A new axiomatization for likelihood gambles

TL;DR

This paper introduces a novel axiomatization for preferences over likelihood gambles, allowing decision-making without assuming prior probabilities, inspired by Jensen's axiomatization of probabilistic gambles.

Contribution

It presents a more general axiomatization for likelihood gambles that does not rely on prior probabilities, offering a new perspective on data's role in decision-making under ambiguity.

Findings

Provides a new axiomatization framework for likelihood gambles

Avoids the controversial assumption of prior probabilities in Bayesian methods

Offers insights into decision-making with ambiguous data

Abstract

This paper studies a new and more general axiomatization than one presented previously for preference on likelihood gambles. Likelihood gambles describe actions in a situation where a decision maker knows multiple probabilistic models and a random sample generated from one of those models but does not know prior probability of models. This new axiom system is inspired by Jensen's axiomatization of probabilistic gambles. Our approach provides a new perspective to the role of data in decision making under ambiguity. It avoids one of the most controversial issue of Bayesian methodology namely the assumption of prior probability.