The Dodgson ranking and the Borda count: a binary comparison Christian Klamler * Institute of Public Economics, University of Graz, Universitaetsstr. 15, Graz A-8010, Austria Received 1 April 2003; received in revised form 1 October 2003; accepted 1 November 2003 Abstract This paper provides a binary comparison of two preference aggregation rules, the Borda rule and Dodgson’s rule. Both of these rules guarantee a transitive ranking of the alternatives for every list of individual preferences and therefore avoid the problem of voting cycles. It will be shown that for certain lists of individual preferences the rankings derived from the Borda rule and Dodgson’s rule are antagonistic. D 2004 Elsevier B.V. All rights reserved. Keywords: Voting paradox; Voting rules; Borda rule; Dodgson rule; Distance functions JEL classification: D70 1. Introduction The purpose of this paper is to provide a binary comparison of two preference aggregation rules, Borda’s rule and Dodgson’s rule. Both of these rules guarantee a transitive ranking of the alternatives for every list of individual preferences. Hence, they avoid the problems of voting cycles which affect the simple majority rule and are therefore discussed in the literature as simple majority rule extensions (Fishburn, 1977). For the aggregation of individual preferences over a set of m alternatives, Borda (1781) suggested to assign m  1 points to the top alternative in an individual’s ranking, m  2 points to its second ranked alternative down to 0 points to an individual’s bottom ranked alternative. 0165-4896/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.mathsocsci.2003.11.003 *Tel.: +43-316-380-3465; fax: +43-316-380-9530. E-mail address: christian.klamler@uni-graz.at (C. Klamler). www.elsevier.com/locate/econbase Mathematical Social Sciences 48 (2004) 103 – 108