A geometric examination of Kemeny's rule

By using geometry, a fairly complete analysis of Kemeny's rule (KR) is obtained. It is shown that the Borda Count (BC) always ranks the KR winner above the KR loser, and, conversely, KR always ranks the BC winner above the BC loser. Such KR relationships fail to hold for other positional methods. The geometric reasons why KR enjoys remarkably consistent election rankings as candidates are added or dropped are explained. The power of this KR consistency is demonstrated by comparing KR and BC outcomes. But KR's consistency carries a heavy cost; it requires KR to partially dismiss the crucial "individual rationality of voters" assumption. <!--ID="" Saari's research is supported by a Pancoe Professorship and NSF grant DMI-9971794. When we started this work, Merlin was visiting The Center for Political Economy at Washington University (Fall, 1996); he thanks his host N. Schofield. We thank M. Le Breton for his conversations about Kemeny's rule.-->