Construction of aggregation paradoxes through load-sharing models

Abstract

We show that load-sharing models (a very special class of multivariate probability models for nonnegative random variables) can be used to obtain basic results about a multivariate extension of stochastic precedence and related paradoxes. Such results can be applied in several different fields. In particular, applications of them can be developed in the context of paradoxes which arise in voting theory. Also, an application to the notion of probability signature may be of interest, in the field of systems reliability.

Construction of voting situations concordant with ranking patterns

“…In fact, concerning with weak ranking patterns, Theorem 2 leads to a general existence result about p-concordant voting situations (Corollary 1). Such a generalization of the results presented in De Santis and Spizzichino (2023) would not be smooth without the passage through the logic and the language of voting theory.…”

“…The family A (m) is determined by P J . In this respect a detailed formula is shown in Proposition 1 of De Santis and Spizzichino (2023).…”

“…In De Santis and Spizzichino (2023), the definition was given of ranking pattern p-concordant with a multivariate survival model and it has been proven that, for any strict ranking pattern, there exist p-concordant survival models (see Theorem 2 in De Santis and Spizzichino (2023), recalled here as Theorem 7 in "Appendix"). Starting from this result, here we prove the existence of q-concordant voting situations for any (strict or weak) ranking pattern (Theorems 1, 2).…”

“…Section 3 is devoted to presenting results concerning the construction of qconcordant voting situations. By exploiting and extending results presented in De Santis and Spizzichino (2023), we in particular single out a method to construct voting situations concordant with weak ranking patterns, by starting from voting situations concordant with strict ranking patterns (see Theorem 2).…”

“…For the sake of self-consistency, in the Appendix we review definitions and main results on load-sharing models, which have been used in De Santis and Spizzichino (2023) for the construction of survival models p-concordant with strict ranking patterns.…”