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Geometry, voting, and paradoxes. (English) Zbl 1037.91028

The authors first introduce problems that arise in voting among three or more alternatives by comparing plurality, pairwise and Borda results for an example. Concentrating on the case of three alternatives, they describe positional voting methods and their analysis via Saari triangles. After explaining pairwise voting cycles, the authors show how the geometric viewpoint can be used to answer easily many questions involving possible outcomes and, what is more important, their probabilities. The exposition is clear and straightforward and provides an excellent brief intrduction to some of the applications of Saari’s geometrical approach to voting theory.

MSC:

91B12 Voting theory
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