The learnability of voting rules

Ariel D. Procaccia*, Aviv Zohar, Yoni Peleg, Jeffrey S. Rosenschein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


Scoring rules and voting trees are two broad and concisely-representable classes of voting rules; scoring rules award points to alternatives according to their position in the preferences of the voters, while voting trees are iterative procedures that select an alternative based on pairwise comparisons. In this paper, we investigate the PAC-learnability of these classes of rules. We demonstrate that the class of scoring rules, as functions from preferences into alternatives, is efficiently learnable in the PAC model. With respect to voting trees, while in general a learning algorithm would require an exponential number of samples, we show that if the number of leaves is polynomial in the size of the set of alternatives, then a polynomial training set suffices. We apply these results in an emerging theory: automated design of voting rules by learning.

Original languageAmerican English
Pages (from-to)1133-1149
Number of pages17
JournalArtificial Intelligence
Issue number12-13
StatePublished - Aug 2009

Bibliographical note

Funding Information:
The authors wish to thank anonymous AIJ, AAAI, and AAMAS reviewers, for their very helpful comments. This work was partially supported by Israel Science Foundation grant #898/05.

Funding Information:
✩ This paper subsumes two earlier conference papers [A.D. Procaccia, A. Zohar, Y. Peleg, J.S. Rosenschein, Learning voting trees, in: Proceedings of the 22nd AAAI Conference on AI (AAAI), 2007, pp. 110–115; A.D. Procaccia, A. Zohar, J.S. Rosenschein, Automated design of scoring rules by learning from examples, in: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2008, pp. 951–958]. * Corresponding author. E-mail addresses: [email protected] (A.D. Procaccia), [email protected] (A. Zohar), [email protected] (Y. Peleg), [email protected] (J.S. Rosenschein). 1 The author was supported in this work by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.


  • Computational learning theory
  • Computational social choice
  • Multiagent systems


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