The literature on the theory of social choice has grown considerably beyond the few items in existence at the time the first edition of this book appeared in 1951. Some of the new literature has dealt with the technical, mathematical aspects, more with the interpretive. My own thinking has also evolved somewhat, although I remain far from satisfied with present formulations. The exhaustion of the first edition provides a convenient time for a selective and personal stocktaking in the form of (...) an appended commentary entitled, 'Notes on the Theory of Social Choice, 1963, ' containing reflections on the text and its omissions and on some of the more recent literature. This form has seemed more appropriate than a revision of the original text, which has to some extent acquired a life of its own. (shrink)

Philip Pettit (2001) has suggested that there are parallels between his republican account of freedom and Amartya Sen's (1970) account of freedom as decisive preference. In this paper, I discuss these parallels from a social-choice-theoretic perspective. I sketch a formalization of republican freedom and argue that republican freedom is formally very similar to freedom as defined in Sen's “minimal liberalism” condition. In consequence, the republican account of freedom is vulnerable to a version of Sen's liberal paradox, an inconsistency between universal (...) domain, freedom, and the weak Pareto principle. I argue that some standard escape routes from the liberal paradox – those via domain restriction – are not easily available to the republican. I suggest that republicans need to take seriously the challenge of the impossibility of a Paretian republican. Footnotes1 I am grateful to Luc Bovens, Geoffrey Brennan, Keith Dowding, Philip Pettit, and Wlodek Rabinowicz for very helpful comments and discussion. (shrink)

Sen's Liberal Paradox has received a good deal of attention in the literature. However, it is worth re-opening the discussion since the solutions offered so far have serious problems and since there is more to say about the nature of the problem displayed by the Liberal Paradox. I propose a new solution to the paradox in the following sense: First, I argue that its range of applicability is not very broad. Second, there is nothing paradoxical about a conflict of the (...) principles involved in the Liberal Paradox. (Nagel's thesis of the ``fragmentation of value'' is important to make this point.) Third, I make a recommendation about how to remove conflicts when they occur in a restricted class of cases. For the other cases, no recommendation of similar appeal is available. But in the light of the first point, the availability of a generally applicable recommendation was not to be expected. (shrink)

It is not uncommon to be frustrated by the outcome of an election or a decision in voting, law, economics, engineering, and other fields. Does this 'bad' result reflect poor data or poorly informed voters? Or does the disturbing conclusion reflect the choice of the decision/election procedure? Nobel Laureate Kenneth Arrow's famed theorem has been interpreted to mean 'no decision procedure is without flaws'. Similarly, Nobel Laureate Amartya Sen dashes hope for individual liberties by showing their incompatibility with societal needs. (...) This highly accessible book offers a new, different interpretation and resolution of Arrow's and Sen's theorems. Using simple mathematics, it shows that these negative conclusions arise because, in each case, some of their assumptions negate other crucial assumptions. Once this is understood, not only do the conclusions become expected, but a wide class of other phenomena can also be anticipated. (shrink)

The purpose of this article is to introduce a Cartesian product structure into the social choice theoretical framework and to examine if new possibility results to Gibbard’s and Sen’s paradoxes can be developed thanks to it. We believe that a Cartesian product structure is a pertinent way to describe individual rights in the social choice theory since it discriminates the personal features comprised in each social state. First we define some conceptual and formal tools related to the Cartesian product structure. (...) We then apply these notions to Gibbard’s paradox and to Sen’s impossibility of a Paretian liberal. Finally we compare the advantages of our approach to other solutions proposed in the literature for both impossibility theorems. (shrink)

Many studies have considered the probability that a pairwise majority rule (PMR) winner exists for three candidate elections. The absence of a PMR winner indicates an occurrence of Condorcet's Paradox for three candidate elections. This paper summarizes work that has been done in this area with the assumptions of: Impartial Culture, Impartial Anonymous Culture, Maximal Culture, Dual Culture and Uniform Culture. Results are included for the likelihood that there is a strong winner by PMR, a weak winner by PMR, and (...) the probability that a specific candidate is among the winners by PMR. Closed form representations are developed for some of these probabilities for Impartial Anonymous Culture and for Maximal Culture. Consistent results are obtained for all cultures. In particular, very different behaviors are observed for odd and even numbers of voters. The limiting probabilities as the number of voters increases are reached very quickly for odd numbers of voters, and quite slowly for even numbers of voters. The greatest likelihood of observing Condorcet's Paradox typically occurs for small numbers of voters. Results suggest that while examples of Condorcet's Paradox are observed, one should not expect to observe them with great frequency in three candidate elections. (shrink)

A defining characteristic of a liberal democratic society is the assignment of basic rights and liberties that protect each person’s private sphere. Hence, social choice made in a liberal democratic society must at the very least be consistent with the exercise of each person’s basic rights. However, even when everybody agrees to this basic principle, there could still remain irreconcilable social conflict and disagreement when it comes to the specific assignment of basic rights. This is especially so in a pluralistic (...) society where there is a clash among radically different and incompatible world views. Philosophers have now started to focus on this issue, which now goes by the name “perspectival diversity.” This paper extends the basic social choice theoretic framework of liberal rights by extending the domain to include individual perspectives alongside individual preferences. In this new framework, different individuals are able to see or perceive the same social alternative differently based on their own unique perspectives. The formal results of the paper imply that generating a viable social choice that is consistent with the assignment of basic rights can quickly break down once we start to increase the level of perspectival diversity in society. (shrink)