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Computational Social Choice - or - Political Science meets Computer Science

This article explores computational methods for electing committees and maximizing voter satisfaction in social choice scenarios. It discusses various techniques such as approval ballots and fixed-size minimax, and highlights the challenges in computing optimal outcomes.

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Computational Social Choice - or - Political Science meets Computer Science

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  1. Computational Social Choice - or - Political Science meets Computer Science Ron K. Cytron http://www.cs.wustl.edu/~cytron/ Joint work with Lorrie Cranor (Wash U Ph.D. student, now at CMU) Rob LeGrand (Wash U Ph.D. student, now at Angelo State) 16 May 2014

  2. Some voting results are difficult to compute • Voters say yes or no to each of k candidates • Elect a subset of the candidates so that • Least pleased voter is as happy as possible • Bring as many people “forward” as possible

  3. Electing a committee from approval ballots[ Brams, NYU ] approves of candidates 4 and 5 11110 00011 k = 5 candidates n = 6 ballots 01111 00111 10111 00001 • What’s the best committee of size m = 2?

  4. Sum of Hamming distances How happy? 11110 00011 m = 2 winners 2 4 4 5 01111 11000 00111 4 3 sum = 22 10111 00001

  5. Fixed-size minisum How happy? 11110 00011 m = 2 winners 4 0 2 1 01111 00011 00111 2 1 sum = 10 10111 00001 • Minisum elects winner set with smallest sumscore • Easy to compute (pick candidates with most approvals)

  6. Maximum Hamming distance 11110 00011 m = 2 winners 4 0 2 1 01111 00011 00111 2 1 sum = 10 max = 4 10111 00001

  7. Fixed-size minimax [Brams, Kilgour & Sanver ’04] 11110 00011 m = 2 winners 2 2 2 1 01111 00110 00111 2 3 sum = 12 max = 3 10111 00001 • Minimax elects winner set with smallest maxscore • Hard to compute! Currently have to try all outcomes

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