Sequential Elimination vs. Instantaneous Voting∗ Parimal Kanti Bag† Hamid Sabourian‡ Eyal Winter§ April 22, 2007 Abstract A class of sequential elimination voting eliminating candidates one-at-a- time based on repeated ballots is superior to well-known single-round and semi-sequential elimination voting rules: if voters are strategic the former will induce the Condorcet winner in unique equilibrium, whereas the latter may fail to select it. In addition, when there is no Condorcet winner the outcome of sequential elimination voting always belongs to the ‘top cycle’. The proposed sequential family includes an appropriate adaptation of almost all standard single-round voting procedures. The importance of one-by-one elimination and repeated ballots for Condorcet consistency are further em- phasized by its failure for voting rules such as plurality runoff rule, exhaus- tive ballot method, and a variant of instant runoff voting. JEL Classification Numbers: P16, D71, C72. Key Words: Sequential elimination voting, Con- dorcet winner, top cycle, weakest link voting, scoring rule, exhaustive ballot, instant runoff voting, Markov equilibrium, complexity aversion. ∗At various stages this work has been presented at the 2003 Econometric Society European Meetings, 2005 Wallis Political Economy Conference, 2005 Conference at the Indian Statistical Institute, 2006 Econometric Society Far Eastern Meetings, and seminars at Birmingham, Keele, LSE, NUS (Singapore), Oxford and York universities. We thank the conference and seminar participants for important feedbacks. For errors or omissions, we remain responsible. †Department of Economics, University of Surrey, Guildford, Surrey, GU2 7XH, U.K.; E-mail:
[email protected] ‡Faculty of Economics, University of Cambridge, Sidgwick Avenue, Cambridge CB39 DD, U.K.; E-mail:
[email protected] §Economics Department, The Hebrew University of Jerusalem, Jerusalem 91905, Israel; E-mail:
[email protected] 1 Introduction Any assessment of a voting rule is likely to be based on the extent it aggregates individual preferences.