On the theory of reference-dependent preferences

A theory is proposed in which preferences are conditional on reference points. It is related to Tversky and Kahneman’s reference-dependent preference theory, but is simpler and deviates less from conventional consumer theory. Preferences conditional on any given reference point satisfy conventional assumptions. Apart from a continuity condition, the only additional restriction is to rule out cycles of pairwise choice. The theory is consistent with observations of status quo bias and related effects. Reference points are treated as subject to change during the course of trade. The implications of endogeneity of reference points for behaviour in markets are investigated.     

Context effects: A representation of choices from categories

This paper studies a model of reference-dependent choice from sets of options grouped into categories. The proposed model is consistent with experimental evidence documenting context effects in a variety of choice situations. In our model, the reference point for any given category is subjective, and corresponds to the least preferred element in the category under consideration. Every object in a category is evaluated relative to the corresponding reference point; this may distort the objective ranking of options across different categories, and thus possibly give rise to a context-effects bias. The resulting representation is essentially unique. We also provide an economic application of the preferences that we axiomatize to principal-agent models. We show how sellers facing consumers exhibiting the context-effects bias can increase their profits by exploiting their bounded rationality.     

Staying ahead and getting even: Risk attitudes of experienced poker players

Frequent online poker players with extensive experience calculating probabilities and expected values might be expected to behave as Expected Utility maximizers, in that small shocks to their wealth would not affect risk preferences (Rabin, 2000). By contrast, reference-dependent loss aversion (as in Prospect Theory) (Koszegi and Rabin, 2006, Kahneman and Tversky, 1979) predicts that risk aversion decreases as wealth moves away from the reference point in either direction. In terms of continuing to play, as well as a more aggressive playing style, we find strong evidence for the break-even effect, the increased pursuit of risk as a player is losing within a session. Players' behavior also appears consistent with existing evidence on reference-dependent labor supply, in their tendency to reduce effort and risk-taking in response to being ahead. Our findings provide evidence for reference-dependent behavior in a flexible, high-skilled setting, under conditions of well-understood monetary risk.     

Reference-dependent subjective expected utility

A reference-dependent generalisation of subjective expected utility theory is presented. In this theory, preferences between acts depend both on final outcomes and on reference points (which may be uncertain acts). It is characterised by a set of axioms in a Savage-style framework. A restricted form of the theory separates attitudes to end states (encoded in a ‘satisfaction function’) from attitudes to gains and losses of satisfaction. Given weak additional assumptions, the restricted theory excludes cycles of choice, explains observed disparities between willingness-to-pay and willingness-to-accept valuations of lotteries, and predicts preference reversal.     

Money matters: an axiomatic theory of the endowment effect

We develop a framework that allows us to state precisely the relationship between leading concepts of the theoretical and empirical research on reference-dependent preferences, namely the status quo bias, the endowment effect and the willingness to accept (WTA)/willingness to pay (WTP) gap. We show that a monetary version of the status quo bias is a necessary condition for the WTA/WTP gap, and show how to factor out the part of the gap due to income effects from the part of the gap due to the endowment effect. As a byproduct, we show that reference-dependent phenomena are generated by reference-independent factors, i.e., an underlying reference-independent preference relation the properties of which are discussed at length.     

Anticipated regret as an explanation of uncertainty aversion

The paper provides a psychological explanation of uncertainty aversion based on the fear of regret. We capture an agent’s regret using a reference-dependent utility function in which the agent’s utility depends on the performance of his chosen option relative to the performance of the option that would have been best ex post. An uncertain option is represented as a compound lottery. The basic idea is that selecting a compound lottery reveals information, which alters the ex post assessment of what the best choice would have been, inducing regret. We provide sufficient conditions under which regret implies uncertainty aversion in the sense of quasi-concave preferences over compound lotteries.     

Why rationality may be a consequence of Hume's theory of choice

Facing R. Sugden's criticism of our interpretation, it is shown in this paper that rationality appears as a possible consequence of Hume's theory of choice. We first argue that Sugden's dismissal of the preference relation from the type of rationality through which Hume's theory is apprehended, is highly disputable, from the point of view of both standard choice theory and Hume's theory of passions. Nonetheless, Sugden's criterion of rationality might be restated in Humean terms as a condition of non-revision of preferences in the dynamics of passions. But, since the process of choice that we have described explicitly takes into account the revision of preferences, and shows that, when this last is no longer required, rationality occurs as an outcome of this process, it is not really concerned by Sugden's criticism.     

The endowment effect and the reference state: Evidence and manipulations

Recent reports suggest that the “endowment effect” may be due to conditions under which it is observed and explained by incentives long recognized in standard theory. Evidence from new experiments, reported here, provides empirical support for the role of the economic environment on people's perceived reference state and consequently on their valuations, as suggested by Köszegi and Rabin [Köszegi, B., Rabin, M., 2006. A model of reference-dependent preferences. Quarterly Journal of Economics 121, 1133–1165], and indicates that the disappearance of the valuation disparity is more likely due instead to conditions that weaken the perception of reference states. Further, these conditions appear to be poor approximations of those that prevail in most cases for which valuations are normally made.     

When expectations become aspirations: reference-dependent preferences and liquidity constraints

A large body of literature suggests that consumers derive utility from gains and losses relative to a reference point. This paper shows that such reference dependence can affect savings in opposite directions depending on whether people face liquidity constraints. Existing models for wealth and intertemporal choice predict that reference dependence reduces savings, but these models abstract from liquidity constraints. Introducing a liquidity constraint, I find that reference dependence can increase optimal savings for people without access to credit. Ex post, after reference points have been formed, liquidity constraints force consumers to take part of an income loss in early periods, inducing those who are reference dependent to concentrate the full loss in early periods and save in order to eliminate future losses. Further, anticipating a liquidity constraint raises the expected level of future consumption and thus the expectations-based reference point for future periods, creating an ex-ante savings motive. These findings underscore that it is important to account for financial market imperfections when applying or testing reference-dependent models in low-income settings, and potentially explain heterogeneity in how much the poor save when facing binding liquidity constraints.     

Self-rewards and personal motivation

Self-administered rewards are ubiquitous. They serve as incentives for personal accomplishments and are widely recommended to increase personal motivation. We show that in a model with time-inconsistent and reference-dependent preferences, self-rewards can be a credible and effective tool to overcome self-control problems. We also discuss the different types of self-rewards the individual can use, such as vice goods and virtue goods, and analyze which types of goods the individual prefers.     

Risk, ambiguity, and state-preference theory

The state-preference framework for modeling choice under uncertainty, in which objects of choice are allocations of wealth or commodities across states of the world, is a natural one for modeling ??smooth?? ambiguity-averse preferences. It does not require reference to objective probabilities, personalistic consequences, or counterfactual acts, and it allows for state dependence of utility and unobservable background risk. The decision maker??s local revealed beliefs are encoded in her risk-neutral probabilities (her relative marginal rates of substitution between states) and her local risk preferences are encoded in the matrix of derivatives of the risk-neutral probabilities. This matrix plays a central but generally unappreciated role in the modeling of risk attitudes in the state-preference framework. It can be computed by inverting a bordered Slutsky matrix and vice versa, it generalizes the Arrow?CPratt measure for approximating local risk premia, and its structure reveals whether the decision maker??s risk preferences are ambiguity averse as well as risk-averse. Two versions of the smooth ambiguity model are analyzed??the source-dependent risk aversion model and the second-order uncertainty (KMM) model??and it is shown that in both cases, the overall premium for local uncertainty can be decomposed as the sum of a risk premium and an ambiguity premium.     

Inter-temporal choices with temporal reference dependence

I develop an intertemporal choice model for rational deviators whose preferences depend not only on their actual consumption but also on comparison to their beliefs about the optimal consumption. The standard decision maker is loss averse with respect to this belief-dependent reference point. When psychologically weighted loss aversion is low, a decision maker deviates from the standard intertemporal choice behavior and over-consumption, as well as the alternative possibility of under-consumption can be rationalized. When the decision maker has time-varying degrees of loss aversion, he re-optimizes the consumption plan through adjusted beliefs as subsequent selves realize that past decision for the present period is no longer optimal. In the dynamic model, I solve for consistent intertemporal optimization rules by which a dynamic deviator should meet rational intertemporal consistency at each point in time. Finally, I demonstrate that the dynamic reference dependent model can solve a puzzling feature in lifecycle consumption data.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

On the independence from irrelevant alternatives in probabilistic choice models

Probabilistic choice models often invoke a behavioral assumption referred to as the independence from irrelevant alternatives. The implications of this condition have not been fully developed in probabilistic choice contexts. It is well known that nonpathological preferences may not exhibit the independence from irrelevant alternatives, which is apparently an assumption of convenience; and the obvious question is then whether the assumption is very restrictive. This paper addresses this question. A common model of probabilistic choice is constructed. A measure of the likelihood that independence from irrelevant alternatives holds is seen to arise naturally in this model. Given this measure, it is demonstrated that the condition will almost always fail to hold.     

Utility from anticipation and personal equilibrium

I develop a dynamic model of individual decisionmaking in which the agent derives utility from physical outcomes as well as from rational beliefs about physical outcomes (“anticipation”), and these two payoff components can interact. Beliefs and behavior are jointly determined in a personal equilibrium by the requirement that behavior given past beliefs must be consistent with those beliefs. I explore three phenomena made possible by utility from anticipation, and prove that if the decisionmaker’s behavior is distinguishable from a person’s who cares only about physical outcomes, she must exhibit at least one of these phenomena. First, the decisionmaker can be prone to self-fulfilling expectations. Second, she might be time-inconsistent even if her preferences in all periods are identical. Third, she might exhibit informational preferences, where these preferences are intimately connected to her attitudes toward disappointments. Applications of the framework to reference-dependent preferences, impulsive behaviors, and emotionally difficult choices are discussed.     

On the correspondence between multivariate risk aversion and risk aversion with state-dependent preferences

This paper establishes the correspondence between multivariate risk aversion and risk aversion with state-dependent preferences. It shows that the prerequisite for comparability of risk aversion in the multivariate case, namely, identical ordinal preferences on the commodity space, corresponds to identical, properly defined, reference sets in the case of state-dependent preferences. For comparable decision makers the condition that the utility function of one is a concave transformation of that of the other on the commodity space corresponds to the condition that the expected utility of one is a concave transformation of that of the other on the reference set.     

A comparison of responses to single and repeated discrete choice questions

According to neoclassical economic theory, a stated preference elicitation format comprising a single binary choice between the status quo and one alternative is incentive compatible under certain conditions. Formats typically used in choice experiments comprising a sequence of discrete choice questions do not hold this property. In this paper, the effect on stated preferences of expanding the number of binary choice tasks per respondent from one to four is tested using a split sample treatment in an attribute-based survey relating to the undergrounding of overhead low-voltage electricity and telecommunications wires. We find evidence to suggest that presenting multiple choice tasks per respondent decreases estimates of expected willingness to pay. Preferences stated in the first of a sequence of choice tasks are not significantly different from those stated in the incentive compatible single binary choice task, but, in subsequent choice tasks, responses are influenced by cost levels observed in past questions. Three behavioural explanations can be advanced – weak strategic misrepresentation, reference point revision, and asymmetric value learning. The evidence is contrary to the standard assumption of truthful response with stable preferences.     

Decomposable Strategy-Proof Social Choice Functions

This article shows that a social choice function defined on a domain of separable preferences which satisfies a relatively weak domain-richness condition on a product set of alternatives is (i) strategy-proof and only depends on the tops of the individual preferences if and only if (ii) the range of the social choice function is a product set and the social choice function can be decomposed into the product of one-dimensional, strategy-proof, nontop-insensitive social choice functions.
JEL Classification Number: D71.     

A cardinal approach to straightforward probabilistic mechanisms

In every probabilistic mechanism, society selects an alternative, through a random device, out of a subset of indifferent alternatives. Consequently, in this context individuals face uncertainty and value the different lotteries on alternatives by their expected utility, so that they make use of a Von Neumann-Morgenstern cardinal utility function. Surprisingly, the social choice approach to probabilistic mechanisms assumes the use of ballots which preclude the complete expression of behaviour towards risk: individuals can only announce their ordinal preferences, or an approximation of their cardinal preferences, since in any case only a finite number of representations of preferences is available. This paper attempts to study voting systems in which individuals can express the cardinality of their preferences by assigning weights to the alternatives. It is shown that by voting with ballots which reflect weighting a new class of straightforward probabilistic mechanisms is defined, and that this class strictly contains the class of probabilistic straightforward mechanism designed by Gibbard.     

Membership size in the educable cooperative facing uncertain demand

This article explicitly incorporates layoff and hiring costs into a discretetime dynamic model with stationary demand uncertainty, in which managers in a cooperative learn something about the demand process over time, and anticipate learning something about that process. It is shown how the opportunity to learn affects initial membership size and how the knowledge gained induces changes in membership, as well as how risk preferences impact on membership size at any point in time.