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Bribery in voting with CP-nets

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Abstract

We investigate the computational complexity of finding optimal bribery schemes in voting domains where the candidate set is the Cartesian product of a set of variables and voters use CP-nets, an expressive and compact way to represent preferences. To do this, we generalize the traditional bribery problem to take into account several issues over which agents vote, and their inter-dependencies. We consider five voting rules, three kinds of bribery actions, and five cost schemes. For most of the combinations of these parameters, we find that bribery in this setting is computationally easy.

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References

  1. Ahuja, R., Magnanti, T., Orlin, J.: Network Flows: Theory, Algorithms, and Applications. Prentice Hall (1993)

  2. Arrow, K.J.: Social Choice and Individual Values. Wiley (1963)

  3. Arrow, K.J., Sen, A.K., Suzumura, K.: Handbook of Social Choice and Welfare. Elsevier, North-Holland (2002)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Birrell, E., Pass, R.: Approximately strategy-proof voting. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011), pp. 67–72 (2011)

  6. Boutilier, C., Bacchus, F., Brafman, R.: UCP-networks: a directed graphical representation of conditional utilities. In: Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence (UAI 2001), pp. 56–64 (2001)

  7. Boutilier, C., Brafman, R.I., Domshlak, C., Hoos, H.H., Poole, D.: CP-nets: a tool for representing and reasoning with conditional ceteris paribus preference statements. J. Artif. Intell. Res. 21(1), 135–191 (2004)

    MATH  MathSciNet  Google Scholar 

  8. Brafman, R.I., Rossi, F., Salvagnin, D., Venable, K.B., Walsh, T.: Finding the next solution in constraint- and preference-based knowledge representation formalisms. In: Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning (KR 2010) (2010)

  9. Brams, S., Kilgour, D., Zwicker, W.: The paradox of multiple elections. Soc. Choice Welf. 15(2), 211–236 (1998)

    Article  MATH  Google Scholar 

  10. Brandt, F., Conitzer, V., Endriss, U.: Computational social choice. In: Weiss, G. (ed.) Multiagent Systems. MIT Press (2012)

  11. Christian, R., Fellows, M., Rosamond, F., Slinko, A.: On complexity of lobbying in multiple referenda. Rev. Econ. Des. 11(3), 217–224 (2007)

    MATH  MathSciNet  Google Scholar 

  12. Conitzer, V., Lang, J., Xia, L.: How hard is it to control sequential elections via the agenda? In: Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI 2009), pp. 103–108 (2009)

  13. Conitzer, V., Sandholm, T., Lang, J.: When are elections with few candidates hard to manipulate? JACM 54(3), 1–33 (2007)

    MathSciNet  Google Scholar 

  14. Conitzer, V., Xia, L.: Approximating common voting rules by sequential voting in multi-issue domains. In: Proc. International Symposium on Artificial Intelligence and Mathematics (ISAIM 2012)—Special Session on Computational Social Choice (2012)

  15. Dorn, B., Schlotter, I.: Multivariate complexity analysis of swap bribery. Algorithmica 64, 126–151 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  16. Downey, R., Fellows, M.: Parameterized Complexity. Springer (1999)

  17. Elkind, E., Faliszewski, P.: Approximation algorithms for campaign management. In: Proceedings of the 6th International Workshop on Internet and Network Economics (WINE 2010), pp. 473–482 (2010)

  18. Elkind, E., Faliszewski, P., Slinko, A.: Swap bribery. Algorithmic Game Theory, pp. 299–310 (2009)

  19. Erdélyi, G., Fernau, H., Goldsmith, J., Mattei, N., Raible, D., Rothe, J.: The complexity of probabilistic lobbying. In: Proc. 1st International Conference on Algorithmic Decision Theory (ADT 2009), pp. 86–97 (2009)

  20. Faliszewski, P.: Nonuniform bribery. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2008), pp. 1569–1572 (2008)

  21. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.: How hard is bribery in elections? J. Artif. Intell. Res. 35, 485–532 (2009)

    MATH  MathSciNet  Google Scholar 

  22. Faliszewski, P., Hemaspaandra, E., Schnoor, H.: Copeland voting: ties matter. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2008) (2008)

  23. Gibbard, A.: Manipulation of voting schemes: a general result. Econometrica 41(4), 587–601 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  24. Lang, J.: Vote and aggregation in combinatorial domains with structured preferences. In: Proceedings of the 20nd International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 1366–1371 (2007)

  25. Lang, J., Pini, M.S., Rossi, F., Salvagnin, D., Venable, K.B., Walsh, T.: Winner determination in voting trees with incomplete preferences and weighted votes. JAAMAS 25(1), 130–157 (2012)

    Google Scholar 

  26. Lang, J., Pini, M.S., Rossi, F., Venable, K.B., Walsh, T.: Winner determination in sequential majority voting. In: Proceedings of the 20nd International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 1372–1377 (2007)

  27. Lang, J., Xia, L.: Sequential composition of voting rules in multi-issue domains. Math. Soc. Sci. 57(3), 304–324 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  28. Magrino, T., Rivest, R., Shen, E., Wagner, D.: Computing the margin of victory in IRV elections. In: Proc. Electronic Voting Technology Workshop/Workshop on Trustworthy Elections (2011)

  29. Mattei, N., Pini, M.S., Rossi, F., Venable, K.B.: Bribery in voting over combinatorial domains is easy. In: Proceedings of the 11th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2012), pp. 1407–1408 (2012) (Extended Abstract)

  30. May, K.: A set of independent necessary and sufficient conditions for simple majority decisions. Econometrica 20(4), 680–684 (1952)

    Article  MATH  Google Scholar 

  31. Obraztsova, S., Elkind, E.: On the complexity of voting manipulation under randomized tie-breaking. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011), pp. 319–324 (2011)

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

  33. Pini, M.S., Rossi, F., Venable, K.B., Walsh, T.: Incompleteness and incomparability in preference aggregation. In: Proceedings of the 20nd International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 1464–1469 (2007)

  34. Pini, M.S., Rossi, F., Venable, K.B., Walsh, T.: Incompleteness and incomparability in preference aggregation: complexity results. Artif. Intell. 175(7–8), 1272–1289 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  35. Pini, M.S., Rossi, F., Venable, K.B., Walsh, T.: Possible and necessary winners in voting trees: majority graphs vs. profiles. In: Proceedings of the 10th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), pp. 311–318 (2011)

  36. Satterthwaite, M.: Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J. Econ. Theory 10(2), 187–216 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  37. Xia, L.: Computing the margin of victory for various voting rules. In: Proceedings of the 13th ACM Conference on Electronic Commerce (EC 2012), pp. 982–999 (2012)

  38. Xia, L., Conitzer, V.: Strategy-proof voting rules over multi-issue domains with restricted preferences. In: Proceedings of the 6th International Workshop on Internet and Network Economics (WINE 2010), pp. 402–414 (2010)

  39. Xia, L., Conitzer, V.: Determining possible and necessary winners given partial orders. J. Artif. Intell. Res. 41, 25–67 (2011)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. NICTA and University of New South Wales, Sydney, Australia

    Nicholas Mattei

  2. Department of Information Engineering, University of Padova, Padova, Italy

    Maria Silvia Pini

  3. Department of Mathematics, University of Padova, Padova, Italy

    Francesca Rossi

  4. Department of Computer Science, Tulane University and IHMC, New Orleans, LA, USA

    K. Brent Venable

Authors
  1. Nicholas Mattei
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  2. Maria Silvia Pini
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  3. Francesca Rossi
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  4. K. Brent Venable
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Correspondence to Nicholas Mattei.

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Mattei, N., Pini, M.S., Rossi, F. et al. Bribery in voting with CP-nets. Ann Math Artif Intell 68, 135–160 (2013). https://doi.org/10.1007/s10472-013-9330-5

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  • DOI: https://doi.org/10.1007/s10472-013-9330-5

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