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Manipulation Complexity of Same-System Runoff Elections

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Abstract

Do runoff elections, using the same voting rule as the initial election but just on the winning candidates, increase or decrease the complexity of manipulation? Does allowing revoting in the runoff increase or decrease the complexity relative to just having a runoff without revoting? For both weighted and unweighted voting, we show that even for election systems with simple winner problems the complexity of manipulation, manipulation with runoffs, and manipulation with revoting runoffs are independent. On the other hand, for some important, well-known election systems we determine what holds for each of these cases. For no such systems do we find runoffs lowering complexity, and for some we find that runoffs raise complexity. Ours is the first paper to show that for natural, unweighted election systems, runoffs can increase the manipulation complexity.

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References

  1. Aziz, H., Gaspers, S., Mattei, N., Narodytska, N., Walsh, T.: Ties matter: Complexity of manipulation when tie-breaking with a random vote. In: Proceedings of the 27th AAAI Conference on Artificial Intelligence, pp 74–80. AAAI Press (2013)

  2. Bag, P., Sabourian, H., Winter, E.: Multi-stage voting, sequential elimination and Condorcet consistency. J. Econ. Theory 144(3), 1278–1299 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bartholdi III, J, Orlin, J.: Single transferable vote resists strategic voting. Soc. Choice Welf. 8(4), 341–354 (1991)

    MathSciNet  MATH  Google Scholar 

  4. Bartholdi III, J., Tovey, C., Trick, M.: The computational difficulty of manipulating an election. Soc. Choice Welf. 6(3), 227–241 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bartholdi III, J., Tovey, C., Trick, M.: Voting schemes for which it can be difficult to tell who won the election. Soc. Choice Welf. 6(2), 157–165 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  6. Brandt, F., Conitzer, V., Endriss, U.: Computational social choice. In: Weiss, G. (ed.) Multiagent Systems. 2nd edn. MIT Press, Cambridge (2013)

    Google Scholar 

  7. Buhrman, H., Hitchcock, J.: NP-hard sets are exponentially dense unless coNP\(\,\subseteq \,\)NP/poly. In: Proceedings of the 23rd Annual IEEE Conference on Computational Complexity, pp 1–7. IEEE Computer Society Press, Los Alamitos (2008)

  8. Cai, J., Chakaravarthy, V., Hemaspaandra, L., Ogihara, M.: Competing provers yield improved Karp–Lipton collapse results. Inf. Comput. 198(1), 1–23 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. California Elections Code, Division 15/Chapter 10/Statute 15650-15673: Tie Votes. http://leginfo.legislature.ca.gov/ (2013)

  10. Chevaleyre, Y., Endriss, U., Lang, J., Maudet, N.: A short introduction to computational social choice. In: Proceedings of the 33rd International Conference on Current Trends in Theory and Practice of Computer Science, Springer-Verlag Lecture Notes in Computer Science #4362, pp 51–69 (2007)

  11. Conitzer, V., Sandholm, T.: Universal voting protocol tweaks to make manipulation hard. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence, pp 781–788. Morgan Kaufmann, San Mateo (2003)

  12. Conitzer, V., Sandholm, T.: Nonexistence of voting rules that are usually hard to manipulate. In: Proceedings of the 21st National Conference on Artificial Intelligence, pp 627–634. AAAI Press (2006)

  13. Conitzer, V., Sandholm, T., Lang, J.: When are elections with few candidates hard to manipulate?. J. ACM 54(3) (2007). Article 14

  14. Conitzer, V., Walsh, T.: Barriers to manipulation in voting. In: Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A. (eds.) Handbook of Computational Social Choice. Cambridge University Press. To appear

  15. Copeland, A.: A “reasonable” social welfare function. Mimeographed notes from Seminar on Applications of Mathematics to the Social Sciences, University of Michigan (1951)

  16. Davies, J., Narodytska, N., Walsh, T.: Eliminating the weakest link: Making manipulation intractable?. In: Proceedings of AAAI-12, pp 1333–1339. AAAI Press (2012)

  17. Elkind, E., Erdélyi, G.: Manipulation under voting rule uncertainty. In: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems, International Foundation for Autonomous Agents and Multiagent Systems, pp 624–634 (2012)

  18. Elkind, E., Lipmaa, H.: Hybrid voting protocols and hardness of manipulation. In: Proceedings of the 16th Annual International Symposium on Algorithms and Computation, Springer-Verlag Lecture Notes in Computer Science #3872, pp 206–215 (2005)

  19. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.: Using complexity to protect elections. Commun. ACM 53(11), 74–82 (2010)

    Article  Google Scholar 

  20. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: A richer understanding of the complexity of election systems. In: Fundamental Problems in Computing, pp 375–406. Springer, Berlin (2009)

  21. Faliszewski, P., Hemaspaandra, E., Schnoor, H.: Copeland voting: Ties matter. Tech. Rep. TR-926, Department of Computer Science, University of Rochester, Rochester, NY (2007)

  22. Faliszewski, P., Hemaspaandra, E., Schnoor, H.: Copeland voting: Ties matter. In: Proceedings of the 7th International Conference on Autonomous Agents and Multiagent Systems, pp 983–990 (2008)

  23. Faliszewski, P., Hemaspaandra, E., Schnoor, H.: Weighted manipulation for four-candidate Llull is easy. In: Proceedings of the 20th European Conference on Artificial Intelligence, pp 318–323. IOS Press, Amsterdam (2012)

  24. Faliszewski, P., Procaccia, A.: AI’s war on manipulation: Are we winning? AI Mag. 31(4), 53–64 (2010)

    Google Scholar 

  25. Fitzsimmons, Z., Hemaspaandra, E., Hemaspaandra, L.: X THEN X: Manipulation of same-system runoff elections. Tech. Rep., Computing Research Repository (2013). arXiv:1301.6118v1 [cs.GT]

  26. Guo, J., Shrestha, Y.: Controlling two-stage voting rules. In: Proceedings of the 21st European Conference on Artificial Intelligence, pp 411–416 (2014)

  27. Hägele, G., Pukelsheim, F.: The electoral writings of Ramon Llull. Studia Lulliana 41(97), 3–38 (2001)

    Google Scholar 

  28. Hemaspaandra, E., Hemaspaandra, L.: Dichotomy for voting systems. J. Comput. Syst. Sci. 73(1), 73–83 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  29. Hemaspaandra, E., Hemaspaandra, L., Menton, C.: Search versus decision for election manipulation problems. In: Proceedings of the 30th Annual Symposium on Theoretical Aspects of Computer Science, Leibniz International Proceedings in Informatics (LIPIcs), pp 377–388 (2013)

  30. Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Exact analysis of Dodgson elections: Lewis Carroll’s 1876 voting system is complete for parallel access to NP. J. ACM 44(6), 806–825 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  31. Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Anyone but him: The complexity of precluding an alternative. Artif. Intell. 171(5–6), 255–285 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  32. Hemaspaandra, E., Spakowski, H., Vogel, J.: The complexity of Kemeny elections. Theor. Comput. Sci. 349(3), 382–391 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  33. Hemaspaandra, L., Williams, R.: An atypical survey of typical-case heuristic algorithms. SIGACT News 43(4), 71–89 (2012)

    Article  Google Scholar 

  34. Lev, O., Rosenschein, J.: Convergence of iterative voting. In: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems, International Foundation for Autonomous Agents and Multiagent Systems, pp 611–618 (2012)

  35. McGarvey, D.: A theorem on the construction of voting paradoxes. Econometrica 21(4), 608–610 (1953)

    Article  MathSciNet  Google Scholar 

  36. Meir, R., Polukarov, M., Rosenschein, J., Jennings, N.: Convergence to equilibria in plurality voting. In: Proceedings of AAAI-10, pp 823–828. AAAI Press (2010)

  37. Narodytska, N., Walsh, T.: Manipulating two stage voting rules. In: Proceedings (Workshop Notes) of the 4th International Workshop on Computational Social Choice, pp 323–334 (2012)

  38. Narodytska, N., Walsh, T.: Manipulating two stage voting rules. In: Proceedings of the 12th International Conference on Autonomous Agents and Multiagent Systems, International Foundation for Autonomous Agents and Multiagent Systems, pp 423–430 (2013)

  39. North Carolina General Statues, Chapter 163/Article 15A/Statute 163-182.8: Elections and Election Laws. http://www.ncleg.net/ (2013)

  40. Obraztsova, S., Elkind, E.: On the complexity of voting manipulation under randomized tie-breaking. In: Proceedings of IJCAI-11, pp 319–324. AAAI Press (2011)

  41. Obraztsova, S., Elkind, E., Hazon, N.: Ties matter: Complexity of voting manipulation revisited. In: Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems, International Foundation for Autonomous Agents and Multiagent Systems, pp 71–78 (2011)

  42. Reijngoud, A., Endriss, E.: Voter response to iterated poll information. In: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems, International Foundation for Autonomous Agents and Multiagent Systems, pp 635–644 (2012)

  43. Reyhani, R., Wilson, M.: Best reply dynamics for scoring rules. In: Proceedings of the 20th European Conference on Artificial Intelligence, pp 672–677. IOS Press, Amsterdam (2012)

  44. Rothe, J., Schend, L.: Challenges to complexity shields that are supposed to protect elections against manipulation and control: A survey. Ann. Math. Artif. Intell. 68(1–3), 161–193 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  45. Rothe, J., Spakowski, H., Vogel, J.: Exact complexity of the winner problem for Young elections. Theory Comput. Syst. 36(4), 375–386 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  46. Shoham, Y., Leyton-Brown, K.: Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, Cambridge (2009)

    MATH  Google Scholar 

  47. Walsh, T.: Where are the hard manipulation problems? J. Artif. Intell. Res. 42, 1–29 (2011)

    MathSciNet  MATH  Google Scholar 

  48. Xia, L., Conitzer, V., Procaccia, A.: A scheduling approach to coalitional manipulation. In: Proceedings of the 11th ACM Conference on Electronic Commerce, pp 275–284. ACM Press (2010)

  49. Zuckerman, M., Procaccia, A., Rosenschein, J.: Algorithms for the coalitional manipulation problem. Artif. Intell. 173(2), 392–412 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Computing and Information Sciences, Rochester Institute of Technology, Rochester, NY, 14623, USA

    Zack Fitzsimmons

  2. Department of Computer Science, Rochester Institute of Technology, Rochester, NY, 14623, USA

    Edith Hemaspaandra

  3. Department of Computer Science, University of Rochester, Rochester, NY, 14627, USA

    Lane A. Hemaspaandra

Authors
  1. Zack Fitzsimmons
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  2. Edith Hemaspaandra
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  3. Lane A. Hemaspaandra
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Correspondence to Lane A. Hemaspaandra.

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Fitzsimmons, Z., Hemaspaandra, E. & Hemaspaandra, L.A. Manipulation Complexity of Same-System Runoff Elections. Ann Math Artif Intell 77, 159–189 (2016). https://doi.org/10.1007/s10472-015-9490-6

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