Choice Behavior

Abstract

Choice behavior is a form of decision making in which an organism selects one option from a set of two or more alternatives. Its quantitative study began with Herrnstein's matching law, which found that animals allocate responses in proportion to the reinforcement each option yields, and with Luce's choice axiom, whose ratio-scale representation grounds the random-utility and logit models that dominate the econometric analysis of choice. A second tradition documents that choice is context-dependent: adding a third option can reverse the preference between the original two, violating the independence axioms of rational-choice theory. Sequential-sampling models such as the diffusion decision model recast a choice as noisy evidence accumulated to a threshold, jointly predicting which option is chosen and how long the choice takes. Neuroeconomics then locates these computations in the valuation circuits of the primate brain.

Keywords: choice behavior, matching law, choice axiom, context effects, sequential sampling

Choice behavior is the observable act of selecting one alternative from a set, and it is the behavioral endpoint through which preferences, values, and decision processes reveal themselves to measurement. Where the study of judgment asks how a person appraises the world, the study of choice asks what they do about it: which option is taken, how often, and how quickly. That shift from appraisal to selection makes choice unusually tractable, because a choice is a discrete event that can be counted, timed, and modeled, and the same formal tools recur whether the chooser is a pigeon on two response keys, a shopper facing a shelf, or a monkey fixating a target (Luce, 1977). The literatures surveyed here have circled one question: what rule maps the values of the options onto the probability that each is chosen, and how is that rule implemented in behavior and brain?

What Choice Behavior Is

A choice task has a recognizable structure: a set of two or more alternatives, each carrying some value to the chooser, and a selection that resolves to exactly one of them. The dependent measures are correspondingly simple — which option was taken, the proportion of times each is taken over repeated opportunities, and the time from onset to commitment — and this simplicity is what has let choice become the common currency of behavioral economics, mathematical psychology, and systems neuroscience alike. A theory of choice is a rule that turns the values of the options into a probability distribution over which one is selected.

Two features make the problem interesting rather than trivial. First, choice is stochastic: presented with the same pair of options on different occasions, a chooser does not always take the same one, so the object to be explained is a probability, not a deterministic selection (Luce, 1977). Second, choice is relational: the probability of taking an option depends not on its value in isolation but on the values of the alternatives it is set against, which is why the composition of the choice set matters and why adding or removing options can move preferences in ways a value-maximizing account does not anticipate. Everything that follows is an attempt to characterize that value-to-probability rule — from the reinforcement schedules that shape it, through the axioms it should obey, to the accumulation process that generates it in real time.

Types of Choice Behavior

The Medical Subject Headings thesaurus files Choice Behavior under Decision Making and gives it two narrower descriptors, shown in Table 1. These subtypes are how the biomedical literature is indexed, not a theory of how choice divides at its joints: MeSH is a classification for retrieval, so the categories need not be mutually exclusive — a choice of career is also, in part, a series of intertemporal trade-offs — and the list reflects indexing practice rather than a claim about the natural structure of the mind. Neither child is yet a live article on this site, so both are named in plain text.

Table 1
Direct Subtypes of Choice Behavior in the MeSH Classification (tree F02.463.785.373.346)
Note. The two narrower descriptors of Choice Behavior in Medical Subject Headings. The subtypes are an indexing convenience and need not be mutually exclusive or jointly exhaustive.

The Matching Law

The first quantitative law of choice came from the operant laboratory. Richard Herrnstein put pigeons on a pair of response keys, each delivering food on its own variable-interval schedule, and found a strikingly orderly result: the proportion of pecks a bird directed at a key matched the proportion of reinforcements that key delivered (Herrnstein, 1961). This is the matching law — the relative rate of a response equals the relative rate of the reinforcement it earns — and it converted choice from a matter of preference into a measurable function of consequences. Its reach extends well beyond the pigeon chamber: matching-like allocation appears in human work, foraging, and communication, wherever behavior is distributed across concurrently rewarded options.

Real data rarely obey strict matching exactly, so the law is written in its generalized form, in which the log ratio of responses is a linear function of the log ratio of reinforcements with two free parameters, a sensitivity exponent and a bias term. Sensitivity below one — the common finding — is called undermatching: the chooser is less sensitive to the reinforcement ratio than strict matching demands, allocating behavior more evenly than the payoffs alone would dictate. Herrnstein read matching as the outcome of melioration, a moment-to-moment tendency to shift behavior toward whichever option currently yields the higher local rate of reinforcement, a process that produces matching at equilibrium but can lock a chooser into globally suboptimal patterns. The demonstration below sweeps the reinforcement ratio and the sensitivity exponent so the matching relation, and its departures, can be traced directly.

Choice Axioms and Random Utility

While Herrnstein was measuring choice in animals, R. Duncan Luce was axiomatizing it. His choice axiom posits that the probability of selecting an option from a set can be written as the ratio of a positive scale value assigned to that option to the sum of the scale values of all options in the set (Luce, 1977). The axiom's central and most consequential implication is independence from irrelevant alternatives: the relative odds of choosing between any two options depend only on their own scale values and are unaffected by which other options are present. From this ratio rule follows the entire family of random-utility models — including the logit and its econometric descendants — in which each option's utility carries a random component and the chooser selects the option whose realized utility is highest, generating exactly Luce's choice probabilities. Daniel McFadden turned this insight into the empirical workhorse of choice analysis: his conditional-logit model derives estimable choice probabilities from random utility, so that observed choices become measurements of the values that drive them, work that reshaped econometrics and applied demand analysis (McFadden, 2001).

Independence from irrelevant alternatives is a powerful simplification, but Amos Tversky argued it is descriptively false in an instructive way and proposed a mechanism for the violation. In elimination by aspects, a chooser does not weigh options as wholes but screens them sequentially: an aspect is selected with probability proportional to its importance, options lacking that aspect are eliminated, and the process repeats among the survivors until one remains (Tversky, 1972). The model reduces to Luce's rule when options share no aspects, but when options overlap it predicts systematic violations of independence, because a new option that shares aspects with an existing one draws probability away from it selectively rather than proportionally. Elimination by aspects thus stands as the first process model of choice to derive context effects from a plausible cognitive strategy rather than positing them.

Context Effects

The clearest refutations of independence come from context effects, in which the presence of a third option reshapes the choice between two others. Joel Huber, John Payne, and Christopher Puto demonstrated the attraction effect (also called the asymmetric-dominance effect): adding a decoy that is clearly worse than one of two existing options on every attribute — dominated by it but not by the other — raises the choice share of the option that dominates it, a direct violation of the regularity condition that no new option should increase an existing option's share (Huber et al., 1982). The decoy is never chosen; its whole effect is to make its neighbor look good by comparison.

Itamar Simonson extended the phenomenon to the compromise effect: when three options fall along a trade-off, the middle option gains share simply by being the compromise, the one that is extreme on nothing (Simonson, 1989). Simonson argued that these effects arise because choosers construct reasons from the context — dominance and compromise are easy justifications a chooser can give — so preference is assembled at the moment of choice rather than read off from stable, pre-existing utilities. The related framing effect makes the same point from a different angle: Tversky and Kahneman showed that describing formally identical options as gains or as losses reliably reverses choices, because a frame changes the reference point against which outcomes are coded (Tversky & Kahneman, 1981). Together these findings establish that choice is relational and constructed, and the demonstration below shows how a decoy moves the shares of the options it is added to.

Sequential Sampling and Response Time

The models so far predict which option is chosen; sequential-sampling models add when. Their common idea is that a choice is not a single act but the endpoint of a process in which noisy evidence about the options is accumulated over time until the total for one option reaches a decision threshold, at which point that option is chosen and the accumulation stops. Roger Ratcliff's diffusion decision model is the canonical instance: it decomposes a two-choice response into a drift rate (the average quality of evidence), a boundary separation (how much evidence is required, trading speed against accuracy), a starting point (any prior bias), and a non-decision time, and from these it predicts the full distribution of response times for correct and error responses along with the choice proportions (Ratcliff & McKoon, 2008). Because faster and slower responses carry different information, fitting the whole distribution rather than the mean gives the model unusual power to separate the causes of a choice.

Figure 1

Evidence Accumulation in the Diffusion Decision Model

The same accumulation logic was developed within psychology as decision field theory. Jerome Busemeyer and James Townsend derived preferential choice from a diffusion process in which attention shifts among the attributes of the options over deliberation time, so that momentary preferences fluctuate and accumulate toward a threshold; the theory recovers a range of choice phenomena — including the effect of time pressure and certain violations of independence — from a single dynamic mechanism (Busemeyer & Townsend, 1993). Whether framed as diffusion of evidence or of preference, these models share a claim that reframes the whole field: a choice and the time it takes are two readings of one underlying process, and any complete theory of choice must predict both. The demonstration below lets the drift rate and the decision boundary vary so their joint effect on choice probability and mean response time is visible.

The Neuroscience of Value-Based Choice

If choice is the comparison of values, where are those values computed? Camillo Padoa-Schioppa and John Assad recorded single neurons in the primate orbitofrontal cortex while monkeys chose between flavored juices and found cells whose firing rate encoded the subjective economic value of an offered good — scaling with the quantity and the animal's preference — in a manner invariant to the visual and motor details of how the choice was made (Padoa-Schioppa & Assad, 2006). A value represented on a common scale, abstracted from the particular goods and actions, is exactly what a general comparator would need, and its discovery gave value-based choice a neural substrate.

Antonio Rangel, Colin Camerer, and Read Montague drew these strands into a framework for the neurobiology of value-based decision making, decomposing a choice into the computation of the values of the options, their comparison, and the evaluation of the outcome, and mapping each stage onto candidate neural systems (Rangel et al., 2008). The comparison stage was given a concrete, testable form by Ian Krajbich, Carrie Armel, and Rangel, whose attentional drift-diffusion model married the accumulation account to eye-tracking: value evidence accumulates toward a boundary, but the option currently being fixated is weighted more heavily, so where a chooser looks, and for how long, biases what they choose (Krajbich et al., 2010). The model predicts choices and response times from gaze alone, and it closed the loop between the abstract value signals of the orbitofrontal cortex and the moment-to-moment dynamics of selection.

Worked Example

Matching can be turned into arithmetic. Suppose a chooser faces two options, A and B, that deliver reinforcement at rates of 30 and 10 per hour respectively, for a total of 40. Strict matching predicts that the proportion of behavior allocated to A equals the proportion of reinforcement A provides:

P(A) = R_A / (R_A + R_B) = 30 / (30 + 10) = 30 / 40 = 0.75.

Strict matching therefore predicts three-quarters of responses on A. Real choosers, though, usually undermatch: they are less sensitive to the reinforcement ratio than strict matching requires. The generalized matching law captures this with a sensitivity exponent a, so that the allocation becomes the value of A raised to the power a, divided by the sum of both values each raised to a:

P(A) = R_A^a / (R_A^a + R_B^a).

Take the commonly observed value a = 0.8. Then R_A^0.8 = 30^0.8 ≈ 15.20 and R_B^0.8 = 10^0.8 ≈ 6.31, so

P(A) = 15.20 / (15.20 + 6.31) = 15.20 / 21.51 ≈ 0.707.

Undermatching pulls the predicted allocation down from 0.75 to about 0.71, closer to indifference than the reinforcement ratio alone would imply. The matching-law demonstration above computes exactly this proportion for any reinforcement ratio and sensitivity exponent, so the departure from strict matching is the visible gap between the diagonal and the fitted curve.

Discussion

The study of choice has produced a layered but coherent account. The matching law supplied the first quantitative regularity, tying the allocation of behavior to the reinforcement it earns and grounding choice in its consequences (Herrnstein, 1961). Luce's choice axiom supplied the measurement theory, expressing choice probabilities as ratios of scale values and generating the random-utility models that remain the workhorses of applied choice analysis (Luce, 1977). Each framework is clean, and each is systematically violated: context effects show that the independence property at the heart of the ratio rule fails whenever options are compared rather than valued in isolation (Huber et al., 1982; Simonson, 1989).

The response to those violations was to model the process rather than only the outcome. Elimination by aspects derived context effects from a sequential screening strategy (Tversky, 1972); sequential-sampling models derived choice and its timing together from evidence accumulated to a threshold (Ratcliff & McKoon, 2008); and neuroeconomics located the values being accumulated in identifiable brain circuits and tied their comparison to overt attention (Padoa-Schioppa & Assad, 2006; Krajbich et al., 2010). The trajectory of the field is from static rules that describe choice to dynamic mechanisms that generate it, and the payoff is a single framework in which the same parameters explain what is chosen, how often, how fast, and where in the brain the computation runs.

Current Directions

One active front asks how the brain's representation of value shapes the choices that follow from it. Divisive normalization — a canonical cortical computation in which each option's value signal is scaled by the total value on offer — predicts that choices should depend on the value of unavailable or background options, and studies pit it against value-based attentional weighting as competing explanations of context-dependent choice, with evidence that attention rather than pure normalization drives some of the multi-alternative effects (Gluth et al., 2020). Richard Webb has drawn the neural dynamics of accumulation directly into economic models of stochastic choice, showing that a sequential-sampling foundation implies specific, testable departures from the standard random-utility form (Webb, 2019).

A second strand deepens the role of attention. Ian Krajbich's synthesis of sequential-sampling models argues that accounting for where and when people look is now essential to predicting choice, since gaze both reflects and causes the accumulation of value (Krajbich, 2019). A third recasts the whole enterprise in terms of resource-rational analysis, which treats the biases and stochasticity of choice as the optimal behavior of an agent that must decide under genuine limits on time and computation, so that undermatching, context effects, and noisy selection appear not as failures of rationality but as rational adaptations to the cost of thinking (Bhui et al., 2021). Across all three, the trend is to unify the value, the attention, and the timing of choice within a single computational account.

Common Misconceptions

Choice and decision making are the same thing.

Choice is the observable selection of one option from a set; decision making is the broader appraisal-and-selection process of which choice is the endpoint. MeSH files choice behavior as a narrower kind of decision making, and much of the science treats choice as the measurable output that theories of decision are tested against (Luce, 1977).

People always choose the option with the highest value.

Choice is stochastic: the same chooser facing the same options does not always select the same one, which is why the object of theory is a choice probability, not a deterministic pick. Sequential-sampling models make this explicit by adding noise to the evidence accumulated for each option (Ratcliff & McKoon, 2008).

Adding an option cannot change the choice between the others.

The independence-from-irrelevant-alternatives property says it should not, but the attraction and compromise effects show that it does: a decoy that is never itself chosen can reliably shift the shares of the options it is added among (Huber et al., 1982; Simonson, 1989).

The matching law means animals maximize reinforcement.

Matching and maximizing coincide only in special cases. Herrnstein attributed matching to melioration, a local shifting toward the momentarily richer option, which produces matching at equilibrium but can leave the chooser short of the globally optimal allocation (Herrnstein, 1961).

Glossary

Attentional drift-diffusion model.

A sequential-sampling model of value-based choice in which evidence accumulates toward a boundary while the currently fixated option is weighted more heavily, so gaze biases choice.

Attraction effect.

The rise in an option's choice share when a decoy that it dominates — one worse than it on every attribute — is added to the set; also called the asymmetric-dominance effect.

Choice axiom.

Luce's postulate that the probability of choosing an option is its scale value divided by the summed scale values of the set, implying independence from irrelevant alternatives.

Choice behavior.

The observable selection of one alternative from a set of two or more; the behavioral endpoint through which preference and value are measured.

Compromise effect.

The rise in the choice share of a middle option that represents a compromise along a trade-off, chosen because it is extreme on no attribute.

Context effect.

Any change in the preference between options caused by the composition of the choice set rather than by the options' own values.

Decision field theory.

Busemeyer and Townsend's dynamic model deriving preferential choice from a diffusion of momentary preference as attention shifts among the options' attributes over deliberation time.

Diffusion decision model.

Ratcliff's model of two-choice decisions as evidence accumulated at a drift rate to one of two boundaries, jointly fitting choice proportions and response-time distributions.

Drift rate.

In sequential-sampling models, the average rate at which evidence favoring one option accumulates; higher drift yields faster and more accurate choices.

Elimination by aspects.

Tversky's process model in which options are screened sequentially on attributes selected in proportion to their importance, eliminating options that lack each aspect.

Independence from irrelevant alternatives.

The property that the relative odds of choosing between two options are unaffected by the other options present; implied by the choice axiom and violated by context effects.

Matching law.

Herrnstein's finding that the relative rate of a response matches the relative rate of reinforcement it earns across concurrently available options.

Melioration.

A choice process that shifts behavior toward whichever option currently yields the higher local rate of reinforcement, producing matching at equilibrium but not always global maximization.

Random utility model.

A class of models in which each option's utility has a random component and the chooser selects the option of highest realized utility, generating probabilistic choice.

Response threshold.

In accumulation models, the amount of evidence required before a choice is committed; raising it improves accuracy at the cost of speed.

Sequential sampling.

The family of models in which a choice results from noisy evidence accumulated over time until it reaches a decision boundary.

Undermatching.

The common departure from strict matching in which behavior is less sensitive to the reinforcement ratio than matching predicts, captured by a generalized-matching sensitivity below one.

Value-based decision making.

Choice governed by the subjective values of the options, as studied in neuroeconomics, where valuation signals are computed and compared to a decision bound.

Key Researchers

Jerome R. Busemeyer (b. 1954). Distinguished Professor at Indiana University Bloomington; with Townsend he developed decision field theory, deriving choice probability and deliberation time from a dynamic diffusion of preference. Homepage - Google Scholar - ORCID

Richard J. Herrnstein (1930-1994). Professor at Harvard University; he formulated the matching law, extending the analysis of choice from the operant laboratory into behavioral economics. Wikipedia

Daniel Kahneman (1934-2024). Nobel laureate and Emeritus Professor at Princeton University; with Tversky he showed that the framing of formally equivalent options systematically reverses choices, breaking descriptive invariance. Wikipedia - Google Scholar

Ian Krajbich (contemporary). Professor at the University of California, Los Angeles; with Rangel he developed the attentional drift-diffusion model, linking eye fixations to the accumulation and comparison of value. Homepage - Google Scholar - ORCID

R. Duncan Luce (1925-2012). Professor at the University of California, Irvine; he formalized the choice axiom, whose ratio-scale representation grounds the class of random-utility and logit choice models. Wikipedia

Camillo Padoa-Schioppa (contemporary). Professor at Washington University in St. Louis; with Assad he recorded orbitofrontal neurons that encode the subjective economic value of goods, a neural substrate for value-based choice. Homepage - Google Scholar - ORCID

Antonio Rangel (contemporary). Professor at the California Institute of Technology; a founder of neuroeconomics, he framed value-based choice as the computation and comparison of stimulus values and co-developed the attentional drift-diffusion model. Homepage - Google Scholar

Roger Ratcliff (contemporary). Distinguished University Professor at Ohio State University; he developed the diffusion decision model, which decomposes two-choice responses into evidence rate, threshold, and non-decision time. Homepage - Google Scholar - ORCID

Itamar Simonson (contemporary). Emeritus Professor at the Stanford Graduate School of Business; he demonstrated the compromise and attraction effects, showing that choices are often constructed from context-supplied reasons. Wikipedia - Google Scholar - ORCID

Amos Tversky (1937-1996). Professor at Stanford University; he proposed elimination by aspects and, with Kahneman, showed that choice violates the invariance and independence axioms of expected utility. Wikipedia

Frequently Asked Questions

What is choice behavior in cognitive psychology?
Choice behavior is the observable act of selecting one alternative from a set of two or more. Because a choice can be counted, timed, and modeled, it is the behavioral endpoint through which preferences and values are measured, and MeSH classifies it as a narrower kind of decision making (Luce, 1977).

What is the matching law?
The matching law, discovered by Herrnstein, states that the relative rate of a response matches the relative rate of reinforcement it earns across concurrently available options. Its generalized form adds a sensitivity exponent that captures the common finding of undermatching (Herrnstein, 1961).

What is Luce's choice axiom?
It is the postulate that the probability of choosing an option equals its positive scale value divided by the summed scale values of all options in the set. The axiom implies independence from irrelevant alternatives and underwrites the random-utility and logit models used across economics (Luce, 1977).

What are context effects in choice?
Context effects are changes in the preference between options caused by the composition of the choice set. The attraction and compromise effects show that adding a third option — even one never chosen — can reverse the preference between two others, violating independence from irrelevant alternatives (Huber et al., 1982; Simonson, 1989).

How do sequential-sampling models explain choice?
They treat a choice as noisy evidence accumulated over time until it reaches a decision threshold, with the boundary crossed determining the choice and the time taken determining the response time. The diffusion decision model fits choice proportions and full response-time distributions together (Ratcliff & McKoon, 2008).

Where in the brain is choice value computed?
Neurons in the orbitofrontal cortex encode the subjective economic value of options on a common scale, abstracted from the specific goods and actions involved. Neuroeconomic models cast value-based choice as the comparison of such signals to a decision bound (Padoa-Schioppa & Assad, 2006; Rangel et al., 2008).

Does attention influence what we choose?
Yes. The attentional drift-diffusion model shows that the option a person is fixating is weighted more heavily in the accumulation of evidence, so gaze both reflects and biases choice, and accounting for attention improves the prediction of choices and response times (Krajbich et al., 2010; Krajbich, 2019).

Is stochastic choice irrational?
Not necessarily. Resource-rational analysis treats the noise and biases of choice as the optimal behavior of an agent deciding under real limits on time and computation, so undermatching and context effects can appear as rational adaptations to the cost of thinking rather than as failures (Bhui et al., 2021).

References