A new axiomatization for likelihood gambles
This work addresses foundational issues in decision theory for researchers and practitioners dealing with ambiguous probabilistic models, though it appears incremental as it builds on existing axiomatizations.
The paper tackles the problem of decision making under ambiguity by proposing a new axiomatization for likelihood gambles, which avoids the controversial assumption of prior probabilities in Bayesian methods, providing a new perspective on the role of data.
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.