Abstract
In voting, the main idea of the distance rationalizability framework is to view the voters’ preferences as an imperfect approximation to some kind of consensus. This approach, which is deeply rooted in the social choice literature, allows one to define (“rationalize”) voting rules via a consensus class of elections and a distance: a candidate is said to be an election winner if she is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be distance-rationalized. In this article, we provide new results on distance rationalizability of several Condorcet-consistent voting rules. In particular, we distance-rationalize the Young rule and Maximin using distances similar to the Hamming distance. It has been claimed that the Young rule can be rationalized by the Condorcet consensus class and the Hamming distance; we show that this claim is incorrect and, in fact, this consensus class and distance yield a new rule, which has not been studied before. We prove that, similarly to the Young rule, this new rule has a computationally hard winner determination problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baigent N (1987) Metric rationalisation of social choice functions according to principles of social choice. Math Soc Sci 13(1): 59–65
Brams S, Fishburn P (2002) Voting procedures. In: Arrow K, Sen A, Suzumura K (eds) Handbook of social choice and welfare, vol 1. Elsevier, Amsterdam, pp 173–236
Condorcet J (1785) Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. (Facsimile reprint of original published in Paris, 1972, by the Imprimerie Royale)
Downey R, Fellows M (1999) Parameterized complexity. Springer-Verlag, New York
Elkind E, Faliszewski P, Slinko A (2009) On distance rationalizability of some voting rules. In: Proceedings of the 12th conference on theoretical aspects of rationality and knowledge. ACM Press, Stanford, pp 108–117
Elkind E, Faliszewski P, Slinko, A (2010a) Good rationalizations of voting rules. In: Proceedings of the 24th AAAI conference on artificial intelligence. AAAI Press, Menlo Park, California, pp 774–779
Elkind E, Faliszewski P, Slinko A (2010b) On the role of distances in defining voting rules. In: Proceedings of the 9th international conference on autonomous agents and multiagent systems. International Foundation for Autonomous Agents and Multiagent Systems, Toronto, pp 375–382
Faliszewski P, Hemaspaandra E, Hemaspaandra L (2009) How hard is bribery in elections?. J Artif Intell Res 35: 485–532
Hemaspaandra L, Ogihara M (2002) The complexity theory companion. Springer-Verlag, New York
Kendall M, Gibbons J (1990) Rank correlation methods. Oxford University Press, Oxford
Klamler C (2005a) Borda and Condorcet: some distance results. Theory Decis 59(2): 97–109
Klamler C (2005b) The Copeland rule and Condorcet’s principle. Econ Theory 25(3): 745–749
Meskanen T, Nurmi H (2008) Closeness counts in social choice. In: Braham M, Steffen F (eds) Power, freedom, and voting. Springer-Verlag, Heidelberg
Niedermeier R (2006) Invitation to fixed-parameter algorithms. Oxford University Press, Oxford
Nitzan S (1981) Some measures of closeness to unanimity and their implications. Theory Decis 13(2): 129–138
Papadimitriou C (1994) Computational complexity. Addison-Wesley, Reading
Rothe J, Spakowski H, Vogel J (2003) Exact complexity of the winner problem for Young elections. Theory Comput Syst 36(4): 375–386
Young H (1977) Extending Condorcet’s rule. J Econ Theory 16(2): 335–353
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Elkind, E., Faliszewski, P. & Slinko, A. Rationalizations of Condorcet-consistent rules via distances of hamming type. Soc Choice Welf 39, 891–905 (2012). https://doi.org/10.1007/s00355-011-0555-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00355-011-0555-0