The learnability of voting rules

  • Authors:

  • Ariel D. Procaccia;Aviv Zohar;Yoni Peleg;Jeffrey S. Rosenschein

  • Affiliations:

  • Microsoft Israel R&D Center, 13 Shenkar Street, Herzeliya 46725, Israel;School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel and Microsoft Israel R&D Center, 13 Shenkar Street, Herzeliya 46725, Israel;School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel;School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2009

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Abstract

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.