Thibault Gajdos

Unequal Uncertainties and Uncertain Inequalities: An Axiomatic Approach

In this paper, we provide an axiomatic characterization of social welfare functions for uncertain incomes. Our most general result is that a small number of reasonable assumptions regarding welfare orderings under uncertainty rule out pure ex ante as well as pure ex post evaluations. Any social welfare function that satisfies these axioms should lie strictly between the ex ante and the ex post evaluations of income distributions. We also provide an axiomatic characterization of the weighted average of the minimum and the maximum of ex post and the ex ante evaluations.

Representation and aggregation of preferences under uncertainty

We axiomatize in the Anscombe–Aumann setting a wide class of preferences called rank-dependent additive preferences that includes most known models of decision under uncertainty as well as state dependent versions of these models. We prove that aggregation is possible and necessarily linear if and only if (societys) preferences are uncertainty neutral. The latter means that society cannot have a non-neutral attitude toward uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate multiple prior agents, even when they all have the same set of priors. A number of ways to restore the possibility of aggregation are then discussed.

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 Yaaris 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 withmore than k members is equal to zero.

Decisions with conflicting and imprecise information

When facing situations involving uncertainty, experts might provide imprecise and conflicting opinions. Recent experiments have shown that decision makers display aversion towards both disagreement among experts and imprecision of information. We provide an axiomatic foundation for a decision criterion that allows one to distinguish on a behavioral basis the decision maker’s attitude towards imprecision and disagreement. This criterion accommodates patterns of preferences observed in experiments that are precluded by two-steps procedures, where information is first aggregated, and then used by the decision maker. This might be seen as an argument for having experts transmitting a more detailed information to the decision maker.

Social rationality, separability, and equity under uncertainty

Harsanyi (1955) proved that, in the context of uncertainty, social rationality and the Pareto principle impose severe constraints on the degree of priority for the worst-off that can be adopted in the social evaluation. Since then, the literature has hesitated between an ex ante approach that relaxes rationality (Diamond, 1967) and an ex post approach that fails the Pareto principle (Hammond, 1983; Broome, 1991). The Hammond–Broome ex post approach conveniently retains the separable form of utilitarianism but does not make it explicit how to give priority to the worst-off, and how much disrespect of individual preferences this implies. Fleurbaey (2010) studies how to incorporate a priority for the worst-off in an explicit formulation, but leaves aside the issue of ex ante equity in lotteries, retaining a restrictive form of consequentialism. We extend the analysis to a framework allowing for ex ante equity considerations to play a role in the ex post evaluation, and find a richer configuration of possible criteria. But the general outlook of the Harsanyian dilemma is confirmed in this more general setting.

Confidence measurement in the light of signal detection theory

We compare three alternative methods for eliciting retrospective confidence in the context of a simple perceptual task: the Simple Confidence Rating (a direct report on a numerical scale), the Quadratic Scoring Rule (a post-wagering procedure), and the Matching Probability (MP; a generalization of the no-loss gambling method). We systematically compare the results obtained with these three rules to the theoretical confidence levels that can be inferred from performance in the perceptual task using Signal Detection Theory (SDT). We find that the MP provides better results in that respect. We conclude that MP is particularly well suited for studies of confidence that use SDT as a theoretical framework.

Single crossing Lorenz curves and inequality comparisons

Since the order generated by the Lorenz criterion is partial, it is a natural question to wonder how to extend this order. Most of the literature that is concerned with that question focuses on local changes in the income distribution. We follow a different approach, and define uniform

Metacognition about the past and future: quantifying common and distinct influences on prospective and retrospective judgments of self-performance

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Revealing subthreshold motor contributions to perceptual confidence

-spreads, which are global changes in the income distribution. We give necessary and sufficient conditions for an Expected Utility or Rank-Dependent Expected Utility maximizer to respect the principle of transfers and to be favorable to uniform

ELF: A new measure of response capture

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