Load-sharing dependence models and construction of voting situations for any arbitrary ranking schemes

Abstract

In this paper we present a study about minima among random variables, about the context of voting theory, and about paradoxes related with such topics. In the field of reliability theory, the term load-sharing model is commonly used to designate a special type of multivariate survival models. We demonstrate the effectiveness that such dependence models can have also in some other fields, such as those of interest here. Several important, and by now classic, papers have been devoted to single out and to prove general conclusions in the field of voting theory. We reformulate and achieve such conclusions by developing a method of proof, alternative to the existing ones, and completely probabilistic in nature. As main features of this method, we focus attention on ranking schemes associated to m-tuples of non-negative random variables and suitably single out a special subclass of load-sharing models. Then we show that all possible ranking schemes can be conveniently obtained by only considering such a special family of survival models. This result leads to some new insight about the construction of voting situations which give rise to all possible types of voting paradoxes. Our method and related implications will be also illustrated by means of some examples and informative remarks.