User:Kristomun/Proposed voting methods

From electowiki

This is a list of voting methods not separately described in articles on Electowiki but that have been proposed in academic articles or by election-methods members.

Condorcet-Approval hybrids

  • RA*1, RA*2, RA*3, XA*1, XA*2,and XA*3.[1]

Condorcet methods

  • Second order Copeland.[2]

Interactive methods

These methods require interaction by the candidates, e.g. asset voting and similar:

  • Dodgson-Hare.[3]

Nondeterministic methods

  • GT method (Rivest-Shen).[4]
  • Randomized Condorcet.[5]

Ranked methods

  • Competition graph method.[6]
  • Keener Eigenvector.[7]
  • Minimum hillside violations.[8]
  • Minimum hillside distance.[9]
  • Offense-defense model.[10]
  • Voting with Bidirectional Elimination.[11]
  • Kemeny analog for simultaneous domninace over positional, pairwise, and relative rankings.[12]

Self-voting methods

In these methods, the voters are also the candidates. For instance: web pages ranking other pages in a search engine.

  • PageRank and HITS.[13]

Proposed by EM members

  • Harmonic voting, Psi voting (Warren D. Smith).[14]
  • Maximal partial consensus, Nash lottery (Heitzig and Simmons).[15]
  • Maxtree, Sinkhorn voting (Warren D. Smith).[16]
  • Schulze STV-MMP (Markus Schulze).[17]
  • Warren's 0.495 apportionment method (Warren D. Smith).[18]


  1. Potthoff, Richard F. (2011-08-31). "Simple manipulation-resistant voting systems designed to elect Condorcet candidates and suitable for large-scale public elections". Social Choice and Welfare. Springer Science and Business Media LLC. 40 (1): 101–122. doi:10.1007/s00355-011-0589-3. ISSN 0176-1714.
  2. Bartholdi, J. J.; Tovey, C. A.; Trick, M. A. (1989). "The computational difficulty of manipulating an election" (PDF). Social Choice and Welfare. Springer Science and Business Media LLC. 6 (3): 227–241. doi:10.1007/bf00295861. ISSN 0176-1714.
  3. Green-Armytage, James (2023-02-04). "A Dodgson-Hare synthesis". Constitutional Political Economy. Springer Science and Business Media LLC. 34 (3): 458–470. doi:10.1007/s10602-023-09392-2. ISSN 1043-4062.
  4. Rivest, Ronald L.; Shen, Emily (2010-09-13). "An Optimal Single-Winner Preferential Voting System Based on Game Theory" (PDF). Proceedings Third International Workshop on Computational Social Choice. Düsseldorf University Press.
  5. Hoang, Lê Nguyên (2017-02-13). "Strategy-proofness of the randomized Condorcet voting system". Social Choice and Welfare. Springer Science and Business Media LLC. 48 (3): 679–701. doi:10.1007/s00355-017-1031-2. ISSN 0176-1714.
  6. Xiao, Yu; Deng, Hong-Zhong; Lu, Xin; Wu, Jun (2019-12-12). "Graph-based rank aggregation method for high-dimensional and partial rankings" (PDF). Journal of the Operational Research Society. Informa UK Limited. 72 (1): 227–236. doi:10.1080/01605682.2019.1657365. ISSN 0160-5682.
  7. Keener, James P. (1993). "The Perron–Frobenius Theorem and the Ranking of Football Teams" (PDF). SIAM Review. Society for Industrial & Applied Mathematics (SIAM). 35 (1): 80–93. doi:10.1137/1035004. ISSN 0036-1445.
  8. Pedings, Kathryn E.; Langville, Amy N.; Yamamoto, Yoshitsugu (2011-01-22). "A minimum violations ranking method" (PDF). Optimization and Engineering. Springer Science and Business Media LLC. 13 (2): 349–370. doi:10.1007/s11081-011-9135-5. ISSN 1389-4420.
  9. Fallang, Marthe (2015). Ranking and Hillside Form (MSc thesis). University of Oslo.
  10. Govan, Anjela Y; Langville, Amy N; Meyer, Carl D (2009-01-15). "Offense-Defense Approach to Ranking Team Sports". Journal of Quantitative Analysis in Sports. Walter de Gruyter GmbH. 5 (1). doi:10.2202/1559-0410.1151. ISSN 1559-0410.
  11. Cook, Matthew S. (2011). Voting with Bidirectional Elimination. Stanford Digital Repository (Thesis). Retrieved 2024-04-08.
  12. Pérez-Fernández, Raúl; Alonso, Pedro; Díaz, Irene; Montes, Susana; De Baets, Bernard (2017). "Monotonicity-based consensus states for the monometric rationalisation of ranking rules and how they are affected by ties". International Journal of Approximate Reasoning. Elsevier BV. 91: 131–151. doi:10.1016/j.ijar.2017.09.004. ISSN 0888-613X.
  13. Ding, Chris; He, Xiaofeng; Husbands, Parry; Zha, Hongyuan; Simon, Horst D. (2002-08-11). PageRank, HITS and a unified framework for link analysis. New York, NY, USA: ACM. doi:10.1145/564376.564440.
  14. Smith, Warren D. (1991-02-11). "Optimal proportional representation". Retrieved 2023-10-09.
  15. Heitzig, Jobst; Simmons, Forest W. (2020-06-10). "Efficient democratic decisions via nondeterministic proportional consensus". arXiv:2006.06548 [econ.GN].
  16. Smith, Warren D. (2007-06-12). "Descriptions of single-winner voting systems" (PDF). pp. 14–15. Retrieved 2023-10-09.
  17. Schulze, Markus (2008-08-04). "A New MMP Method (Part 2)" (PDF). Retrieved 2023-10-09.
  18. Smith, Warren D. "New Apportionment Method". Retrieved 2023-10-09.