The Distortion of Distributed Voting

  • Aris Filos-Ratsikas
  • Evi Micha
  • Alexandros A. VoudourisEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11801)


Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the voting process on the societal welfare for the outcome, by bounding the distortion of voting rules. Even though there has been significant progress towards this goal, all previous works have so far neglected the fact that in many scenarios (like presidential elections) voting is actually a distributed procedure. In this paper, we consider a setting in which the voters are partitioned into disjoint districts and vote locally therein to elect local winning alternatives using a voting rule; the final outcome is then chosen from the set of these alternatives. We prove tight bounds on the distortion of well-known voting rules for such distributed elections both from a worst-case perspective as well as from a best-case one. Our results indicate that the partition of voters into districts leads to considerably higher distortion, a phenomenon which we also experimentally showcase using real-world data.


Distributed voting District-based elections Distortion 


  1. 1.
    Anshelevich, E., Bhardwaj, O., Elkind, E., Postl, J., Skowron, P.: Approximating optimal social choice under metric preferences. Artif. Intell. 264, 27–51 (2018)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Anshelevich, E., Postl, J.: Randomized social choice functions under metric preferences. J. Artif. Intell. Res. 58, 797–827 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bachrach, Y., Lev, O., Lewenberg, Y., Zick, Y.: Misrepresentation in district voting. In: Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI), pp. 81–87 (2016)Google Scholar
  4. 4.
    Benade, G., Nath, S., Procaccia, A.D., Shah, N.: Preference elicitation for participatory budgeting. In: Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI), pp. 376–382 (2017)Google Scholar
  5. 5.
    Bhaskar, U., Dani, V., Ghosh, A.: Truthful and near-optimal mechanisms for welfare maximization in multi-winner elections. In: Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI), pp. 925–932 (2018)Google Scholar
  6. 6.
    Borodin, A., Lev, O., Shah, N., Strangway, T.: Big city vs. the great outdoors: voter distribution and how it affects gerrymandering. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI), pp. 98–104 (2018)Google Scholar
  7. 7.
    Boutilier, C., Caragiannis, I., Haber, S., Lu, T., Procaccia, A.D., Sheffet, O.: Optimal social choice functions: a utilitarian view. Artif. Intell. 227, 190–213 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Caragiannis, I., Nath, S., Procaccia, A.D., Shah, N.: Subset selection via implicit utilitarian voting. J. Artif. Intell. Res. 58, 123–152 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Cohen-Zemach, A., Lewenberg, Y., Rosenschein, J.S.: Gerrymandering over graphs. In: Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp. 274–282 (2018)Google Scholar
  10. 10.
    Erdélyi, G., Hemaspaandra, E., Hemaspaandra, L.A.: More natural models of electoral control by partition. In: Walsh, T. (ed.) ADT 2015. LNCS (LNAI), vol. 9346, pp. 396–413. Springer, Cham (2015). Scholar
  11. 11.
    Feldman, M., Fiat, A., Golomb, I.: On voting and facility location. In: Proceedings of the 17th ACM Conference on Economics and Computation (EC), pp. 269–286 (2016)Google Scholar
  12. 12.
    Filos-Ratsikas, A., Micha, E., Voudouris, A.A.: The distortion of distributed voting. CoRR abs/1905.01882 (2019)Google Scholar
  13. 13.
    Filos-Ratsikas, A., Miltersen, P.B.: Truthful approximations to range voting. In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 175–188. Springer, Cham (2014). Scholar
  14. 14.
    Goel, A., Hulett, R., Krishnaswamy, A.K.: Relating metric distortion and fairness of social choice rules. In: Proceedings of the 13th Workshop on the Economics of Networks, Systems and Computation (NetEcon), p. 4:1 (2018)Google Scholar
  15. 15.
    Goel, A., Krishnaswamy, A.K., Munagala, K.: Metric distortion of social choice rules: lower bounds and fairness properties. In: Proceedings of the 18th ACM Conference on Economics and Computation (EC), pp. 287–304 (2017)Google Scholar
  16. 16.
    Goldberg, K., Roeder, T., Gupta, D., Perkins, C.: Eigentaste: a constant time collaborative filtering algorithm. Inf. Retrieval 4, 133–151 (2001)CrossRefGoogle Scholar
  17. 17.
    Gross, S., Anshelevich, E., Xia, L.: Vote until two of you agree: mechanisms with small distortion and sample complexity. In: Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI), pp. 544–550 (2017)Google Scholar
  18. 18.
    Lesser, O., Naamani-Dery, L., Kalech, M., Elovici, Y.: Group decision support for leisure activities using voting and social networks. Group Decis. Negot. 26(3), 473–494 (2017)CrossRefGoogle Scholar
  19. 19.
    Lev, O., Lewenberg, Y.: “reverse gerrymandering”: a decentralized model for multi-group decision making. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI) (2019)Google Scholar
  20. 20.
    Lewenberg, Y., Lev, O., Rosenschein, J.S.: Divide and conquer: using geographic manipulation to win district-based elections. In: Proceedings of the 16th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp. 624–632 (2017)Google Scholar
  21. 21.
    Pierczynski, G., Skowron, P.: Approval-based elections and distortion of voting rules. CoRR abs/1901.06709 (2019)Google Scholar
  22. 22.
    Procaccia, A.D., Rosenschein, J.S.: The distortion of cardinal preferences in voting. In: Klusch, M., Rovatsos, M., Payne, T.R. (eds.) CIA 2006. LNCS (LNAI), vol. 4149, pp. 317–331. Springer, Heidelberg (2006). Scholar
  23. 23.
    Schuck, P.H.: The thickest thicket: partisan gerrymandering and judicial regulation of politics. Columbia Law Rev. 87(7), 1325–1384 (1987)CrossRefGoogle Scholar
  24. 24.
    Wikipedia: 2016 United States presidential election (2016).

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Aris Filos-Ratsikas
    • 1
  • Evi Micha
    • 2
  • Alexandros A. Voudouris
    • 3
    Email author
  1. 1.École polytechnique fédérale de LausanneLausanneSwitzerland
  2. 2.University of TorontoTorontoCanada
  3. 3.University of OxfordOxfordUK

Personalised recommendations