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NYT obituary here. His work on voting and social choice has often attracted the interest of philosophers. Any suggestions about particularly good or fruitful philosophical treatments of his work?
I think that Alfred MacKay's, Arrow's Theorem: The Paradox of Social Choice is the best starting point for philosophers. Much more technical but hugely important is AK Sen, Collective Choice and Social Welfare. A beautiful little book–though hard to find–is Robin Farqhuarson, Theory of Voting: it explains some main issues with pretty diagrams, but without the generality of the Arrow result.
Sen's book is just out in a new edition by Penguin. I saw it in our University Bookshop the other day.
There are also extensions of Arrow's result to other domains, which is of interest. Arrow's Theorem along with some other bits of social choice theory feature in the Pettit and List's treatment of group agency (and other treatments as well), and Samir Okasha and others have investigated the import of Arrow's Theorem to theory choice in the sciences.
Logicians unfamiliar with social choice theory can consult from Samson Abramsky's "Arrow's theorem by arrow theory" in the /Logic without borders/ volume by Villaveces, Kossak, Kontinen, and Hirvonen. He casts it all in terms familiar to category theorists and theoretical computer scientists and thereby brings out its logical structure vividly.
Had Les Green not gotten in ahead of me, I would have mentioned MacKay's book, which is very nice. (Whether or not there is a plausible "social" choice depends on what the range of positions in the population is: if everybody has the same view, that view is the obvious "social" one. Arrow's Theorem says that there is no way of getting a "social" choice that is guaranteed to work plausibly under every possible distribution of individual views. Despite which, it at least used to seem (before last November) that democracy can "work" a lot of the time. One of the valuable things in MacKay's book– something that I think will be helpful to any reader new to the topic who wants to think about it– is the formulation of a condition on ranges of individual choice which suffices to guarantee a "social" choice. Exercise for the reader: think of real life political situations in which, plausibly, MacKay's condition fails!)
I first learned about Arrow's Theorem from (the long out of print, I suppose) "Logic and Social Choice" by Y.Murakami (Routledge/Dover, 1968): one of the pamphlets (this one is 135 small format pages and most others were smaller) in the sadly vanished series "Monographs in Modern Logic" — introductory introductions to topics or areas, affordable on a student budget!
Amartya Sen and Eric Maskin edited a slim volume of papers called THE ARROW IMPOSSIBILITY THEOREM; Sen's own contribution shows some of the philosophical implications he sees to Arrow's Theorem. Those who want to teach Arrow should consider William Riker's book LIBERALISM AGAINST POPULISM. While it is not philosophically sophisticated and parts of it are somewhat dated, the book illustrates the implications of Arrow's theorem for an election with which American students, at least, should be familiar: the election of Abraham Lincoln in 1860. The mathematician Donald Saari also has a couple of books on voting theory that are clearly written and are accessible to undergraduates. Finally, anyone who wants to see a really elegant proof of Arrow's theorem should google 'Terence Tao Arrow's Theorem'. (Tao is a Fields Medalist who teaches mathematics at UCLA.)
Samir Okasha has started a discussion of the relevance of Arrow's theorem in theory choice. Michael Morreau has provided a generalization of Arrow's theorem showing the impossibility of relations of comparative overall similarity (which, for example, have been appealed to by David Lewis to account for de re predication and counterfactuals).
Philosophers will be interested in the Stanford Encyclopedia entry by Michael Morreau.
Many political science researchers have used the framework to study legislatures and electoral systems, emphasizing the ways in which these respond to instabilities (e.g., think of the ways in which violations of transitivity might lead to voting results which could be overturned). In this connection a book by Thomas Schwartz (UCLA), The Logic of Collective Choice (1986) is both a good (advanced) introduction and one that emphasizes the instabilities that interest students of politics. I mention this book in part because Schwartz's Phd is from Pitt in philosophy.
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