Pierre Bardier | Searcharxiv

arXiv2025

The probability of satisfying axioms: a non-binary perspective on economic design

We provide a formal framework accounting for a widespread idea in the theory of economic design: analytically established incompatibilities between given axioms should be qualified by the likelihood of their violation. We define the degree to which rules satisfy an axiom, as well as several axioms, on the basis of a probability measure over the inputs of the rules. Armed with this notion of degree, we propose and characterize i) a criterion to evaluate and compare rules given a set of axioms, allowing the importance of each combination of axioms to differ, and ii) a criterion to measure the compatibility between given axioms, building on a analogy with cooperative game theory.

econ.TH↗

arXiv2024

Hoping for the best while preparing for the worst in the face of uncertainty

We propose and axiomatize a new model of incomplete preferences under uncertainty, hope-and-prepare preferences: one act is preferred to another if and only if both its optimistic evaluation -- the welfare level attained in the best-case scenario-- and its pessimistic evaluation --the welfare level attained in the worst-case scenario-- rank it above the other. Both evaluations are computed over sets of probability distributions. We make the case that, compared to existing incomplete criteria under ambiguity, hope-and-prepare preferences address the trade-off between conviction and decisiveness in a new way, which is more favorable to decisiveness. We characterize a completion of an incomplete hope-and-prepare preference relation admitting an (asymmetric) $\alpha$-\textit{maxmin expected utility} representation, in which $\alpha$ is unique. Conversely, given a standard $\alpha$-MEU preference and a fixed value of $\alpha$, we recover the concordant hope-and-prepare preference that it completes.

econ.TH↗