[UTMD-010] An Axiomatic Approach to Failures in Contingent Reasoning(by Masaki Miyashita, Yuta Nakamura)


Masaki Miyashita, Yuta Nakamura


In this paper, we study incomplete preferences with optimism and pessimism (IPOP) over Anscombe-Aumann acts, a class of preference orders that may fail axioms that require the decision-maker (DM) to think contingently. The main result axiomatizes a preference order ≿ represented by the following rule:
for any distinct acts f and g. Here u is a utility function over outcomes, and C♯ and C♭ are non-disjoint sets of beliefs over states of the world. This representation can be interpreted as capturing the DM’s conservative attitudes toward uncertainty: An act f is deemed superior to another act g if the pessimistic expected utility of f is greater than the optimistic expected utility of g. The representation reduces to a standard SEU preference when belief sets are minimal. Conversely, when belief sets are maximal, the representation encapsulates obvious dominance, the decision rule introduced by Li (2017).