The Method of Majority Decision: The Necessary and Sufficient Conditions for Transitivity and Quasi-Transitivity

Abstract

This paper establishes the necessary and sufficient conditions for transitivity and quasi-transitivity under the method of majority decision. The terms 'necessary' and 'sufficient' here are used in the sense of logic, and not in the sense of usage common in the restricted domain literature. These necessary and sufficient conditions enable derivation of all existing theorems pertaining to transitivity and quasi-transitivity under the method of majority decision very simply, almost trivially.