Frequency Based Analysis of Voting Rules

In a large electorate it is natural to consider voters’ preference profiles as frequency distributions over the set of all possible preferences. We assume coherence in voters’ preferences resulting in accumulation of voters preferences. We show that such distributions can be studied via superpositions of simpler so called unimodal distributions. At these, it is shown that all well-known rules choose the mode as the outcome. We provide a set of sufficient conditions for a rule to have this trait of choosing the mode under unimodal distributions. Further we show that Condorcet consistent rules, Borda rule, plurality rule are robust under tail-perturbations of unimodal distributions.