Analysis and optimization of multi-dimensional percentile mechanisms

  • Authors:
  • Xin Sui;Craig Boutilier;Tuomas Sandholm

  • Affiliations:
  • University of Toronto, Dept. of Computer Science;University of Toronto, Dept. of Computer Science;Carnegie Mellon University, Computer Science Department

  • Venue:
  • IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
  • Year:
  • 2013

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Abstract

We consider the mechanism design problem for agents with single-peaked preferences over multi-dimensional domains when multiple alternatives can be chosen. Facility location and committee selection are classic embodiments of this problem. We propose a class of percentile mechanisms, a form of generalized median mechanisms, that are strategy-proof, and derive worst-case approximation ratios for social cost and maximum load for L1 and L2 cost models. More importantly, we propose a sample-based framework for optimizing the choice of percentiles relative to any prior distribution over preferences, while maintaining strategy-proofness. Our empirical investigations, using social cost and maximum load as objectives, demonstrate the viability of this approach and the value of such optimized mechanisms vis-à-vis mechanisms derived through worst-case analysis.