A correspondence between voting procedures and stochastic orderings

In voting theory, two different settings are commonplace: either voters express a preference ordering on the set of candidates or they express an individual evaluation of each candidate. In either case, the aim may be to obtain a global ranking of the candidates and, in particular, to determine the winner of the election. We introduce a probabilistic framework that allows us to explore a correspondence between some usual voting procedures based on either preference orderings (e.g. the Borda count and the Condorcet procedure) or individual evaluations (e.g. the Borda majority count and the majority judgment) and some classical stochastic orderings (e.g. comparison of expected values, comparison of medians and statistical preference). We also consider a recently-introduced multivariate stochastic ordering, called probabilistic preference, and show its connection with the plurality and veto procedures.