Qualitative Robust Bayesianism and the Likelihood Principle
Conor Mayo‐Wilson, Aditya Saraf · arXiv (Cornell University) · 2020
We argue that the likelihood principle (LP) and weak law of likelihood (LL) generalize naturally to settings in which experimenters are justified only in making comparative, non-numerical judgments of the form $A$ given $B$ is more likely than $C$ given $D$. To do so, we first \emph{formulate} qualitative analogs of those theses. Then, using a framework for qualitative conditional probability, just as the characterizes when all Bayesians (regardless of prior) agree that two pieces of evidence are equivalent, so a qualitative/non-numerical version of LP provides sufficient conditions for agreement among experimenters' whose degrees of belief satisfy only very weak coherence constraints. We prove a similar result for LL. We conclude by discussing the relevance of results to stopping rules.