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International audience; Social choice functions are generalized to handle Nash's independence of irrelevant alternatives. Possibility and impossibility results are established.

International audience; Kenneth J. Arrow’s contributions to knowledge in the twentieth century can only be compared with the contributions of giants such as Kurt Godel,Alan Turing or John von Neumann. It is on purpose that I write knowledge rather than economics because these contributions go well beyond economics to encompass political science, mathematics, operations research, and philosophy. I will restrict myself here to economics, only mentioning in passing the other domains. Regarding economics, the main contributions are his works on social choice theory, general economic equilibrium, individual choice theory, the treatment of uncertainty in general equilibrium models, and information theory. In particular, Arrow’s name is associated with two topics of paradigmatic importance for modern economics: the Arrow (im)possibility theorem and Arrow-Debreu equilibrium (along with Gerard Debreu)

This paper describes an unknown episode in the development of the theory of social choice. In the Summer 1949, while at RAND, Quine worked on Arrow’s (im)possibility theorem. This work was eventually published as a paper on (applied) set theory totally disconnected from social choice. The working paper directly linked to Arrow’s work was never published. I alluded to this (then unwritten) paper in a number of presentations I made on ‘Logic and Social Choice’ in Turku, Bucharest, Boston, Strasbourg and Munich, between October 2013 and January 2015. It was eventually first presented during a conference at Queen Mary, University of London, 19–20 June 2015, on ‘Social Welfare, Justice and Distribution: Celebrating John Roemer’s Contributions to Economics, Political Philosophy and Political Science’, organized by Roberto Veneziani and Juan Moreno-Ternero. I am grateful to the participants for interesting reactions and comments, in particular Richard Arneson, Jon Elster, Marc Fleurbaey, Klaus Nehring and Gil Skillman. Jon Elster contacted Dagfinn Føllesdal, a well-known philosopher and a pre-eminent Quine scholar, who kindly responded to some queries. A more developed version was presented in Aix-en-Provence during the International Conference on Economic Philosophy and in Lund during the meeting of the Society for Social Choice and Welfare in June 2016. Comments of participants to these two events revealed to be very helpful, among which comments by Gilles Campagnolo, Christian List and John Weymark. While in Lund, I also greatly benefitted from conversations with Adrian Miroiu. Finally, I am very grateful to an Associate Editor of this journal for excellent suggestions and for detecting some very annoying slips.

The birth (or should we say the re-birth) of voting theory at the end of 18th century in France exemplifies the victory of Condorcet over Borda. This victory was confirmed by the rebirth of voting theory in the 1940s with the magisterial works of Arrow and Black. Only since publications by Dummett, Young and Saari, did Borda systems recover their importance. In this chapter, I will explain how and why this happened. I am grateful to Peter Emerson and Louis Aim. Fono for helpful comments.

Social choice and welfare economics are subjects at the frontier of many disciplines. Even if economics played the major role in their development, sociology, psychology and, principally, political science, mathematics and philosophy have been central for the manifold inventiveness of the employed methods and for the diversity of the studied topics. This phenomenon can be compared with game theory, a subject which has, of course, many connections with social choice and welfare. This fact is reflected by the disciplinary origins of the contributors to the subject and, as an anecdote, by the disciplinary origins of the board of editors of this journal. Philosophers are expected to contribute mainly to the study of social justice and related ethical questions. But there is a tradition among logicians for studying voting theory. A famous example is C. L. Dodgson (Lewis Carroll), even though the complete works of Dodgson on voting occupy only a few pages. A major recent example is Michael Dummett. Michael Dummett is famous among social choice theorists for his joint paper with Robin Farquharson published in Econometrica in 1961. Later he wrote two important books on voting (Dummett (1984, 1997); for an overview see Salles (2006)). But it must be outlined that Michael Dummett is also, and above all, one of the greatest contemporary philosophers whose work on the German logician Frege, on intuitionism, realism, anti-realism, justificationism has been central for the development of analytical philosophy in the second part of the last century and in this century (an example is the Symposium in a recent issue of Mind (see Peacocke (2005) and Dummett (2005)). Sir Michael Dummett is Wykeham Professor of Logic emeritus at Oxford University. His interview was conducted at New College, Oxford in September 2004.

International audience; The paper axiomatises a generalised utilitarian aggregation rule, under which different weights are assigned to utilities depending on the different rights involved. The relationship between actions, rights and the evaluation of utilities is investigated. Application is made to a famous example, Edwin-Angelina-the Judge, which appears in the social choice literature.

The paper explores the problem of aggregating ordinally fuzzy individual preferences into ordinally fuzzy social preferences. Using Goguen's ordinal formulation of fuzziness, it is shown that, given certain plausible conditions, the requirement that the society's preferences should satisfy any of several alternative transitivity conditions creates a dilemma: either power in the society is rather unevenly distributed, or the society tends to be indecisive. The problem increases as weaker transitivity conditions are replaced by stronger ones.