Applying Majority Judgment over a Polyhedral Candidate Space

50 Pages Posted: 14 Mar 2016 Last revised: 1 Aug 2017

See all articles by Chiwei Yan

Chiwei Yan

Uber Technologies, Inc.; University of Washington

Prem Swaroop

University of Maryland - Decision and Information Technologies Department

Michael O. Ball

University of Maryland - Decision and Information Technologies Department

Cynthia Barnhart

Massachusetts Institute of Technology (MIT) - Operations Research Center

Vikrant Vaze

Thayer School of Engineering

Date Written: May 1, 2017

Abstract

Most of the existing voting methods deal with a moderate (or at least finite) number of candidates. In practice, there are important voting applications where candidate space is huge or even of infinite size. We describe new methods in voting by extending the Majority Judgment voting and ranking method to handle a candidate space of infinite size. Specifically, the candidate space is modeled as a polyhedral set. Two approaches are developed. The first approach relies on multiple rounds of grading and iterative candidate generation. The candidate generation employs a novel mixed-integer programming model. The second approach employs a robust optimization framework and only takes as input each voters most preferred candidate. This results in an output vector which is the candidate that has the best worst-case guarantee in terms of majority grade. We demonstrate the effectiveness of our approaches through two case studies involving voting over polyhedral candidate space.

Keywords: Majority Judgment, Polyhedral Candidate Space, Computational Social Choice

Suggested Citation

Yan, Chiwei and Swaroop, Prem and Ball, Michael O. and Barnhart, Cynthia and Vaze, Vikrant, Applying Majority Judgment over a Polyhedral Candidate Space (May 1, 2017). Available at SSRN: https://ssrn.com/abstract=2746568 or http://dx.doi.org/10.2139/ssrn.2746568

Chiwei Yan (Contact Author)

Uber Technologies, Inc. ( email )

San Francisco, CA 94158
United States

HOME PAGE: http://web.mit.edu/chiwei/www

University of Washington ( email )

Seattle, WA 98195
United States

Prem Swaroop

University of Maryland - Decision and Information Technologies Department ( email )

Robert H. Smith School of Business
4313 Van Munching Hall
College Park, MD 20815
United States

Michael O. Ball

University of Maryland - Decision and Information Technologies Department ( email )

Robert H. Smith School of Business
4313 Van Munching Hall
College Park, MD 20815
United States
301-405-2227 (Phone)
301-405-8655 (Fax)

Cynthia Barnhart

Massachusetts Institute of Technology (MIT) - Operations Research Center ( email )

77 Massachusetts Avenue
Bldg. E 40-149
Cambridge, MA 02139
United States

Vikrant Vaze

Thayer School of Engineering ( email )

14 Engineering Drive
Hanover, NH New Hampshire 03755
United States
6036469147 (Phone)

HOME PAGE: http://engineering.dartmouth.edu/people/faculty/vikrant-vaze/

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