Measuring Inequalities without Linearity in Envy: Choquet Integrals for Symmetric Capacities

The (generalized) Gini indices rely on the social welfare function of a decision maker who behaves in accordance with Yaari's model, with a function f that transforms frequencies. This SWF can also be represented as the weighted sum of the welfare of all the possible coalitions in the society, where the welfare of a coalition is defined as the income of the worst-off member of that coalition. We provide a set of axioms (Ak) and prove that the three following statements are equivalent: (i) the decision maker respects (Ak), (ii) f is a polynomial of degree k, (iii) the weight of all coalitions with more than k members is equal to zero. Journal of Economic Literature Classification Number: D63.     

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.     

Persuasion,binary choice,and the costs of dishonesty

We study the strategic interaction between a decision maker who needs to take a binary decision but is uncertain about relevant facts and an informed expert who can send a message to the decision maker but has a preference over the decision. We show that the probability that the expert can persuade the decision maker to take the expert’s preferred decision is a hump-shaped function of his costs of sending dishonest messages.     

Subjective random discounting and intertemporal choice

This paper provides an axiomatic foundation for a particular type of preference shock model called the random discounting representation where a decision maker believes that her discount factors change randomly over time. For this purpose, we formulate an infinite horizon extension of [E. Dekel, B. Lipman, A. Rustichini, Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934], and identify the behavior that reduces all subjective uncertainties to those about future discount factors. We also show uniqueness of subjective belief about discount factors. Moreover, a behavioral comparison about preference for flexibility characterizes the condition that one's subjective belief second-order stochastically dominates the other. Finally, the resulting model is applied to a consumption-savings problem.     

New product launch: herd seeking or herd preventing?

A decision maker offers a new product to a number of potential adopers. He does not know the value of the product, but adopers receive some private information about it. We study how the decision maker may influence learning among adopers by manipulaing the launch sequence when both the decision maker and adopers can learn about the value of the product from previous adoption decisions. The conditions under which the decision maker prefers a sequential launch to a simultaneous launch depend on adopers?? prior beliefs about the value of the product and adoption costs. We derive the decision maker??s optimal launch sequence and study how it endogenizes informational herding.     

The art of conversation: eliciting information from experts through multi-stage communication

We examine the strategic interaction between an informed expert and an uninformed decision maker, extending the analysis of Crawford and Sobel (Econometrica 50 (1982) 1431). We modify their model to allow for more extensive communication between the two parties and show that face-to-face communication between the expert and the uninformed decision maker followed by a written report from the expert leads to improved information transmission. In (almost) all cases, there exists an equilibrium in our modified model that ex ante Pareto dominates all of the equilibria identified by Crawford and Sobel. This remains true even if the expert's bias is so great that in their model no information would be disclosed.     

Confidence and decision

Many real-life decisions have to be taken on the basis of probability judgements of which the decision maker is not entirely sure. This paper develops a decision rule for taking such decisions, which incorporates the decision makerʼs confidence in his probability judgements according to the following maxim: the larger the stakes involved in a decision, the more confidence is required in a probability judgement for it to play a role in the decision. A formal representation of the decision makerʼs confidence is proposed and used to formulate a family of decision models conforming to this maxim. A natural member of this family is studied in detail. It is structurally simpler than other recent models of decision under uncertainty, which may make it easier to apply to practical decisions, whilst being axiomatically sound, permitting the separation of beliefs and tastes, and allowing comparative statics analysis of attitudes to choosing in the absence of confidence.     

Emotional Temperature,Probabilistic Choice and the Optimal Power of Incentives*

From the time of Plato it has been assumed that emotions cloud rational thinking. Fully rational individuals were supposed to be completely free of emotions. Modern psychological research challenged this paradigm. One of the insights of this research is that though emotions indeed interfere with the ability to evaluate the objective consequences of choices, they also allow the decision maker to feel the difference in utility arising from those choices. In this article, I formalise this intuition by introducing the concept of emotional temperature. I show that there exists a positive optimal emotional temperature, which leads to an irreducible probability of suboptimal choice. I apply the model to characterise the optimal contracts under moral hazard, assuming that the emotional temperature of the decision maker increases when the contract provides more powerful incentives. A more general point the article makes is that a mechanism designer needs to be aware that the mechanism will not only affect incentives but also the degree of rationality of the agents.     

Choosing the two finalists

This paper studies a decision maker who for each choice set selects a subset of (at most) two alternatives. We axiomatize three types of procedures: (i) The top two: the decision maker has in mind an ordering and chooses the two maximal alternatives. (ii) The two extremes: the decision maker has in mind an ordering and chooses the maximal and the minimal alternatives. (iii) The top and the top: the decision maker has in mind two orderings and he chooses the maximal element from each.     

Debates and Decisions: On a Rationale of Argumentation Rules

We view a debate as a mechanism by which an uninformed decision maker (the listener) extracts information from two informed debaters, who hold contradicting positions regarding the right decision. During the debate, the debaters raise arguments and, based on these arguments, the listener reaches a conclusion. Using a simple example, we investigate the mechanism design problem of constructing rules of debate that maximize the probability that the listener reaches the right conclusion, subject to constraints on the form and length of the debate. It is shown that optimal debate rules have the property that the conclusion drawn by the listener is not necessarily the same as the conclusion he would have drawn, had he interpreted the information, revealed to him or her during the debate, literally. The optimal design of debate rules requires that the information elicited from a counterargument depends on the argument it counterargues. We also link our discussion with the pragmatics literature. Journal of Economic Literature Classification Numbers: C72, D78.     

Partial equilibrium approach to the free-rider problem

Groves and others have shown that truthful answers concerning preferences for public goods can be elicited as dominant strategies if appropriate tax-subsidies rules are applied. This paper studies the statistical properties of the total revenues generated by one of the mechanisms with this desirable dominant strategy property. For particular specifications, it is shown that the expected total revenues increase like √N. Further, if these revenues are rebated equally to the individuals in the model, then, although the dominant strategy property no longer obtains, the optimal responses converge to the truth in large economies. As a result, it can be shown that the mechanism with rebates will make the Pareto optimal decision with arbitrarily high probability, provided that the willingness to pay distribution is assumed to be symmetric.     

Robust estimation and control under commitment

In a Markov decision problem with hidden state variables, a decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby as measured by their expected log likelihood ratios (entropies). Sets of martingales represent alternative models. Within a two-player zero-sum game under commitment, a minimizing player chooses a martingale at time 0. Probability distributions that solve distorted filtering problems serve as state variables, much like the posterior in problems without concerns about misspecification. We state conditions under which an equilibrium of the zero-sum game with commitment has a recursive representation that can be cast in terms of two risk-sensitivity operators. We apply our results to a linear quadratic example that makes contact with findings of T. Ba?ar and P. Bernhard [H^∞-Optimal Control and Related Minimax Design Problems, second ed., Birkhauser, Basel, 1995] and P. Whittle [Risk-sensitive Optimal Control, Wiley, New York, 1990].     

Minimax regret with imperfect ex-post knowledge of the state

We consider decision problems under complete ignorance and extend the minimax regret principle to situations where, after taking an action, the decision maker does not necessarily learn the state of the world. For example, if the decision maker only learns what the outcome is, then all she knows is that the actual state is one of the (possibly several) states that yield the observed outcome under the chosen action. We refer to this situation as imperfect ex-post information. We show that, given a choice between more information and less information, the decision maker prefers the latter. We also extend the framework to encompass the possibility of less than the extreme degree of pessimism that characterizes the minimax regret criterion.     

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.     

Veto-based delegation

In a principal-agent model with hidden information and no monetary transfers, I establish the veto-power principle: the principal can implement an optimal outcome through veto-based delegation with a properly chosen default decision. This result demonstrates the exact nature of commitment powers required by the principal: to design the default outcome and to ensure that she has almost no formal control over the agent's decisions.     

Aggregation of multiple prior opinions

Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker?s utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker?s set of priors is precisely all the weighted-averages of priors, where an expert?s prior is taken from her set and the weight vector is taken from Λ; (ii) the decision maker?s valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the experts? valuations.     

The best choice problem under ambiguity

We model and solve best choice problems in the multiple prior framework: An ambiguity averse decision maker aims to choose the best among a fixed number of applicants that appear sequentially in a random order. The agent faces ambiguity about the probability that a candidate—a relatively top applicant—is actually best among all applicants. We show that our model covers the classical secretary problem, but also other interesting classes of problems. We provide a closed form solution of the problem for time-consistent priors using backward induction. As in the classical case, the derived stopping strategy is simple. Ambiguity can lead to substantial differences to the classical threshold rule.     

Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice

We develop a model which reflects the tendency of people to simplify the decision problems they face. The decision maker chooses among alternate strategies only on the basis of the payoff she assesses she would obtain from them, and these assessments do not explicitly take into account her subjective judgements regarding the likelihood of alternate states of the world. At each stage, the decision maker chooses the strategy that she assesses to give the highest payoff. She updates her assessments adaptively. We show that such behavior leads to maxmin choices. We also consider the decision maker who experiences shocks. Journal of Economic Literature Classification Numbers: C7, D8.     

Increases in Risk Aversion

This note gives sufficient conditions for signing the effect of an increase in risk aversion on the optimal level of the choice variable selected by a decision maker under conditions of risk. The results are illustrated with a decision model taken from the theory of insurance demand.