Subjective probabilities and utility with event-dependent preferences

This article generalizes Savage's theory to include event-dependent preferences. The state space is partitioned into finitely many events. The induced preferences over consequences are assumed independent of the underlying states within, but not across, these events. This results in an additively separable representation of preferences over acts. The dependence of the preference relation over consequences on the events is represented by event-dependent mappings of the set of consequences onto itself. Given these mappings, the preferences on acts are represented by the expectation of event-dependent utilities on the consequences with respect to unique subjective probabilities on the states.Helpful discussions with David Schmeidler are gratefully acknowledged.     

Italian Children's Understanding of War: A Domain-Specific Approach

Studies of children's conceptions of war, which have been carried out up to now mainly by asking for a definition of war and associating it with other notions, have found few age-related changes after the age of 6. Considering the complexity of the concept, and its embeddedness in the political conceptual domain, which emerges at around 11 years, we expect that greater differences should emerge if children's ideas on the causes and consequences of war, and the actors involved, are carefully assessed. Semi-structured interviews carried out with a total of 80 Italian children from 2nd to 8th grades confirmed this hypothesis. Many 2nd graders described war as a clash between collectives without structure, attributing all decisions about starting, the development of, and ending a war to the individual fighters and explaining these decisions (when they did) as due to emotions such as hatred, envy, revenge, or being tired or unwilling to fight any longer. Most 6th and 8th graders depicted war as a clash between nation-states, attributing decisions about its starting and ending to political authorities on the basis of political and economic reasons, and the actual fighting of battles to an organized army collaborating with, or subordinate to, political authorities. Many 2nd and 4th graders also showed a mixed pattern of answers, involving both political authorities and individual fighters, thus showing that the transition from the rudimentary backward conception to the more advanced one occurs through the piecemeal addition and deletion of concepts and beliefs.     

Moral sentiments and social choice

We examine the implications, for social choice, of individuals having an intrinsic sense of fairness. Taking the viewpoint that social justice reflects the moral attitudes of the constituent members, we analyze the effect of the intensity of the individual sense of fairness on the solution of Nash bargaining over random allocation procedures. We use a stylized model of university admission policies to illustrate our approach. We show that even if social policies are ultimately determined by the bargaining power of the different groups, a society whose members have a common notion of fairness tends to implement fairer admission policies when the intensity of the sense of fairness of individual members increases. While working on the research that is summarized in this paper the authors visited several institutions. Edi Karni visited the Berglas School of Economics, Tel Aviv University and GRID, at Ecole Normale Superieur de Cachan. Zvi Safra visited CERMCEM and EUREQua, at the University of Paris I and LIP6, at the University of Paris 6. The hospitality of these institutions is gratefully acknowledged. We are also grateful to the editor and two anonymous referees for their very useful comments and suggestions. Zvi Safra thanks The Israel Science Foudation (grant 1299/05) for its support.     

Unbounded behaviorally consistent stopping rules

In this article we study behaviorally consistent stopping rules in an unbounded search from a known distribution with no recall and with positive search cost. We show that if the searcher's preferences are quasi-convex in the probabilities, then behaviorally consistent search strategies in the unbounded case are obtained as limits of the corresponding bounded search strategies and are characterized by reservation levels property. Unlike optimal stopping rules under expected utility theory, however, the reservation levels may not be monotonically increasing in the number of permissible stages of the search process, and, in the unbounded case, may not be unique.     

David Schmeidler’s contributions to decision theory

Theory and Decision -     

Helping patients and physicians reach individualized medical decisions: theory and application to prenatal diagnostic testing

This paper presents a procedure designed to aid physicians and patients in the process of making medical decisions, and illustrates its implementation to aid pregnant women, who decided to undergo prenatal diagnostic test choose a physician to administer it. The procedure is based on a medical decision-making model of Karni (J Risk Uncertain 39: 1–16, 2009). This model accommodates the possibility that the decision maker’s risk attitudes may vary with her state of health and incorporates other costs, such as pain and inconvenience, associated with alternative treatments. The medical decision problem was chosen for its relative simplicity and the transparency it affords.     

On the Representation of Beliefs by Probabilities

This paper explores two axiomatic structures of subjective expected utility assuming a finite state-space and state-dependent, connected, topological outcome-spaces. Building on the work of Karni and Schmeidler (1981) the analytical framework includes, in addition to the preference relation on acts, introspective preferences on hypothetical lotteries that are linked to the preference relation on acts by consistency axioms. The two models accommodate state-dependent preferences and yield subjective probabilities that correctly represent the decision-maker's beliefs. State-independent preferences are a special case.     

An informationally parsimonious impartial observer theorem

In Harsanyi's impartial observer theorem, an impartial observer determines a social ordering of the lotteries on the set of social alternatives based on a sympathetic but impartial concern for all individuals in society. This ordering is derived from a more primitive ordering on the set of all extended lotteries. An extended lottery is a lottery which determines both the observer's personal identity and the social alternative. We establish a version of Harsanyi's theorem in which the observer is only required to have preferences on the extended lotteries in which there is an equal chance of being any person in society. Received: 19 June 1996 / Accepted: 30 December 1996     

Ambiguity attitudes and social interactions: An experimental investigation

This paper reports the results of experiments testing prevalence of non-neutral ambiguity attitudes and how these attitudes change as a result of interpersonal interactions. To address the first question we conducted experiments involving individual choice between betting on ambiguous and unambiguous events of the subject’s choice. We found that a large majority of subjects display ambiguity neutral attitudes, many others display ambiguity incoherent attitudes, and few subjects display either ambiguity-averse attitudes or ambiguity-seeking attitudes. To address the second question we designed a new experiment with a built-in incentive to persuade. We found that interpersonal interactions without incentives to persuade have no effect on behavior. However, when incentives were introduced, the ambiguity neutral subjects were better able to persuade ambiguity seeking and ambiguity incoherent subjects to adopt ambiguity neutral choice behavior and, to a lesser extent, also ambiguity averse subjects.     

Probabilities and beliefs

Choice-theoretic definitions of subjective probabilities originated with the work of Ramsey and de Finetti and attained their definitive form in the work of Savage. These probabilities are intended to provide a numerical representation of a decision maker's beliefs regarding the likely realization of alternative events. In this article, I argue that the choice-theoretic definitions of subjective probabilities involve a tacit convention—namely, state-independent utility functions—that is not implied by the axioms, and, as a consequence, choice-theoretic subjective probabilities, even when they exist, do not necessarily represent the decision makers' beliefs.