A passion for exactitude
It’s time for a long quotation from the philosopher Michael Dummett. I mention him once or twice every ten years.
(I just realized that, as of December, I’ve been blogging for twenty years. I started on Xanga, and when that service became costly I switched to Blogger/Blogspot. I may write a recapitulation soon.)
This is from pp. 3–5 of Voting Procedures (1984), one of Dummett’s excursions into what, for him, is “popular” philosophy.
Once, eleven years ago, I mentioned Dummett by way of griping about George Saunders. Since then, I’ve read and enjoyed four full books by Saunders and zero by Dummett. It wouldn’t hurt to finish Dummett’s trenchant On Immigration and Refugees; completing one of his Frege books, much as I adore them (all too often uncomprehendingly, it must be admitted), is above my pay grade.
(I just realized that, as of December, I’ve been blogging for twenty years. I started on Xanga, and when that service became costly I switched to Blogger/Blogspot. I may write a recapitulation soon.)
This is from pp. 3–5 of Voting Procedures (1984), one of Dummett’s excursions into what, for him, is “popular” philosophy.
In view of all this, one would expect that voting procedures and their operation would have been the subject of a considerable amount of intellectual enquiry. One would expect also that the results of such investigations would be well known both to political and social theorists and to all those concerned with practical affairs, and would be applied both by those who have frequently to take part in voting and, above all, by those concerned to devise voting procedures to be as fair and as satisfactory as possible. Of these two natural expectations, the first is indeed satisfied, but the second hardly at all. In the period since the end of the Second World War, a considerable body of theory concerning voting has been built up. This topic was pioneered by Professor Duncan Black, an economist, who published some articles about it in the late 1940s, and a book, The Theory of Committees and Elections, in 1958: an important contribution, not expressed specifically in terms of voting, was made by Professor Kenneth Arrow in his book Social Choice and Individual Values of 1951 [see note 1 below]. Since then, and especially in the last two decades, the theory initiated by Black and Arrow has been extensively developed, principally in articles published in learned journals. One of the most surprising features of all this is how recent this work is. Duncan Black devoted a section of his book to a historical survey. From this it emerged that almost the only serious work on the theory of voting that had previously been done was carried out in France just before and during the Revolution, by Borda, Condorcet, and Laplace; this work had subsequently been almost entirely forgotten, save by a few British mathematicians of the nineteenth and early twentieth centuries, who made insignificant contributions to it. A minor exception, not noticed by Black, is the unimpressive section devoted to the subject by the German philosopher Hermann Lotze in his Logik of 1874. The only exception mentioned by Black is the remarkable intervention by C. L. Dodgson (Lewis Carroll), contained in three pamphlets which he wrote in complete ignorance of the work of his predecessors, and which were directed at the voting procedure to be adopted by the governing body of Christ Church, Oxford, to which he belonged [see note 2 below].I especially like Dummett’s asides on Dodgson (Carroll) and the also-ran, Lotze.
[Note 1:] See the Bibliography for works by Arrow and Black. Arrow’s possibility theorem (more exactly called an impossibility theorem) is so fundamental to the subject that he is often credited with having been the modern initiator of it, especially since his basic notation has become standard. This is unfair to Black, who was the real twentieth-century pioneer of the theory of voting, as well as a diligent researcher into its earlier history; it may be due in part to the fact that, although Black’s original papers on the subject appeared in 1948–9, his book was not published until 1958, while Arrow’s celebrated monograph came out in 1951. Black was, in particular, the originator of the concept of single-peakedness (not used in the present book), with which Arrow is sometimes credited but which he in fact took over from Black. Single-peakedness is a condition which guarantees the existence of a top. For the case when some preference scales are weak, the condition was weakened by Farquharson and myself in our paper of 1961; alternative though analogous sufficient conditions were later given by Inada, Sen, and Pattanaik.
[Note 2:] See the Bibliography. It is a matter for the deepest regret that Dodgson never completed the book that he planned to write on the subject. Such were his lucidity of exposition and his mastery of the topic that it seems possible that, had he ever published it, the political history of Britain would have been significantly different.
Once, eleven years ago, I mentioned Dummett by way of griping about George Saunders. Since then, I’ve read and enjoyed four full books by Saunders and zero by Dummett. It wouldn’t hurt to finish Dummett’s trenchant On Immigration and Refugees; completing one of his Frege books, much as I adore them (all too often uncomprehendingly, it must be admitted), is above my pay grade.
