Triple-Consistent Social Choice and the Majority Rule

We define generalized (preference) domains D as subsets of the hypercube {− 1, 1 } D , where each of the D coordinates relates to a yes-no issue. Given a finite set of n individuals, a profile assigns each individual to an element of D . We prove that the outcome of issue-wise majority voting ϕ m belongs to D at any profile where ϕ m is well-defined if and only if this is true when ϕ m is applied to any profile involving only 3 elements of D . We call this property triple-consistency. We characterize the class of anonymous issue-wise voting rules that are triple-consistent, and give several interpretations of the result, each being related to a specific collective choice problem.