Construction of voting situations concordant with ranking patterns

Abstract

AbstractReferring to a standard context of voting theory, and to the classic notion of voting situation, here we show that it is possible to observe any arbitrary set of elections’ outcomes, no matter how paradoxical it may appear. In this respect, we consider a set of candidates $$1, 2, \ldots , m $$ 1 , 2 , … , m and, for any subset A of $$\{1, 2, \ldots , m \}$$ { 1 , 2 , … , m } , we fix a ranking among the candidates belonging to A. We wonder whether it is possible to find a population of voters whose preferences, expressed according to the Condorcet’s proposal, give rise to that family of rankings. We will show that, whatever be such family, a population of voters can be constructed that realize all the rankings of it. Our conclusions are similar to those coming from D. Saari’s results. Our results are, however, constructive and allow for the study of quantitative aspects of the wanted voters’ populations.