Skip to main content

Advertisement

SpringerLink
Log in

Electoral manipulation via influence: probabilistic model

  • Published:
Autonomous Agents and Multi-Agent Systems Aims and scope Submit manuscript

Abstract

We consider a natural generalization of the fundamental electoral manipulation problem, where a briber can change the opinion or preference of voters through influence. This is motivated by modern political campaigns where candidates try to convince voters through media such as TV, newspaper, Internet. Compared with the classical bribery problem, we do not assume the briber will directly exchange money for votes from individual voters, but rather assume that the briber has a set of potential campaign strategies. Each campaign strategy represents some way of casting influence on voters. A campaign strategy has some cost and can influence a subset of voters. If a voter belongs to the audience of a campaign strategy, then he/she will be influenced. A voter will be more likely to change his/her opinion/preference if he/she has received influence from a larger number of campaign strategies. We model this through an independent activation model which is widely adopted in social science research and study the computational complexity. In this paper, we give a full characterization by showing NP-hardness results and establishing a near-optimal fixed-parameter tractable algorithm that gives a solution arbitrarily close to the optimal solution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. It is arguable whether we can have a complete input regarding voters’ preferences. As a common assumption in computational social choice, this is a simplified modeling of the information obtained from (for example) pre-election polls or surveys.

  2. Kernelization is a frequently used technique in the field of fixed parameter tractable algorithms which refers to the input length of the problem can be reduced to FPT size with respect to the parameter(s) of the problem. Here, the term “half-kernelization” refers to that part of the input length of the problem can be reduced to FPT size with respect to the parameter(s) of the problem. We will give the specific meaning when we introduce it in Sect. 4.1.3.

  3. Our techniques can be easily modified to handle the case when co-winner is not allowed.

  4. The definition of designated-agreeable is given in the paragraph “Our Contribution”.

  5. Throughout the following, by saying \(O(\epsilon )\)-loss in the objective value we mean there exists a solution with an objective value of at least \(1-O(\epsilon )\) fraction of the optimal value.

  6. If co-winner is not allowed, we can simply replace k with \(k+1\)

  7. if co-winner is not allowed, we can simply replace k with \(k+1\)

References

  1. Bredereck, R., Faliszewski, P., Niedermeier, R., & Talmon, N. (2016). Large-scale election campaigns: Combinatorial shift bribery. Journal of Artificial Intelligence Research, 55, 603–652.

    Article  MathSciNet  MATH  Google Scholar 

  2. Faliszewski, P., Manurangsi, P., & Sornat, K. (2021). Approximation and hardness of shift-bribery. Artificial Intelligence, 298, 103520.

    Article  MathSciNet  MATH  Google Scholar 

  3. Kaczmarczyk, A., & Faliszewski, P. (2019). Algorithms for destructive shift bribery. Autonomous Agents and Multi-Agent Systems, 33(3), 275–297.

    Article  Google Scholar 

  4. Knop, D., Kouteckỳ, M., & Mnich, M. (2020). Voting and bribing in single-exponential time. ACM Transactions on Economics and Computation, 8(3), 1–28.

    Article  MathSciNet  MATH  Google Scholar 

  5. Zhang, H., Mishra, S., Thai, M. T., Wu, J., & Wang, Y. (2014). Recent advances in information diffusion and influence maximization in complex social networks. Opportunistic Mobile Social Networks, 37(1.1), 37.

    Article  Google Scholar 

  6. Courgeau, D. (2012). Probability and social science: Methodological relationships between the two approaches. Berlin: Springer.

    Book  MATH  Google Scholar 

  7. Wyer, R. S. (1970). Quantitative prediction of belief and opinion change: A further test of a subjective probability model. Journal of Personality and Social Psychology, 16(4), 559.

    Article  Google Scholar 

  8. Arieli, I., & Babichenko, Y. (2019). Private Bayesian persuasion. Journal of Economic Theory, 182, 185–217.

    Article  MathSciNet  MATH  Google Scholar 

  9. Balachandran, V., & Deshmukh, S. (1976). A stochastic model of persuasive communication. Management Science, 22(8), 829–840.

    Article  MathSciNet  MATH  Google Scholar 

  10. Tsakas, E., Tsakas, N., Xefteris, D. (2021). Resisting persuasion. Economic Theory, 1–20

  11. Elkind, E., Faliszewski, P., Slinko, A. (2009). Swap bribery. In Proceedings of the 2nd international symposium on algorithmic game theory, pp. 299–310. Springer

  12. Elkind, E., Faliszewski, P. (2010). Approximation algorithms for campaign management. In Internet and network economics, pp. 473–482

  13. Faliszewski, P., Hemaspaandra, E., & Hemaspaandra, L. A. (2009). How hard is bribery in elections? Journal of Artificial Intelligence Research, 35, 485–532.

    Article  MathSciNet  MATH  Google Scholar 

  14. Chen, L., Xu, L., Xu, S., Gao, Z., Shi, W. (2019). Election with bribed voter uncertainty: Hardness and approximation algorithm. In Proceedings of 33rd the AAAI conference on artificial intelligence

  15. Bredereck, R., Chen, J., Faliszewski, P., Nichterlein, A., & Niedermeier, R. (2016). Prices matter for the parameterized complexity of shift bribery. Information and Computation, 251, 140–164.

    Article  MathSciNet  MATH  Google Scholar 

  16. Bredereck, R., Faliszewski, P., Niedermeier, R., Talmon, N. (2016). Complexity of shift bribery in committee elections. In Proceedings of the 30th AAAI conference on artificial intelligence, pp. 2452–2458

  17. Brelsford, E., Faliszewski, P., Hemaspaandra, E., Schnoor, H., Schnoor, I. (2008). Approximability of manipulating elections. In Proceedings of the 23rd AAAI conference on artificial intelligence, vol. 1, pp. 44–49

  18. Xia, L. (2012). Computing the margin of victory for various voting rules. In Proceedings of the 13th ACM conference on electronic commerce, pp. 982–999

  19. Faliszewski, P., Reisch, Y., Rothe, J., & Schend, L. (2015). Complexity of manipulation, bribery, and campaign management in Bucklin and Fallback voting. Autonomous Agents and Multi-Agent Systems, 29(6), 1091–1124.

    Article  Google Scholar 

  20. Faliszewski, P., Hemaspaandra, E., & Hemaspaandra, L. A. (2011). Multimode control attacks on elections. Journal of Artificial Intelligence Research, 40, 305–351.

    Article  MathSciNet  MATH  Google Scholar 

  21. Parkes, D.C., Xia, L. (2012). A complexity-of-strategic-behavior comparison between Schulze’s rule and ranked pairs. In Proceedings of the 26th AAAI conference on artificial intelligence, pp. 1429–1435

  22. Magrino, T.R., Rivest, R.L., Shen, E., Wagner, D. (2011). Computing the margin of victory in IRV elections. In Proceedings of the 2011 conference on electronic voting technology/workshop on trustworthy elections, p. 4

  23. Dey, P., Narahari, Y. (2015). Estimating the margin of victory of an election using sampling. In Proceedings of the 24th international joint conference on artificial intelligence

  24. Reisch, Y., Rothe, J., Schend, L. (2014). The margin of victory in Schulze, cup, and Copeland elections: Complexity of the regular and exact variants. In Proceedings of the 7th European starting AI researcher symposium, pp. 250–259

  25. Hobolt, S. B., Spoon, J.-J., & Tilley, J. (2009). A vote against Europe? Explaining defection at the 1999 and 2004 European parliament elections. British Journal of Political Science, 39(1), 93–115.

    Article  Google Scholar 

  26. Wojtas, K., Faliszewski, P. (2012). Possible winners in noisy elections. In Proceedings of the 26th AAAI conference on artificial intelligence, pp. 1499–1505

  27. Erdelyi, G., Hemaspaandra, E., Hemaspaandra, L. A. (2014). Bribery and voter control under voting-rule uncertainty. In Proceedings of the 13th international conference on autonomous agents and multiagent systems, pp. 61–68

  28. Mattei, N., Goldsmith, J., Klapper, A., & Mundhenk, M. (2015). On the complexity of bribery and manipulation in tournaments with uncertain information. Journal of Applied Logic, 13(4), 557–581.

    Article  MathSciNet  MATH  Google Scholar 

  29. Erdélyi, G., Fernau, H., Goldsmith, J., Mattei, N., Raible, D., Rothe, J. (2009). The complexity of probabilistic lobbying. In Proceedings of the 1st international conference on algorithmic decision theory, pp. 86–97

  30. Chen, L., Xu, L., Xu, S., Gao, Z., Shi, W. (2019). Election with bribe-effect uncertainty: A dichotomy result. In Proceedings of the 28th international joint conference on artificial intelligence

  31. Endriss, U. (2017). Trends in computational social choice.

  32. Wilder, B., Vorobeychik, Y. (2018). Controlling elections through social influence. In Proceedings of the 17th international conference on autonomous agents and multiagent systems, pp. 265–273

  33. Faliszewski, P., Gonen, R., Kouteckỳ, M., Talmon, N. (2018). Pinion diffusion and campaigning on society graphs. In Proceedings of the 27th international joint conference on artificial intelligence, pp. 219–225

  34. Bredereck, R., Elkind, E. (2017). Manipulating opinion diffusion in social networks. In Proceedings of the 26th international joint conference on artificial intelligence, pp. 894–900

  35. Talmon, N. (2018). Structured proportional representation. Theoretical Computer Science, 708, 58–74.

    Article  MathSciNet  MATH  Google Scholar 

  36. Mitzenmacher, M., Upfal, E. (2005). Probability and computing: Randomized algorithms and probabilistic analysis.

  37. Lin, A. (2011). The complexity of manipulating \(\kappa \)-approval elections. In Proceedings of the 3rd international conference on agents and artificial intelligence, vol. 2, pp. 212–218

  38. Yao, A. C. (1980). New algorithms for bin packing. Journal of the ACM, 27(2), 207–227.

    Article  MathSciNet  MATH  Google Scholar 

  39. Bredereck, R., Faliszewski, P., Niedermeier, R., Skowron, P., & Talmon, N. (2020). Mixed integer programming with convex/concave constraints: Fixed-parameter tractability and applications to multicovering and voting. Theoretical Computer Science, 814, 86–105.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Research of Liangde Tao was partly supported by “New Generation of AI 2030" Major Project (2018AAA0100902). Research of Lin Chen was partly supported by NSF Grant 2004096. Research of Shouhuai Xu was partly supported by Colorado State Bill 18-086. Research of Weidong Shi was partly supported by NSF Grant 1433817.

Author information

Authors and Affiliations

  1. Zhejiang University, Hangzhou, China

    Liangde Tao

  2. Texas Tech University, Lubbock, USA

    Lin Chen

  3. Kent State University, Kent, USA

    Lei Xu

  4. University of Colorado Colorado Springs, Colorado Springs, USA

    Shouhuai Xu

  5. University of Houston, Houston, USA

    Zhimin Gao & Weidong Shi

Authors
  1. Liangde Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lin Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lei Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shouhuai Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhimin Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Weidong Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lin Chen.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tao, L., Chen, L., Xu, L. et al. Electoral manipulation via influence: probabilistic model. Auton Agent Multi-Agent Syst 37, 18 (2023). https://doi.org/10.1007/s10458-023-09602-z

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10458-023-09602-z

Keywords

Search

Navigation