Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected* Dan S. Felsenthal University of Haifa and Centre for Philosophy of Natural and Social Science London School of Economics and Political Science Revised 26 May 2010 This paper will be presented at the Leverhulme Trust sponsored 2010 Voting Power in Practice workshop held at Chateau du Baffy, Normandy, France, 30 July – 2 August, 2010 Please send by email all communications regarding this paper to the author at:
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[email protected] * I wish to thank Vincent Chua, Rudolf Fara, and Moshé Machover for helpful comments, as well as Hannu Nurmi for sending me several examples contained in this paper. No member of the Voting Power & Procedures (VPP) project at LSE, except myself, bears any responsibility whatsoever for the opinions and recommendations expressed here. Abstract The paper surveys 17 deterministic electoral procedures for selecting one out of two or more candidates, as well as the susceptibility of each of these procedures to various paradoxes. A detailed appendix exemplifies the paradoxes to which each electoral procedure is susceptible. It is concluded that from the perspective of vulnerability to serious paradoxes, as well as in light of additional technical-administrative criteria, Copeland’s or Kemeny’s proposed procedures are the most desirable. 1. Introduction Three factors motivated me to write this paper: • The recent passage (25 February 2010) by the British House of Commons of the Constitutional Reform and Governance Bill, clause #29 of which states that a referendum will be held by 31 October 2011 on changing the current single member plurality (aka first-past- the-post, briefly FPTP) electoral procedure for electing the British House of Commons to the (highly paradoxical) alternative vote (AV) procedure (aka Instant Runoff).