Construction of voting situations concordant with ranking patterns. (English) Zbl 1519.91097
This paper considers the context of voting theory based on a family of possible elections with a fixed set of voters and a fixed set of potential candidates. Attention is focused on the concept of voting situation \(q\)-concordant with a ranking pattern. The concept of ranking pattern \(p\)-concordant with probability models for non-negative random variables is also explored. Results concerning with existence and construction and with cardinalities of the related voters’ populations are obtained. New proofs are obtained of the possibility of observing any arbitrary set of elections’ outcomes. Information about the number of voters needed to construct concordant voting situations is provided. The analysis distinguishes between the two cases of weak and strict ranking patterns. For strict ranking patterns, the solutions can be presented in closed forms.
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