Hoping for the best while preparing for the worst in the face of uncertainty: a new type of incomplete preferences

TL;DR

This paper introduces hope-and-prepare preferences, a new model of incomplete preferences under uncertainty that balances optimism and pessimism using multiple priors, offering a more decisive decision criterion.

Contribution

It proposes and axiomatizes hope-and-prepare preferences, a novel approach that improves decisiveness in incomplete preference models under ambiguity.

Findings

Addresses trade-off between conviction and decisiveness

Characterizes a unique alpha-maxmin expected utility representation

Provides axiomatic foundation for the new preference model

Abstract

We propose and axiomatize a new model of incomplete preferences under uncertainty, which we call \textit{hope-and-prepare preferences}. An act is considered more desirable than an other act when, and only when, both an optimistic evaluation, computed as the welfare level attained in a best-case scenario, and a pessimistic one, computed as the welfare level attained in a worst-case scenario, rank the former above the latter. Our comparison criterion involves multiple priors, as best and worst cases are determined among 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 also 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.