A Minimax Procedure for Electing Committees

Steven J. Brams (1) , Marc Kilgour (2) , Remzi Sanver (3)

1 Department of Politics
2 Department of Mathematics
3 Department of Economics

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. The composition of the council would have changed by 4 members; there would have been more substantial differences between minimax and minisum outcomes if the number of candidates to be elected had been endogenous rather than being fixed at 12. The minimax procedure, which renders central voters more influential but does not antagonize any voter too much, may produce a committee that better represents the interests of all voters than a minisum committee.

Mots clés: committees; minimax; minisum

Domaines: Complexité [cs.CC]; Recherche opérationnelle [math.OC]

Steven J. Brams, Marc Kilgour, Remzi Sanver. A Minimax Procedure for Electing Committees. 2006. ⟨hal-00119026⟩