Bøger af Donald G. Saari

We decide by elections, but do we elect who the voters really want? The answer, as we have learned over the last two centuries, is 'not necessarily'. What a negative, frightening assertion about a principal tool of democracy! This negativism has been supported by two hundred years of published results showing how bad the situation can be. This expository, largely non-technical book is the first to find positive results showing that the situation is not anywhere as dire and negative as we have been led to believe. Instead there are surprisingly simple explanations for the negative assertions, and positive conclusions can be obtained.

This textbook invites the reader to develop a holistic grounding in mathematical finance, where concepts and intuition play as important a role as powerful mathematical tools.

Instead, we now know that when different tallying methods are applied to the same ballots, radically different outcomes can emerge, that most procedures can select the candidate, the voters view as being inferior, and that some commonly used methods have the disturbing anomaly that a winning candidate can lose after receiving added support.

Dieses Buch beschaftigt sich mit Abstimmungsregeln bei Mehrpersonenentscheidungen. Es wird eine geometrische Theorie entwickelt, die zahlreiche neue Ergebnisse enthalt und neue Einsichten in ein Gebiet bietet, das in der Wirtschafts-, Sozial- und Politikwissenschaft von grosser Bedeutung ist.

Shows that the fundamental problems with the 2000 presidential election are not with the courts, recounts or defective ballots, but are caused by the way Americans vote for president. This book shows how mathematics can help to identify and characterize a large number of paradoxical situations that result from the choice of a voting procedure.