Lewis Carroll, Voting, and the Taxicab Metric.

So begins the first of three pamphlets written by Charles Dodgson (aka Lewis Carroll) for his faculty colleagues at Christ Church, Oxford, between 1873 and 1876. Dodgson was quite disturbed by several decisions that had been made by the faculty at the college, especially the selection of students to Christ Church and the choice of the redesign of the college belfry. Since Dodgson did not agree with the decisions, he concluded that the problem was not a lack of support for his positions but must lie with the decision procedure used! For a wonderful account of the way in which these events shaped Dogson’s work in elections, see Duncan Black’s discussion in Theory of Committees and Elections [2] . In his first pamphlet, Dodgson lays out the trouble with many of the standard voting methods, such as plurality, plurality with elimination, the method of marks, etc. By his third pamphlet, A Method of Taking Votes on More Than Two Issues [3], Dodgson displays an amazing insight into many of the fundamental issues that have shaped modern social choice theory. In this pamphlet, Dodgson uses a specific criterion to critique other voting methods, and although he does not explicitly propose it as a method to determine the winner, this criterion has come to be known as Dodgson’s method. Since this method is computationally expensive, several techniques have been proposed for approximating the Dodgson winner. The focus of this paper is to show how to interpret Dodgson’s method as an almost taxicab metric which helps us understand how different approximations can give different results and which gives us further insight into Dodgson’s method.