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Public Choice (2007) 132: 401420 DOI 10.1007/s11127-007-9165-x
A minimax procedure for electing committees
Steven J. Brams D. Marc Kilgour M. Remzi Sanver
Received: 29 November 2006 / Accepted: 15 March 2007 / Published online: 28 April 2007 Springer Science+Business Media, LLC 2007
Abstract A new voting procedure for electing committees, called the minimax procedure, is described. Based on approval balloting, it chooses the committee that minimizes the maximum Hamming distance to voters ballots, where these ballots are weighted by their proximity to other voters ballots. This minimax outcome may be diametrically opposed to the outcome obtained by aggregating approval votes in the usual manner, which minimizes the sum of the Hamming distances and is called the minisum outcome. The manipulability of these procedures, and their applicability when election outcomes are restricted in various ways, are also investigated.
The minimax procedure is applied to the 2003 Game Theory Society election of a council of 12 new members from a list of 24 candidates. By rendering outlying voters less inuential and not antagonizing any voters too much, it arguably would have produced a committee more representative of the interests of all voters than the minisum committee that was elected.
Keywords Minimax procedure Minisum procedure Approval balloting Committee election Hamming distance
1 Introduction
In this paper we propose a new voting procedure, called the minimax procedure, for electing committees. This procedure is based on approval ballotingwhereby voters approve
S.J. Brams ( )
Department of Politics, New York University, New York, NY 10003, USA e-mail: [email protected]
D.M. KilgourDepartment of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada e-mail: [email protected]
M.R. SanverDepartment of Economics, Istanbul Bilgi University, 34387 Kustepe, Istanbul, Turkey e-mail: [email protected]
402 Public Choice (2007) 132: 401420
of as many candidates as they like (Brams and Fishburn 1978, 1983)but votes are not aggregated in the usual manner.1
Instead of selecting the candidates that receive the most votes, the minimax procedure selects a set of candidates so as to minimize the maximum Hamming distance to voters ballots, where these ballots are weighted by their proximity to other voters ballots. This set of candidates constitutes the minimax outcome. We dene and illustrate Hamming distance in Sect. 2 and show how the proximity weighting of this distance is determined. We...