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Approximability and Inapproximability of Dodgson and Young Elections

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Author Info
Ariel D. Procaccia ()
Michal Feldmany ()
Jeffrey S. Rosenschein ()
Abstract

The voting rules proposed by Dodgson and Young are both designed to find the candidate closest to being a Condorcet winner, according to two different notions of proximity; the score of a given candidate is known to be hard to compute under both rules. In this paper, we put forward an LP-based randomized rounding algorithm which yields an O(log m) approximation ratio for the Dodgson score, where m is the number of candidates. Surprisingly, we show that the seemingly simpler Young score is NP-hard to approximate by any factor.

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Paper provided by Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp466.

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Length: 13 pages
Date of creation: Oct 2007
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Handle: RePEc:huj:dispap:dp466

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  1. Christian Klamler, 2004. "The Dodgson ranking and its relation to Kemeny’s method and Slater’s rule," Social Choice and Welfare, Springer, vol. 23(1), pages 91-102, 08. [Downloadable!] (restricted)
  2. Young, H. P., 1977. "Extending Condorcet's rule," Journal of Economic Theory, Elsevier, vol. 16(2), pages 335-353, December. [Downloadable!] (restricted)
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