Plurality, Borda Count and Preference Polarization

The paper uses the profile decomposition method which decomposes a given profile of voters into hypothetical electorates, to explain disagreement between the induced social rank orders of the candidates under plurality and the Borda count. The family of component profiles responsible for such disagreement are shown to possess a socio-economically interesting feature: In each such profile, a specific candidate is first and last ranked by an equal number of voters. A significant weight of such a profile in the decomposition indicates that the profile of real voters are polarized around the specific candidate in question. The paper proposes preference polarization measures based on the weights of these component profiles and discusses a computationally simple way to obtain these weights, for an arbitrary number of candidates, without resorting to complete profile decomposition of a n!-dimensional vector. The results are potentially useful to measure preference polarization in a field of many candidates.