Probabilities of consistent election outcomes with majorities based on difference in support

Abstract

Computer simulations are used to evaluate the likelihood of consistent outcomes under the class of majorities based on diference in support. These majorities require certain consensus in collective preferences to declare an alternative as the winner. More precisely, individuals show preference intensities in the unit interval among each pair of alternatives and it is required that the winner alternative obtains a diference in the sum of the intensities with respect to the loser alternative. This diference is a real number located between 0 and the total number of voters. We introduce the values of the required threshold for which majorities based on diference in support lead to transitive and triple-acyclic collective decisions with a probability of 1. Ourresults improve the previous theoretical ones since they require softer thresholds to reach consistent collective decisions.