Single-Peakedness

Abstract

Now we know the principle difficulty with the Condorcet winner extension of simple majority voting: sometimes it simply doesn’t work. On the other hand, it often does work. In Chapter 2 it was suggested that simple majority voting will yield a Condorcet winner if there is sufficient “consensus” among the preference orderings of individuals. In this chapter we will try to capture one notion of “consensus” in a property of preference assignments and show this is sufficient to ensure avoidance of a voting paradox.