Monotonicity of a profile of rankings with ties

Abstract

A common problem in social choice theory concerns the aggregation of the rankings expressed by several voters. Two different settings are often discussed depending on whether the aggregate is assumed to be a latent true ranking that voters try to identify or a compromise ranking that (partially) satisfies most of the voters. In a previous work, we introduced the notion of monotonicity of a profile of rankings and used it for statistically testing the existence of this latent true ranking. In this paper, we consider different extensions of this property to the case in which voters provide rankings with ties.