Algorithm Supplement: Single Transferable Vote by Meek's Method

Abstract

The single transferable vote (STV) method of conducting an election exists in a number of different formulations in different countries. Most of the methods are designed to be practicable when counting is by hand, and this necessarily enforces simplicity even at the expense of not always getting the best possible answer. Meek[1, 2] considered the question of the best possible method, within the STV framework, when a computer is available to do the counting, and it is his method that we present here. The method was rediscovered, in a different formulation, by Woodall[4]. However, neither Meek nor Woodall dealt with certain detailed points, such as how to resolve a ‘tie’, so we have had to extend the system to be complete. The algorithm as given here has been adopted by the Royal Statistical Society for its Council elections. The basis of any STV system consists of the following. (1) Voting by order of preference of candidates, the first choice being marked 1, the second 2, and so on, on the ballot papers. (Meek also considered an alternative formulation in which voters would be allowed to indicate equal preference for some candidates instead of a strict ordering; we have not implemented this alternative.) (2) A quota for election, calculated from the number of votes and the number of seats to be filled. (3) A first counting by first preferences only, and the election of any candidate who equals or exceeds the quota (except in the special case of a multi-way tie). (4) Redistribution of surplus votes (above the quota) for any candidate, in accordance with the voters’ further preferences, and election of any who now reach the quota. (5) When no further redistribution of surpluses is possible,