Induced Preferences, Nonadditive Beliefs, and Multiple Priors

We study a decision maker who follows the Savage axioms. We show that if he or she is able to take unobservable actions that influence the probabilities of outcomes, then it can appear to an outsider as if his or her subjective probabilities are nonadditive. Implications for multiperiod decision are explored. We extend the model to include a second individual who is also able to take a hidden action. We show that this may induce uncertainty-averse preferences over some class of acts, even if the second individual acts to help the decision maker with high probability.     

Coping with ignorance: unforeseen contingencies and non-additive uncertainty

Summary. In real-life decision problems, decision makers are never provided with the necessary background structure: the set of states of the world, the outcome space, the set of actions. They have to devise all these by themselves. I model the (static) choice problem of a decision maker (DM) who is aware that her perception of the decision problem is too coarse, as for instance when there might be unforeseen contingencies. I make a “bounded rationality' assumption on the way the DM deals with this difficulty, and then I show that imposing standard subjective expected utility axioms on her preferences only implies that they can be represented by a (generalized) expectation with respect to a non-additive measure, called a belief function. However, the axioms do have strong implications for how the DM copes with the type of ignorance described above. Finally, I show that some decision rules that have been studied in the literature can be obtained as a special case of the model presented here (though they have to be interpreted differently). Received: December 16, 1999; revised version: March 22, 2000     

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.     

The measurement of income mobility: A partial ordering approach

Summary. Given a set of longitudinal data pertaining to two populations, a question of interest is the following: Which population has experienced a greater extent of income mobility? The aim of the present paper is to develop a systematic way of answering this question. We first put forth four axioms for income movement-mobility indices, and show that a familiar class of measures is characterized by these axioms. An unambiguous (partial) ordering is then defined as the intersection of the (complete) orderings induced by the mobility measures which belong to the characterized class; a transformation of income distributions is “more mobile” than another if, and only if, the former is ranked higher than the latter for all mobility measures which satisfy our axioms. Unfortunately, our mobility ordering depends on a parameter, and therefore, it is not readily apparent how one can apply it to panel data directly. In the second part of the paper, therefore, we derive several sets of parameter-free necessary and sufficient conditions which allow one to use the proposed mobility ordering in making unambiguous income mobility comparisons in practice. Received: July 12, 1995; revised version: May 13, 1997     

Subjective recursive expected utility

We axiomatize a subjective version of the recursive expected utility model. This development extends the seminal results of Kreps and Porteus (Econometrica 46:185–200 (1978)) to a subjective framework and provides foundations that are easy to relate to axioms familiar from timeless models of decision making under uncertainty. Our analysis also clarifies what is needed in going from a represention that applies within a single filtration to an across filtration representation.Part of this research was conducted when Ozdenoren visited MEDS in Fall 2003. We thank Tapas Kundu, Costis Skiadas, Jean-Marc Tallon and Tan Wang for helpful discussions and also thank audiences at Koc University, Northwestern University, the CERMSEM conference “ Mathematical Models in Decision Theory” at Universite Paris I, and the FUR XI conference on foundations and applications of utility, risk and decision theory     

A behavioral characterization of plausible priors

Recent decision theories represent ambiguity via multiple priors, interpreted as alternative probabilistic models of the relevant uncertainty. This paper provides a robust behavioral foundation for this interpretation. A prior P is “plausible” if preferences over some subset of acts admit an expected utility representation with prior P, but not with any other prior Q≠P. Under suitable axioms, plausible priors can be elicited from preferences, and fully characterize them; also, probabilistic sophistication implies that there exists only one plausible prior; finally, “plausible posteriors” can be derived via Bayesian updating. Several familiar decision models are consistent with the proposed axioms.     

Certainty Independence and the Separation of Utility and Beliefs

Economists often operate under an implicit assumption that the tastes of a decision maker are quite stable, while his beliefs change with the availability of new information. We show that for a general class of preferences, a separation of a key component of tastes, the utility function, from the other components of the representation is possible only if the decision maker's preferences satisfy a mild but not completely innocuous condition, called ‘certainty independence’. We also outline the axiomatic characterization of the preferences that obtain such separation, which are a subset of the biseparable preferences.     

Subjective ambiguity, expected utility and Choquet expected utility

Summary. Using the Savage set up, this paper provides a simple axiomatization of the Choquet Expected Utility model where the capacity is an inner measure. Two attractive features of the model are its specificity and the transparency of its axioms. The key axiom states that the decision-maker uses unambiguous acts to approximate ambiguous ones. In addition, the notion of ‘ambiguity’ is subjective and derived from preferences. Received: March 23, 2000; revised version: April 24, 2001     

Multiple solutions under quasi-exponential discounting

Infinite horizon dynamic optimization problems with non-exponential time preferences may not only exhibit time inconsistency but may also have multiple solutions with distinct payoffs. We here show that such multiplicity is generic in the sense that it occurs in an open set of such decision problems, even with small state- and action-spaces. Non-exponential discounting allows for an “addictive” equilibrium alongside a “virtuous” equilibrium. We also provide a sufficient condition for uniqueness in infinitely repeated decision problems with general action spaces. Authors thank Philippe Jehiel, Maria Saez-Marti and Bill Sandholm for comments to an earlier version, and the Knut and Alice Wallenberg Research Foundation for financial support.     

Differentiating ambiguity and ambiguity attitude

The objective of this paper is to show how ambiguity, and a decision maker (DM)'s response to it, can be modelled formally in the context of a general decision model. We introduce a relation derived from the DM's preferences, called “unambiguous preference”, and show that it can be represented by a set of probabilities. We provide such set with a simple differential characterization, and argue that it is a behavioral representation of the “ambiguity” that the DM may perceive. Given such revealed ambiguity, we provide a representation of ambiguity attitudes. We also characterize axiomatically a special case of our decision model, the “α-maxmin” expected utility model.     

COMMITTEES AS SUBSTITUTES FOR COMMITMENT*

In this article, policies are negotiated in a committee by playing a dynamic voting game with an endogenous default (or status quo) policy. I show that joining a committee by maintaining a strong agenda setting power is a way for a decision maker to commit to a policy that in absence of committees is not time consistent. The disciplinary role of the endogenous status quo and the heterogeneity of preferences within the committee are two crucial ingredients to obtain this result. As a motivating example, this article focuses on the time consistency of monetary policy.     

Consistent probability attitudes

In this paper, the principle of meaningful measurement of probabilistic attitudes is revisited. A new principle of consistency in probability attitudes is proposed, which allows for the identification of decision weights completely separate from utility. In the familiar and elegant von Neuman–Morgenstern setup of decision under risk with given objective probabilities, it is shown that, in the presence of standard properties for preferences, adding the new consistency principle leads to rank-dependent utility.     

Cognitive constraints, contraction consistency, and the satisficing criterion

A theory of decision making is proposed that offers an axiomatic basis for the notion of “satisficing” postulated by Herbert Simon. The theory relaxes the standard assumption that the decision maker always fully perceives his preferences among the available alternatives, requiring instead that his ability to perceive any given preference be decreasing with respect to the complexity of the choice problem at hand. When complexity is aligned with set inclusion, this exercise is shown to be equivalent to abandoning the contraction consistency axiom of classical choice theory.     

Nest-monotonic two-stage acts and exponential probability capacities

This paper examines conditions for Choquet expected utility (CEU) to satisfy both the reduction of two-stage acts and the recursion axioms, which are taken for granted in economics. A key idea of this paper is to consider nest-monotonic two-stage acts, which share their rankings of states with those of their reduced one-stage acts. Our main theorem shows that the axioms, one of which is restricted to nest-monotonic two-stage acts, and consequentialism are satisfied if and only if the preference is exponential CEU, which is such that the probability capacity is an exponential transformation of a probability measure. This result indicates that within a specified range of decision problems, exponential CEU is the only form of CEU that derives indifference to the timing of information resolution. Furthermore, the relation between first- and second-stage exponential CEU is characterized both by the f*-Bayesian updating rule and by comonotonic dynamic consistency. Conditions to establish the law of iterated expectation for CEU are also discussed.     

On the Composition of Committees

This article is concerned with the role of committees in collectivedecision making processes in a world where agents must be motivatedto collect information. Committees improve the quality of decisionmaking by providing information and by coordinating the collectionof information. We address two types of questions. First, howdoes the composition of a committee affect final decisions?Second, what is the optimal composition of a committee fromthe decision maker's point of view? As to the latter question,we show that the cost of information collection plays an importantrole. If this cost is low, then the preferences of the committeemembers should be aligned to those of the decision maker. Memberswith similar preferences as the decision maker collect the properpieces of information. Moreover, manipulation of informationdoes not occur if the preferences of the decision maker andthe members are consonant. If the cost of searching is high,then the committee should be composed of members with polarizedpreferences. Outliers have a strong incentive to search forinformation.     

Individual sense of fairness: an experimental study

Many prior studies have identified that subjects in experiments demonstrate preferences for fair allocations. We present an experimental study designed to test whether a similar concern for fairness manifests itself when the decision maker is choosing among differing probabilistic allocation mechanisms that will all generate an ex post unfair allocation by assigning an indivisible prize to one individual. This investigation is inspired by Karni and Safra (Econometrica, 70, 263–284, 2002 ) in which a structure for preferences for fairness in such an environment was developed. Here we use this model to design experiments that allow us to test for the presence of concern for fairness in individual choice behavior and examine some factors that may affect the intensity of the concern for fairness.

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Potentializability and consistency for multi-choice solutions

The paper introduces and discusses several characterizations of the multi-choice Shapley value (introduced by Nouweland et al. in ZOR-Math Methods Oper Res 41:289–311, 1995), on the domain of multi-choice games. These characterizations generalize the potential approach and results of Calvo and Santos (Math Soc Sci 34:175–190, 1997) into this domain, and the relations are treated with the axiomatic approach in Calvo and Santos (Math Soc Sci 40:341–354, 2000). Also, based on the axioms of two-person standardness and consistency, we offer an axiomatization of the multi-choice Shapley value. The authors are grateful to Professor Sjaak Hurkens and the anonymous referees for very helpful suggestions and comments.     

Social orderings for the assignment of indivisible objects

In the assignment problem of indivisible objects with money, we study social ordering functions which satisfy the requirement that social orderings should be independent of changes in preferences over infeasible bundles. We combine this axiom with efficiency, consistency and equity axioms. Our result is that the only social ordering function satisfying those axioms is the leximin function in money utility.     

Dynamic consistency for non-expected utility preferences

This paper considers a generalization of the Savage framework in which there are two state spaces as follows: one to model events and one to define acts. The distinction between these two spaces typically induces non-consequentialist motives. The dynamic derivation of the Sure Thing Principle is studied in this framework. When these two spaces are substantially different, there exists a class of preferences that satisfy dynamic consistency and, at the same time, rationalize violations of the Sure Thing Principle. Consequently, it is possible to use non-expected utility preferences to study problems with dynamic consistency, as long as preferences belong to the previous class and as long as problems refer to information structures, defined as partitions over the set that serves to model events.     

Subjective probability over a subjective decision tree

A state space has been assumed as a primitive for modeling uncertainty, which presumes that the analyst knows all the uncertainties a decision maker (DM) perceives. This is problematic because states are private information of the DM, and hence are not directly observable to the analyst. Dekel et al. [Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934] derive, rather than assume, the subjective state space from preference over suitable choice objects.In a dynamic setting, a decision tree, that is, a pair consisting of a state space and a filtration, has been taken as a primitive. This assumption is also problematic—a decision tree should be derived rather than assumed as a primitive. We formulate a three-stage extension of the above literature in order to model a DM who anticipates subjective uncertainty to be resolved gradually over time. We identify also subjective beliefs on the subjective state space.