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.
1. Subtle complexity of social choice; 2. Dethroning dictators; 3. Voting dictionaries; 4. Explaining all voting paradoxes; 5. Deliver us from plurality vote; 6. Appendix.
"Donald G. Saari is a mathematician, economist, systems engineer and astronomer who has brought profound new insights into the theory of voting and social choice. Through his sophisticated methodology based on dynamical systems theory, mechanism design, topology and geometry he has thoroughly invigorated this largely combinatorics and algebra oriented field of research. It is no exaggeration to say that Saari is a leading social choice theorist of our time. The future generations of social choice theorists will certainly find much inspiration and profound insights in this book. For anyone working in the field of voting and social choice the book will provide a rich collection of results, methodological tools and challenging open problems." - Hannu Nurmi, Academy of Finland "Donald Saari provides not only an engaging and accessible explanation of the celebrated dictatorial theorems of Arrow, Sen, and Chichilnisky but also an intuitive argument for why we should not be surprised by the negative results of these seminal theorems. More importantly, Disposing Dictators, Demystifying Voting Paradoxes describes how to obtain positive versions of the theorems. In his usual compelling style, Saari challenges all current and future scholars in social choice to avoid becoming mired in technical difficulties and to strive for similar positive results that will inform and shape the voting procedures in our political and organizational structures." - Tommy Ratliff, Wheaton College "Arrow's theorem is at the origin of the birth of modern social choice theory in the late 1940's and 1950's. Sen's theorem on liberalism and the Pareto principle (published in 1970) created an upsurge of fundamental studies in the so-called non-welfaristic issues in normative economics. Both results are essentially negative (impossibilities). Saari, in this book, demonstrates that we must not overestimate these negative aspects. Particularly noteworthy are the remarkable presentations of the topological approach to social choice and of the generic stability of the core of voting games (including a very short introduction to a new solution concept, the finesse point), where Saari, once again, shows his wonderful pedagogical talent.' - Maurice Salles, University of Caen
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