Under his real name of C. L. Dodgson, Carroll wrote extensively on mathematics and logic. Until recently, most modern mathematicians dismissed his professional work as quirky, elementary - and sometimes just plain wrong. Now they are beginning to see that he was a true original - in mathematics just as in literature.
The process began in the early 1950s when a Glasgow economist named Duncan Black (1908-91) stumbled on the lost works of C. L. Dodgson on the theory of voting. Black, himself one of the two mathematicians who formalised voting theory this century, immediately recognised the lonely greatness of his predecessor. Dodgson was the first person writing in English to point out that sometimes there is a majority for A over B, for B over C, and for C over A - all at the same time! He also wrote pamphlets about proportional representation and about tennis tournaments. Not until a century after he wrote them did anybody realise their importance. Duncan Black spent thirty years writing a book on Lewis Carroll and proportional representation. But it was unfinished at his death.
The book has now been reconstructed from the roomfuls of papers that were in Duncan Black’s house when he died. It has been edited by a transatlantic team of voting scholars, aided by a grant from the Economic and Social Research Council. It explains clearly for the first time what Dodgson was trying to say. Writing in 1884, he praised the unpopular ‘limited vote’ which then operated in the big English cities, in which each voter had fewer votes than there were seats to fill. Most people thought that this was less democratic than giving each voter as many votes as there were seats. Dodgson proved that it was more democratic. To do so, he used concepts we would today label 'game theoretic', although such concepts were not formalised until decades after his death.
The book also contains Duncan Black’s discoveries about Alice and The Hunting of the Snark. It prints three letters to The Times about live frogs allegedly found in lumps of coal that probably gave Carroll the idea for the Frog Footman in Alice. And it suggests that the bullying. incompetent Bellman in the Snark is a savage portrait of the real Alice’s father.
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is an Official Fellow in Politics at Nuffield College, Oxford.
is a Research Officer at Nuffield College, Oxford.,
is Assistant Professor of Political Science, Indiana University.
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