Frequency based analysis of collective aggregation rules

Abstract

A new property for collective aggregation rules called positive discrimination is introduced. This property is satisfied by many anonymous and neutral collective aggregation rules. We discuss unimodal profiles (or distributions) for which this property on its own determines the outcome as the mode of a unimodal distribution. We investigate relaxations of this unimodal distribution condition and show that the Condorcet consistent rules as well as the Borda rule and the plurality rule have the mode as the outcome at such profiles. Further, we show, by an example, how the addition of unimodal profiles and the property of positive discrimination can help to determine an outcome in the case of a large number of voters.