Weak Axiom Of Revealed Preference Research Articles

Choice by elimination then selection

This paper analyzes a decision-making process known as Choice by Elimination then Selection (ES), in which an individual narrows down available alternatives based on a preference order called the elimination relation and then selects the best element from the remaining alternative(s) based on a different preference order called the selection relation. The elimination and selection criteria need not rank alternatives in the same order. ES can be seen as a response to information overload, where shortlisting alternatives can facilitate more informed and beneficial choices. It can also be seen as a method to make a choice when moral or personal values are in the way of utility maximization. The paper uses an axiomatic approach to fully characterize the choices based on the ES method, showing that ES choices may not satisfy the Weak Axiom of Revealed Preference (WARP) and, thus, are not rationalizable under the standard classical framework. Four axioms are introduced to fully characterize the choice correspondence based on ES. The paper also discusses the uniqueness of the elimination and selection ordering relations. The ES method belongs to the class of models that analyze boundedly rational choice behavior, such as choice with frames, limited attention models, list rationalizable models, categorize then choose, and status quo bias.

Disentangling revealed preference from rationalization by a preference

The weak axiom of revealed preference (WARP) ensures that the revealed preference (i) is a preference relation (i.e., it is complete and transitive) and (ii) rationalizes the choices. However, when WARP fails, either one of these two properties is violated, but it is unclear which one it is. We provide an alternative characterization of WARP by showing that WARP is equivalent to the conjunction of two axioms each of which separately guarantees (i) and (ii).

Bad temptation

We study a static self-control model in which an agent’s preference, temptation ranking, and cost of self-control drive her choices among a finite set of options. We show it is without loss to assume the agent’s temptation ranking is the opposite of her preference. We characterize the model by relaxing the Weak Axiom of Revealed Preference (WARP), and exploit WARP violations to identify the model’s parameters.

Cardinal revealed preference: Disentangling transitivity and consistent binary choice

We present a new notion of cardinal revealed preference that exploits the expenditure information in classical consumer theory environments with finite data. We propose a new behavioral axiom, Acyclic Enticement (AE), that requires the acyclicity of the cardinal revealed-preference relation. AE is logically independent from the Weak Axiom of Revealed Preference (WARP). We show that the Generalized Axiom of Revealed Preference (GARP), which characterizes the standard rational consumer, is logically equivalent to AE and WARP. We use our axiomatic decomposition to show, in experimental and scanner consumer-panel data sets, that AE explains the majority of the predictive success of GARP. Moreover, AE taken alone is superior in predictive success to both WARP and GARP.

Social Image Concern and Reference Point Formation

Abstract This paper develops an axiomatic context-dependent model of social image concerns. Allowing for context-dependence based on choice sets, it examines how context-dependence impacts social image concerns, in particular how a decision maker exhibits various social emotions stemming from their intrinsic reference point, which may not be captured by conforming to social norms. To elicit the intrinsic reference point, this paper provides weaker versions of Strategic Rationality and Independence, in addition to the basic axioms, to characterize the model of the Reference-Dependent Image-Conscious utilitarian. This paper also examines how social emotions stemming from the intrinsic reference point are related to preference reversals as violations of the Weak Axiom of Revealed Preference (WARP). Finally, this paper considers the relationship between social image concerns and intrinsic reciprocity. The findings demonstrate that social image plays a large role and the model developed illustrates a condition in which cooperation is sustained in prisoner’s dilemma games.

Revealed Preference Implications of Backward Induction and Subgame Perfection

Consider a decision-maker (DM) who must select an alternative from a set of mutually exclusive alternatives but must take this decision sequentially. If the DM’s choice correspondence over subsets of alternatives satisfies the weak axiom of revealed preference (WARP), then the subgame perfect Nash equilibrium (SPNE) and backward induction (BI) strategies coincide. We study the relation between the SPNE and BI strategies when the DM’s choice correspondence fails to satisfy WARP. First, Sen’s axiom α is necessary and sufficient for the set of SPNE strategies to be a subset of the set of BI strategies; moreover, a mild strengthening of Sen’s axiom β is necessary and sufficient for the set of BI strategies to be a subset of the set of SPNE strategies. These results extend to multiplayer games. (JEL D11, C72, C73)

A Rationalization of the Weak Axiom of Revealed Preference

We offer a rationalization of the weak axiom of revealed preference (WARP) and of the weak generalized axiom of revealed preference (WGARP) for both finite and infinite data sets of consumer choice. We call it maximin rationalization, in which each pairwise choice is associated with a local utility function. We develop its associated revealed-preference theory. We show that preference recoverability and welfare analysis a la Varian (1982) may not be informative enough when the weak axiom holds but when consumers are not utility maximizers. In addition, we show that counterfactual analysis may fail with WGARP/WARP. We clarify the reasons for these failures and provide new informative bounds for the consumer’s true preferences, as well as a new way to perform counterfactual analysis. Finally, by adding the Gorman form and quasilinearity restrictions to the “local” utility functions, we obtain new characterizations of the choices of the Shafer (1974) nontransitive consumer and those choices satisfying the law of demand.

Rationalizable Incentives: Interim Implementation of Sets in Rationalizable Strategies

We offer a rationalization of the weak axiom of revealed preference (WARP) and of the weak generalized axiom of revealed preference (WGARP) for both finite and infinite data sets of consumer choice. We call it maximin rationalization, in which each pairwise choice is associated with a local utility function. We develop its associated revealed-preference theory. We show that preference recoverability and welfare analysis a la Varian (1982) may not be informative enough when the weak axiom holds but when consumers are not utility maximizers. In addition, we show that counterfactual analysis may fail with WGARP/WARP. We clarify the reasons for these failures and provide new informative bounds for the consumer’s true preferences, as well as a new way to perform counterfactual analysis. Finally, by adding the Gorman form and quasilinearity restrictions to the “local” utility functions, we obtain new characterizations of the choices of the Shafer (1974) nontransitive consumer and those choices satisfying the law of demand.

Assessing axioms of theories of limited attention

It is very likely that many decisions made by individuals are made without a complete or exhaustive deliberation process. One of the plausible explanations for this behaviour, that has recently received much recognition in economics, is that people have limited attention. This assumption has motivated many new theories, which are increasingly founded on axioms. This research experimentally tested two of these theories, those of Masatlioglu, Nakajima and Ozbay (2012) and Lleras Masatlioglu Nakajima and Ozbay (2017), which are based on the revealed preference framework and are built on axioms which are weakenings of the Weak Axiom of Revealed Preference (WARP) ̶ the standard axiom of preference theory. This paper uses standard choice data to determine the (relative) validity of their underlying axioms, compared to a benchmark of the violation rate given by random behaviour. WARP(LA) (Masatlioglu et al. (2012)) results in fewer violations, though LC-WARP (Lleras et al. (2017)) has higher correct prediction rates.

Cardinal Revealed Preference, Price-Dependent Utility, and Consistent Binary Choice

We present a new notion of cardinal revealed preference that exploits the expenditure information in classical consumer theory environments with finite data. We propose a new behavioral axiom, Acyclic Enticement (AE), that requires the acyclicity of the cardinal revealed-preference relation. AE is logically independent from the Weak Axiom of Revealed Preference (WARP). We show that the Generalized Axiom of Revealed Preference (GARP), which characterizes the standard rational consumer, is logically equivalent to AE and WARP. We propose a new notion of rationalization by means of a price-dependent utility function that characterizes AE, which in particular is suitable for welfare analysis. We also propose a consistency condition for preference functions that is equivalent to WARP. We use our axiomatic decomposition to show, in experimental and scanner consumer-panel data sets, that AE explains the majority of the predictive success of GARP. Moreover, AE taken alone is superior in predictive success to both WARP and GARP.

Transitivity of preferences: When does it matter?

We define the empirical conditions on prices and incomes under which transitivityof preferences has specific testable implications. In particular, we set out necessaryand sufficient requirements for budget sets under which consumption choices canviolate SARP (Strong Axiom of Revealed Preferences) but not WARP (Weak Axiomof Revealed Preferences). As SARP extends WARP by additionally imposingtransitive preferences, this effectively defines the conditions under which transitivityis separately testable. Our findings have considerable practical relevance, as transitivityconditions are known to substantially aggravate the computational burden ofempirical revealed preference analysis. Our characterization takes the form of triangularconditions that must hold for all three-element subsets of normalized prices,and which are easy to verify in practice. We demonstrate their practical use throughtwo short empirical applications.

WARP and combinatorial choice

For combinatorial choice problems, I show that the Irrelevance of Rejected Items condition is equivalent to the Weak Axiom of Revealed Preference (WARP), and is necessary and sufficient for the existence of a complete, reflexive and antisymmetric rationalization of a combinatorial choice function. I also show the equivalence of WARP to path independence and to other classical choice conditions when the choice domain is combinatorial.

What Types are There?

Preferences differ in the population, and this heterogeneity may not be adequately described by observed characteristics and additive error terms. As a first contribution, this study shows that preference heterogeneity can be represented graphically by means of violations of the Weak Axiom of Revealed Preference (WARP), and that computing the minimum number of partitions necessary to break all WARP violations in the sample is equivalent to computing the chromatic number of this graph. Second, the study builds the bridge between revealed preference theory and cluster analysis to assign individuals to these partitions (i.e. preference types). The practical methods are applied to Dutch labour supply data, to recover reservation wages of individuals who belong to particular preference types.

The Satisfiability Problem for Boolean Set Theory with a Choice Correspondence

Given a set U of alternatives, a choice (correspondence) on U is a contractive map c defined on a family Omega of nonempty subsets of U. Semantically, a choice c associates to each menu A in Omega a nonempty subset c(A) of A comprising all elements of A that are deemed selectable by an agent. A choice on U is total if its domain is the powerset of U minus the empty set, and partial otherwise. According to the theory of revealed preferences, a choice is rationalizable if it can be retrieved from a binary relation on U by taking all maximal elements of each menu. It is well-known that rationalizable choices are characterized by the satisfaction of suitable axioms of consistency, which codify logical rules of selection within menus. For instance, WARP (Weak Axiom of Revealed Preference) characterizes choices rationalizable by a transitive relation. Here we study the satisfiability problem for unquantified formulae of an elementary fragment of set theory involving a choice function symbol c, the Boolean set operators and the singleton, the equality and inclusion predicates, and the propositional connectives. In particular, we consider the cases in which the interpretation of c satisfies any combination of two specific axioms of consistency, whose conjunction is equivalent to WARP. In two cases we prove that the related satisfiability problem is NP-complete, whereas in the remaining cases we obtain NP-completeness under the additional assumption that the number of choice terms is constant.

Monkeys choose as if maximizing utility compatible with basic principles of revealed preference theory

Revealed preference theory provides axiomatic tools for assessing whether individuals make observable choices "as if" they are maximizing an underlying utility function. The theory evokes a tradeoff between goods whereby individuals improve themselves by trading one good for another good to obtain the best combination. Preferences revealed in these choices are modeled as curves of equal choice (indifference curves) and reflect an underlying process of optimization. These notions have far-reaching applications in consumer choice theory and impact the welfare of human and animal populations. However, they lack the empirical implementation in animals that would be required to establish a common biological basis. In a design using basic features of revealed preference theory, we measured in rhesus monkeys the frequency of repeated choices between bundles of two liquids. For various liquids, the animals' choices were compatible with the notion of giving up a quantity of one good to gain one unit of another good while maintaining choice indifference, thereby implementing the concept of marginal rate of substitution. The indifference maps consisted of nonoverlapping, linear, convex, and occasionally concave curves with typically negative, but also sometimes positive, slopes depending on bundle composition. Out-of-sample predictions using homothetic polynomials validated the indifference curves. The animals' preferences were internally consistent in satisfying transitivity. Change of option set size demonstrated choice optimality and satisfied the Weak Axiom of Revealed Preference (WARP). These data are consistent with a version of revealed preference theory in which preferences are stochastic; the monkeys behaved "as if" they had well-structured preferences and maximized utility.

External and internal consistency of choices made in convex time budgets

We evaluate data on choices made from convex time budgets (CTB) in Andreoni and Sprenger (Am Econ Rev 102(7):3333–3356, 2012a) and Augenblick et al. (Q J Econ 130(3):1067–1115, 2015), two influential studies that proposed and applied this experimental technique. We use the weak axiom of revealed preference (WARP) to test for external consistency relative to pairwise choice, and demand, wealth and impatience monotonicity to test for internal consistency. We find that choices made by subjects in the original Andreoni and Sprenger (Am Econ Rev 102(7):3333–3356, 2012a) paper violate WARP frequently; violations of all three internal measures of monotonicity are concentrated in subjects who take advantage of the novel feature of CTB by making interior choices. Wealth monotonicity violations are more prevalent and pronounced than either demand or impatience monotonicity violations. We substantiate the importance of our desiderata of choice consistency in examining effort allocation choices made in Augenblick et al. (Q J Econ 130(3):1067–1115, 2015), where we find considerably more demand monotonicity violations, as well as many classical monotonicity violations which are associated with time inconsistent behavior. We believe that the frequency and magnitude of WARP and monotonicity violations found in the two studies pose important confounds for interpreting and structurally estimating choice patterns elicited through CTB. We encourage researchers employing CTB in present and future experiments to include consistency tests in their design and pre-estimation analysis.

What Types are There?

Preferences differ in the population, and this heterogeneity may not be adequately described by observed characteristics and additive error terms. As a first contribution, this study shows that preference heterogeneity can be represented graphically by means of violations of the Weak Axiom of Revealed Preference (WARP), and that computing the minimum number of partitions necessary to break all WARP violations in the sample is equivalent to computing the chromatic number of this graph. Second, the study builds the bridge between revealed preference theory and cluster analysis to assign individuals to these partitions (i.e. preference types). The practical methods are applied to Dutch labour supply data, to recover reservation wages of individuals who belong to particular preference types.

Impact of satisficing behavior in online surveys on consumer preference and welfare estimates

Conducting online surveys through consumer panels has become increasingly popular for researchers to assess consumers’ preferences and attitudes for the purpose of obtaining welfare estimates because they are inexpensive, flexible, and allow for fast feedback. Interestingly, few studies have examined the behaviors of online survey panelists, particularly their satisficing behaviors on welfare measures. This study demonstrates the use of validation questions (trap questions) to detect survey respondents’ satisficing behavior and its impact on consumer choice, willingness to pay (WTP), and consumer surplus (CS) estimates. We find that respondents who fail a validation question (VQ) are more likely to violate the weak axiom of revealed preferences (WARP) in the choice experiment. The estimates for preference parameters, WTP, and CS are statistically different between those who pass and those who fail the VQ. In addition, the WTP and CS from respondents passing the VQ in general have smaller variances than those from respondents failing the VQ. These results indicate that without controlling for potential satisficing behaviors, online surveys may produce less efficient estimates (estimates with larger variance) of welfare measures.

Menu-dependent self-control

The literature on self-control problems has typically put forth models that imply behavior that is consistent with the weak axiom of revealed preference (WARP). We argue that when choice is the outcome of some underlying internal conflict, the resulting choices may not be perfectly consistent across choice problems: an agent’s ability to resist temptation may well depend on what alternatives are available to him. We generalize Gul and Pesendorfer (2001) so that self-control weakens in the presence of temptation. To model choices from menus explicitly, we consider a choice correspondence as well as a preference over menus and relax both the Independence axiom for the preference and the WARP condition for the choice correspondence. The model is shown to unify a range of well-known findings in the experimental literature on choice under risk and over time within a single specification.

Sharp for SARP: Nonparametric Bounds on Counterfactual Demands

Sharp nonparametric bounds are derived for counterfactual demands and Hicksian compensating and equivalent variations. These “i-bounds” refine and extend earlier results of Blundell, Browning, and Crawford (2008). We show that their bounds are sharp under the Weak Axiom of Revealed Preference (WARP) since they do not require transitivity. The new bounds are sharp under the Strong Axiom of Revealed Preference (SARP). By requiring transitivity they can be used to bound welfare measures. The new bounds on welfare measures are shown to be operationalized through algorithms that are easy to implement. (JEL D04, D11)