Basic Geometry of Voting

by Donald G. Saari

Amazingly, the complexities of voting theory can be explained and resolved with comfortable geometry. A geometry which unifies such seemingly disparate topics as manipulation, monotonicity, and even the apportionment issues of the US Supreme Court. Although directed mainly toward students and others wishing to learn about voting, experts will discover here many previously unpublished results. As an example, a new profile decomposition quickly resolves the age-old controversies of Condorcet and Borda, demonstrates that the rankings of pairwise and other methods differ because they rely on different information, casts serious doubt on the reliability of a Condorcet winner as a standard for the field, makes the famous Arrow's Theorem predictable, and simplifies the construction of examples.

Genres: Mathematics

312 pages, Paperback

First published September 18, 1995

Reviews

[Joshua]

Provides an excellent introduction to the topic of election systems and how to approach them from an axiomatic system. Has many simple examples to illustrate complex concepts and helps prepare the reader for further work on the subject.

[Evan Dower]

The author has a different definition of "basic geometry" than I do. This is grad-school stuff, and thus pretty difficult to follow. I did finish it, and I did get some things out of it, but mostly I'm just glad it's over. I have other voting-related books, and hopefully I'll be able recommend one of them, but I can't recommend this one.