Basic Geometry of Voting [Paperback]

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directed mainly toward students and others wishing to learn about voting, experts will discover here many previously unpublished results.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.A surprise is how the complexities of voting theory can be explained and resolved with the comfortable geometry of our three-dimensional world. This book is directed toward students and others wishing to learn about voting, experts will discover previously unpublished results. As an example, a new profile decomposition quickly resolves two centuries old controversies of Condorcet and Borda, demonstrates, that the rankings of pairwise and other methods differ because they rely on different information, casts series 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. The geometry unifies seemingly disparate topics as manipulation, monotonicity, and even the apportionment issues of the US Supreme Court.I. From an Election Fable to Election Procedures.- 1.1 An Electoral Fable.- 1.1.1 Time for the Dean.- 1.1.2 The Departmental Election.- 1.1.3 Exercises.- 1.2 The Moral of the Tale.- 1.2.1 The Basic Goal.- 1.2.2 Other Political Issues.- 1.2.3 Strategic Behavior.- 1.2.4 Some Procedures Are Better than Others.- 1.2.5 Exercises.- 1.3 From Aristotle to Fast Eddie.- 1.3.1 Selectil6