Preference densities and social choices

We discuss a ranking method that allows social pairwise rankings of alternatives to depend on more than just individuals’ pairwise rankings. This violates Arrow’s Independence of Irrelevant Alternatives, but allows Borda’s rank-order counting, which provides a limited accounting for individual preference intensities. We capture Arrow’s rules (i.e., with IIA) and Borda’s method as two polar cases, and allow cases in between. Our main result provides the critical line dividing those degrees of intensity, or preference density, that yield positive results from those that yield negative results. We thank two referees for helpful comments.