The No-Spoiler Condition for Choice Correspondences

We show that any choice correspondence which satisfies the weak Pareto criterion and the Majority property must violate the no-spoiler condition. Subsequently we strengthen the weak Pareto criterion. We show that if the number of criteria or individuals or states of nature is odd, then there is no choice correspondence which satisfies this strengthened version of weak Pareto criteria, Majority property and no-loser spoiler condition. However if the number of criteria/individuals/states of nature is even, we need two more properties to ensure the impossibility result. The first of these two properties is top neutrality. The second property is top anonymity.