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

Author

Masaki Miyashita, Yuta Nakamura

Abstract

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).

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