How Many Alternatives? Partitions Pose Problems for Predictions and Diagnoses

Abstract

This paper focuses on one matter that poses a problem for both human judges and standard probability frameworks, namely the assumption of a unique (privileged) and complete partition of the state‐space of possible events. This is tantamount to assuming that we know all possible outcomes or alternatives in advance of making a decision, but it is clear that there are many practical situations in prediction, diagnosis, and decision‐making where such partitions are contestable and/or incomplete. The paper begins by surveying the impact of partitions on the choice of priors in formal probabilistic updating frameworks, and on human subjective probability judgements. That material is followed by an overview of strategies for dealing with partition dependence, including considerations of how a rational agent’s preferences may determine the choice of a partition.

Keywords:

• Probability
• Partition
• Sample Space
• Uncertainty
• Judgement Under Uncertainty
• Decision‐making Under Uncertainty