Global independence of irrelevant alternatives, state-salient decision rules and the strict Condorcet choice function

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.