Comparison of Vector Voting Rules and Their Relation to Simple Majority Voting

Abstract

Introduced here are examples of what we call “vector voting rules” : social preference orderings deduced from vectors naturally associated with the group preference matrix. These include higher-order Borda Rules , B p , p = 1, 2, ..., and the Perron Rule (P). We study the properties of these transitive rules and compare them with Simple Majority Voting (SMV). Even when SMV is transitive, it can yield results different from B 1 , B 2 , ... and P, and through simulation, we compile statistics about how often these differ. We also give a new condition ( 2/3+ majorities ) that is (just) sufficient for SMV to be transitive and then quantify the frequency of transitivity for graded failures of this hypothesis.