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Strong and Weak Acyclicity in Iterative Voting

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Algorithmic Game Theory (SAGT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9928))

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Abstract

We cast the various different models used for the analysis of iterative voting schemes into a general framework, consistent with the literature on acyclicity in games. More specifically, we classify convergence results based on the underlying assumptions on the agent scheduler (the order of players) and the action scheduler (the response played by the agent).

Our main technical result is proving that Plurality with randomized tie-breaking (which is not guaranteed to converge under arbitrary agent schedulers) is weakly-acyclic. I.e., from any initial state there is some path of better-replies to a Nash equilibrium. We thus show a separation between restricted-acyclicity and weak-acyclicity of game forms, thereby settling an open question from [17]. In addition, we refute another conjecture by showing the existence of strongly-acyclic voting rules that are not separable.

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Notes

  1. 1.

    All of our results still hold if there are no fixed voters, but allowing fixed voters enables the introduction of simpler examples. For further discussion on fixed voters see [8].

  2. 2.

    We thank an anonymous reviewer for the references.

References

  1. Andersson, D., Gurvich, V., Hansen, T.D.: On acyclicity of games with cycles. Discrete Appl. Math. 158(10), 1049–1063 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Apt, K.R., Simon, S.: A classification of weakly acyclic games. In: Serna, M. (ed.) SAGT 2012. LNCS, vol. 7615, pp. 1–12. Springer, Heidelberg (2012)

    Google Scholar 

  3. Boros, E., Gurvich, V., Makino, K., Papp, D.: Acyclic, or totally tight, two-person game forms: characterization and main properties. Discrete Math. 310(6), 1135–1151 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bowling, M.: Convergence and no-regret in multiagent learning. Adv. Neural Inf. Process. Syst. 17, 209–216 (2005)

    Google Scholar 

  5. Bowman, C., Hodge, J.K., Ada, Y.: The potential of iterative voting to solve the separability problem in referendum elections. Theor. Decis. 77(1), 111–124 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Brânzei, S., Caragiannis, I., Morgenstern, J., Procaccia, A.D.: How bad is selfish voting? In: Proceeding of 27th AAAI (2013)

    Google Scholar 

  7. Cournot, A.-A.: Recherches sur les principes mathématiques de la théorie des richesses par Augustin Cournot. chez L. Hachette (1838)

    Google Scholar 

  8. Elkind, E., Grandi, U., Rossi, F., Slinko, A.: Gibbard-satterthwaite games. In: IJCAI 2015 (2015)

    Google Scholar 

  9. Fabrikant, A., Jaggard, A.D., Schapira, M.: On the structure of weakly acyclic games. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, pp. 126–137. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Gärdenfors, P.: Manipulation of social choice functions. J. Econ. Theory 13(2), 217–228 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gohar, N.: Manipulative voting dynamics. PhD thesis, University of Liverpool (2012)

    Google Scholar 

  12. Grandi, U., Loreggia, A., Rossi, F., Venable, K.B., Walsh, T.: Restricted manipulation in iterative voting: condorcet efficiency and borda score. In: Perny, P., Pirlot, M., Tsoukiàs, A. (eds.) ADT 2013. LNCS, vol. 8176, pp. 181–192. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  13. Kelly, J.S.: Strategy-proofness and social choice functions without singlevaluedness. Econometrica: J. Econometric Soc. 439–446 (1977)

    Google Scholar 

  14. Koolyk, A., Lev, O., Rosenschein, J.S.: Convergence and quality of iterative voting under non-scoring rules (extended abstract). In: Proceeding of 15th AAMAS (2016)

    Google Scholar 

  15. Kukushkin, N.S.: Congestion games: a purely ordinal approach. Econ. Lett. 64, 279–283 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kukushkin, N.S.: Perfect information and congestion games. Games Econ. Behav. 38, 306–317 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kukushkin, N.S.: Acyclicity of improvements in finite game forms. Int. J. Game Theory 40(1), 147–177 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lev, O.: Agent modeling of human interaction: stability, dynamics and cooperation. PhD thesis, The Hebrew University of Jerusalem (2015)

    Google Scholar 

  19. Lev, O., Rosenschein, J.S.: Convergence of iterative voting. In: Proceeding of 11th AAMAS, pp. 611–618 (2012)

    Google Scholar 

  20. Marden, J.R., Arslan, G., Shamma, J.S.: Regret based dynamics: convergence in weakly acyclic games. In: Proceeding of 6th AAMAS. ACM (2007)

    Google Scholar 

  21. Meir, R., Polukarov, M., Rosenschein, J.S., Jennings, N.R.: Acyclic games and iterative voting. ArXiv e-prints (2016)

    Google Scholar 

  22. Meir, R.: Plurality voting under uncertainty. In: Proceeding of 29th AAAI, pp. 2103–2109 (2015)

    Google Scholar 

  23. Meir, R.: Strong and weak acyclicity in iterative voting. In: COMSOC 2016 (2016)

    Google Scholar 

  24. Meir, R., Lev, O., Rosenschein, J.S.: A local-dominance theory of voting equilibria. In: Proceeding of 15th ACM-EC (2014)

    Google Scholar 

  25. Meir, R., Polukarov, M., Rosenschein, J.S., Jennings, N.: Convergence to equilibria of plurality voting. In: Proceeding of 24th AAAI, pp. 823–828 (2010)

    Google Scholar 

  26. Milchtaich, I.: Congestion games with player-specific payoff functions. Games Econ. Behav. 13(1), 111–124 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  27. Monderer, D., Shapley, L.S.: Potential games. Games Econ. Behav. 14(1), 124–143 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  28. Obraztsova, S., Markakis, E., Polukarov, M., Rabinovich, Z., Jennings, N.R.: On the convergence of iterative voting: how restrictive shouldrestricted dynamics be? In: Proceeding of 29th AAAI (2015)

    Google Scholar 

  29. Obraztsova, S., Markakis, E., Thompson, D.R.M.: Plurality voting with truth-biased agents. In: Vöcking, B. (ed.) SAGT 2013. LNCS, vol. 8146, pp. 26–37. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  30. Reijngoud, A., Endriss, U.: Voter response to iterated poll information. In: Proceeding of 11th AAMAS, pp. 635–644 (2012)

    Google Scholar 

  31. Reyhani, R., Wilson, M.C.: Best-reply dynamics for scoring rules. In: Proceeding of 20th ECAI. IOS Press (2012)

    Google Scholar 

  32. Roth, A.E.: The college admissions problem is not equivalent to the marriage problem. J. Econ. Theory 36(2), 277–288 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  33. Tal, M., Meir, R., Gal, Y.: A study of human behavior in voting systems. In: Proceeding of 14th AAMAS, pp. 665–673 (2015)

    Google Scholar 

  34. Xia, L., Lang, J., Ying, M.: Sequential voting rules and multiple elections paradoxes. In: TARK 2007, pp. 279–288 (2007)

    Google Scholar 

  35. Young, H.P.: The evolution of conventions. Econometrica: J. Econometric Soc., 57–84 (1993)

    Google Scholar 

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Authors and Affiliations

  1. Technion—Israel Institute of Technology, Haifa, Israel

    Reshef Meir

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  1. Reshef Meir
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Correspondence to Reshef Meir .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Martin Gairing

  2. University of Liverpool, Liverpool, United Kingdom

    Rahul Savani

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Meir, R. (2016). Strong and Weak Acyclicity in Iterative Voting. In: Gairing, M., Savani, R. (eds) Algorithmic Game Theory. SAGT 2016. Lecture Notes in Computer Science(), vol 9928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53354-3_15

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  • DOI: https://doi.org/10.1007/978-3-662-53354-3_15

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