Egalitarianism in the rank aggregation problem: a new dimension for democracy

Abstract

Winner selection by majority, in elections between two candidates, is the only rule compatible with democratic principles. Instead, when candidates are three or more and voters rank candidates in order of preference, there are no univocal criteria for the selection of the winning (consensus) ranking and the outcome is known to depend sensibly on the adopted rule. Building upon eighteenth century Condorcet theory, whose idea was max- imising total voter satisfaction, we propose here a new basic principle (dimension) to guide the selection: satisfaction should be distributed among voters as equally as possible. With this new criterion we identify an optimal set of rankings, ranging from the Condorcet solution to the the most egalitarian one with respect to the voters. Most importantly, we show that highly egalitarian rankings are much more robust, with respect to random fluctuations in the votes, than consensus rankings returned by classical voting rules (Copeland, Tideman, Schulze). The newly introduced dimension provides, when used together with that of Condorcet, a more informative classification of all the possible rankings. By increasing awareness in selecting a consensus ranking our method may lead to social choices which are more egalitarian compared to those achieved by presently available voting systems.