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Games 2014, 5(4), 204-233; doi:10.3390/g5040204

Condorcet Completion Methods that Inhibit Manipulation through Exploiting Knowledge of Electorate Preferences

Department of Political Science and Social Science Research Institute, Duke University, Erwin Mill, Duke Box 90420, Durham, NC 27708, USA
Received: 4 August 2014 / Revised: 2 October 2014 / Accepted: 6 October 2014 / Published: 30 October 2014
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Abstract

This paper attacks a problem like the one addressed in an earlier work (Potthoff, 2013) but is more mathematical. The setting is one where an election is to choose a single winner from m (> 2) candidates, it is postulated that voters have knowledge of the preference profile of the electorate, and preference cycles are limited. Both papers devise voting systems whose two key goals are to select a Condorcet winner (if one exists) and to resist manipulation. These systems entail equilibrium strategies where everyone votes sincerely, no group of voters sharing the same preference ordering can gain by deviating given that no one else deviates, and the Condorcet candidate wins. The present paper uses two unusual ballot types. One asks voters to rank the candidates with respect both to their own preferences and to their discerned order of preference of the entire electorate. The other just asks voters for their own preference ranks plus approval votes. Novel mathematical elements distinguish this paper. Its Condorcet completion methods examine all candidate triples, sometimes analyze loop(s) of some of those triples, and order candidates in a set by first determining the last-place candidate. Its non-manipulability proofs involve mathematical induction on m. View Full-Text
Keywords: Condorcet completion methods; strategic voting; manipulable; cyclical majorities; approval voting; mathematical induction Condorcet completion methods; strategic voting; manipulable; cyclical majorities; approval voting; mathematical induction
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Potthoff, R.F. Condorcet Completion Methods that Inhibit Manipulation through Exploiting Knowledge of Electorate Preferences. Games 2014, 5, 204-233.

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