Stochastic same-sidedness in the random voting model

Journal: Social Choice and Welfare

Abstract: Social choice theory is the analysis of combining individual opinions, preferences, and welfares to reach a collective decision. To reach a consensus, the social planner chooses a rule (social choice function) which assigns one outcome from a set of total feasible alternatives for every possible combination of individual preferences over these alternatives. One of the main objectives of the planner is to construct rules that are fair and satisfy other good properties eg. efficiency. 

 This recent publication studies the implications of stochastic same-sidedness (SSS) axiom in the random voting model. At a given preference profile if one agent changes her preference ordering to an adjacent one by swapping two consecutively ranked alternatives, then SSS imposes two restrictions on the lottery selected by a voting rule before and after the swap. First, the sum of probabilities of the alternatives which are ranked strictly higher than the swapped pair should remain the same. Second, the sum of probabilities assigned to the swapped pair should also remain the same. 

The main contribution of the paper is to show that every random social choice function (RSCF) that satisfies efficiency and SSS is a random dictatorship provided that there are two voters or three alternatives. For the case of more than two voters and atleast four alternatives, every RSCF that satisfies efficiency, tops-onlyness and SSS is a random dictatorship.