Existence and construction of voting situations concordant with ranking patterns

TL;DR

This paper demonstrates that any set of voting outcomes, even paradoxical ones, can be realized by a voting situation, using extended models based on ranking patterns and load-sharing concepts.

Contribution

It extends previous probabilistic models to show the existence and construction of voting situations matching arbitrary outcome patterns.

Findings

Any voting outcome set can be realized in a constructed voting situation.

Extended models connect ranking patterns with voting outcome probabilities.

The approach applies load-sharing models to voting theory.

Abstract

Referring 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. On this purpose we use results, presented in a recent paper of us, that hinge on the concept of ranking pattern concordant with a probability model for non-negative random variables and on a related role of special load-sharing models. Our results here will be obtained by suitably extending those therein, and by converting them into the context of voting.