Professor Saari's new book is a refreshing and original insight into the most prevalent theme in the Social Choice literature of the second half of the 20^th century: Voting Paradoxes. The point of the book is that looking for a clear winner may be somewhat of a futile exercise. Such clear, or ‘Condorcet’ winners as they are often referred to in the literature, rarely exit due to what the author calls the ‘Dimensionality Curse:’ once enough voters and enough issues are involved it is difficult and usually unrealistic to expect a Condorcet Winner to emerge. A Condorcet winner is an outcome or a candidate that is preferred by a majority of the decision makers (voters) over any other feasible or available outcome.

The book advances two main themes of significant interest. The first theme is that Social Choice literature tends to overemphasize the importance of Voting Paradoxes: instances in which it is hard to extract a clear preference order of the of collective, out of the preferences of individuals in the collective. The second theme is that we should reassess the use of the Borda Count that has been largely neglected in this line of research. A Borda count is any mechanism used to assign point values to alternatives dependent on how they are ranked by the individual decision makers, be it voters or legislators or any other group of decision makers, rather than by pair wise comparisons of any pair of feasible alternatives. Both themes are not new but are well worth the new and refreshing treatments and the read of the book.

The first chapter is an introduction to the personal histories of Condercet and Borda, the founding fathers of social choice theory. The usefulness of the setup is in squaring Condorcet as the one who got all the attention while Borda should have gotten a lot more of it. That is a fair claim that is later developed in some convincing detail. The second chapter gets a first cut at the two main points of the book: First is the ‘curse of dimensionality’ that is so central to this literature. The second and much less commonly understood is the insightful observation that by looking for the Condorcet winner we overlook much of the information that is available from the preference orders of the decision makers at hand. This is where the Borda Count offers some promise as the Borda Count does register much more of the information embedded in the preference profile of the relevant voters, taking into account their preferences over lower ranked, feasible outcomes. Chapter three discusses the usefulness of voting dictionaries. A neat idea that helps Professor Saari argue for the relative advantage of the Borda count. The whole idea of voting dictionaries is that they allow us to establish what can and cannot be expected of different voting schemes under different conditions and preference profiles. Saari demonstrates the advantage of the Borda count with a couple of theorems that highlight it favorably in comparison to similar and not so similar voting schemes under varying conditions. Chapter four returns to the themes of chapter two, articulating the conditions that lead to many of the voting paradoxes and emphasizing the usefulness that may accrue from giving the Borda Count more attention. Chapter five is a very brief and, unfortunately, incomplete account of how all of this relates to the spatial theory of voting that much of the potential readers of the book would be more familiar with.

The two main themes of the book are well deserving of the attention Professor Saari gives them and the accessibility he offers to the reader. These are two important contributions coupled by a fresh and more nuanced new look that is more balanced and subtle than the prevalent view in the discipline of the origin of the recurrence of these paradoxes and the extent and interpretation of their implications.

The book has three mostly stylish shortcomings. First, while the author repetitively promises to remain accessible and stay away from obscure mathematical notation, the repetitive use of examples with so much detail is as distracting as some very long equations would be. Add the recurrent references to mathematical terms that only mathematicians are familiar with and you get similar barriers of entry to those the author purports to avoid. Second is the ‘Saari factor’. More than a third of the reference list is composed of works authored or co-authored by Saari hmself. This is a field of inquiry that preoccupied social scientists of very diverse persuasions for over two centuries and a balanced account of any problem cannot be offered with such limited references to other leading scholars in the field. Which brings me to the final shortcoming the reader should be aware of and that is the fact that she is being exposed to a very skewed account of the literature on the subject. The book presents its argument as a dichotomy. One can either follow the Condorcet program to cycles and paradoxes or take Borda more seriously and may, under some conditions, get it right. While advancing the Borda alternative deserves Sarri's effort, the last three decades of research have shown some clear promise in other directions as well. Sarri barely mentions the work of some of the leading scholars in the field. Twenty pages of historical detail on the perfectly academic and obviously obscure feud between Borda and Condorcet and not a word of the most influential and directly relevant different directions to deal with the same difficulty that currently dominate the literature. This is an unbalanced representation of the issue that could easily be corrected if only the author, who is certainly aware of the current literature would put himself and made a minimal effort to expose the reader to it. Finally, on a lighter note, the reference to ‘disposing dictators’ in the title, may mislead some to believe that there is anything in the book about authoritarian regimes. There isn't. The reference is to the fact that the term ‘dictator’ is overused in this literature to refer to individual decision makers who may get ‘dictatorial power’ by the voting scheme used or their position in the decision making process. The term is overused in the literature but that does not justify its misleading use in the title of the book.

I strongly recommend the book to those interested in the subject matter, but would also encourage whoever reads the book to immediately complement this read with fair doses of works by Cox, Shepsle, Schofield and the more recent multiple authored series of contributions on the usefulness of the solution concept known as the ‘Uncovered Set,’ for the reader to get a minimally balanced perspective of current literature. Austen-Smith and Banks provide a very useful and comprehensive account of earlier research on the subject. Their important contribution is barely mentioned by Saari as well.