’ preferences occurs in both social choice and game theoretic models. Arrow’s theorem is the best-known result in social choice theory. Arrow showed that the rationality of individuals’ preferences could not be readily preserved at the group level when those individuals’ preferences were aggregated. That is, individual-level rationality does not ensure group-level rationality. Put slightly differently, irrationality at the group level cannot impugn rationality at the individual level. Other examples highlighting the difficulty of aggregating individuals’ preferences into a collective outcome abound. For instance, game theoretic presentations of the collective action problem highlight how individually rational decisions can lead to suboptimal outcomes. Rational choice models have been used to model interactions in a wide array of political institutions. Rational choice models have been developed to tackle some of the most challenging concepts in the social sciences, even in areas long thought impenetrable to rational choice theorizing. For instance, concepts such as ideology or personal identification have typically been used as preestablished descriptors. In contrast to treating those concepts as extant descriptors, rational choice theorists have modeled the endogenous development of ideologies and personal identification. Given the complexity of social phenomena, the relative parsimony and the clarity of rational choice models can be particularly helpful. The usefulness of rational choice models stems from their parsimony and their applicability to a wide range of settings.

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Reconciling Emotion and Rational Choice: Negativistic Auto Theft, Consequence Irrelevance, and the Seduction of Destruction

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Abstract:I address an overlooked question about the structure of the cognitive/conative model of the mind that underlies much of the work in economics, psychology and philosophy: namely, whether conative states are fundamentally monistic (desire-like) or comparative (preference-like). I argue that two seemingly promising sets of theoretical considerations – namely, the structure of Rational Choice Theory, and considerations of computational efficiency – are unable to resolve this debate. Given this, I suggest that a consideration that speaks in favour of the preference-based view is the fact that it makes it easier to explain certain empirically observed patterns in decision making.

The Decision to Vote or to Abstain

Why voters turn out on Election Day has eluded a straightforward explanation. Rational choice theorists have proposed a parsimonious model, but its logical implication is that hardly anyone would vote since their one vote is unlikely to determine the election outcome. Attempts to save the rational choice model incorporate factors like the expressive benefits of voting, yet these modifications seem to be at odds with core assumptions of rational choice theory. Still, some people do weigh the expected costs and benefits of voting and take account of the closeness of the election when deciding whether or not to vote. Many more, though, vote out of a sense of civic duty. In contrast to the calculus of voting model, the civic voluntarism model focuses on the role of resources, political engagement, and to a lesser extent, recruitment in encouraging people to vote. It pays particular attention to the sources of these factors and traces complex paths among them. There are many other theories of why people vote in elections. Intergenerational transmission and education play central roles in the civic voluntarism models. Studies that link official voting records with census data provide persuasive evidence of the influence of parental turnout. Education is one of the best individual-level predictors of voter turnout, but critics charge that it is simply a proxy for pre-adult experiences within the home. Studies using equally sophisticated designs that mimic the logic of controlled experiments have reached contradictory conclusions about the association between education and turnout. Some of the most innovative work on voter turnout is exploring the role of genetic influences and personality traits, both of which have an element of heritability. This work is in its infancy, but it is likely that many genes shape the predisposition to vote and that they interact in complex ways with environmental influences. Few clear patterns have emerged in the association between personality and turnout. Finally, scholars are beginning to recognize the importance of exploring the connection between health and turnout.

Complexity, Bounded Rationality and Heuristic Search

Abstract This paper explores the use of heuristic search algorithms for modeling human decision making. It is shown that this algorithm is consistent with many observed behavioral regularities, and may help explain deviations from rational choice. The main insight is that the heuristic function can be viewed as formal implementation of one aspect of emotion as discussed in Descarte's Error by Antonio Damasio. Consistent with Damasio's observations, it is shown that the quality of decision making is very sensitive to the nature of the heuristic ("emotion"), and hence this may help us better understand the role of emotion in rational choice theory.

Rational Choice Theory and the Paradox of Not Voting

Given the extensive evidence of apparently strategic voter behavior, it is unsettling that there is not a canonical rational choice model of voting in elections with costs to vote. But while a canonical model does not yet exist, the literature appears to be converging toward a “group-based” model of turnout, in which group members participate in elections either because they are directly coordinated and rewarded by leaders as in “mobilization” models or because they believe themselves to be ethically obliged to act in a manner that is consistent with the group's interest as in “ethical agent” models. To appreciate the development of group-based models, it will be useful to begin with a discussion of the decision-theoretic literature on voting, with a focus on the paradox of not voting. Then we will move to the game-theoretic and group-based models of voting. A conclusion highlights some of the problems that group-based models of voting must address.

Revisiting the role of process incentives as a determinant of university students’ protest

Drawing on the original data collected during a period of university student protest in Greece, we explore whether the expected gains from the act of protesting itself influence an individual's decision to participate in collective action. More particularly, we investigate the extent to which the process incentives qualify the weight individuals attach to the primary elements of the original cost–benefit equation of rational choice theory as well as other considerations in their decision-making process. Our findings point out that the magnitude of the effect of the process incentives is very strong and its inclusion in a rational choice model improves our understanding of students’ participation in protest activities. Turning to indirect effects, we show that process incentives behave as a first stage precondition for the students’ decision to participate in collective action. In the absence of perceived benefits associated with the process of protesting, the importance of attaining the public good becomes much less important in their decision-making process.

The Nature of Utility Functions in Mass Publics

Survey data are used to test the basic tenets of rational choice theory. We find that (1) voters' preferences are orderly but voters do not always have preferences. When the perceived difference between two candidates is below some threshold, voters are indifferent between them. (2) Most voters choose candidates whose issue positions are congruent with their own. (3) Lack of knowledge about candidates affects choice and utility through two routes—indifference and risk aversion.Most voters have highly structured utility functions, but the thresholds and risk aversion in these functions place relatively unknown candidates at a disadvantage in presidential primaries and other electoral situations. Moreover, the importance of knowledge in these functions suggests that social choice theorists must take seriously the classic concerns of public opinion research—the operation of the media and the dynamics of information in elections.

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