Global Independence of Irrelevant Alternatives, State-Salient Decision Rules and the Strict Condorcet Choice Function

TL;DR

This paper provides axiomatic characterizations of state-salient decision rules and the strict-Condorcet choice function, highlighting conditions under which these rules are uniquely determined by their properties.

Contribution

It offers a simple proof of a known characterization of state-salient decision rules and introduces a new axiomatic characterization of the strict-Condorcet choice function under specific domain conditions.

Findings

Axiomatic characterization of state-salient decision rules using Weak Dominance and Global Independence.

Axiomatic characterization of the strict-Condorcet choice function with a strict-Condorcet winner.

The characterization fails when extended to profiles with a weak-Condorcet winner.

Abstract

We present a simple proof of a well-known axiomatic characterization of state-salient decision rules, using Weak Dominance Criterion and Global Independence of Irrelevant Alternatives. Subsequently we provide a simple axiomatic characterization of the Strict-Condorcet choice function on the domain of all preference profiles that have a strict-Condorcet winner, assuming that if the first two ranks are occupied by the same two alternatives in all states of nature, then the chosen alternative will be the one from these two that is preferred to the other with probability greater than half-provided such an alternative exists. We also show that this result is not valid if we extend the domain to the set of all preference profiles that have a unique weak-Condorcet winner.