Abstract
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.
This work has been supported by the Swiss National Science Foundation under contract number 200021_165522 and by the European Research Council (ERC) under grant number 639945 (ACCORD).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Pareto efficiency usually requires that there is no other alternative who all voters weakly prefer and who one voter strictly prefers. We use the strict definition in our proofs, as it is also without loss of generality with respect to distortion.
References
Anshelevich, E., Bhardwaj, O., Elkind, E., Postl, J., Skowron, P.: Approximating optimal social choice under metric preferences. Artif. Intell. 264, 27–51 (2018)
Anshelevich, E., Postl, J.: Randomized social choice functions under metric preferences. J. Artif. Intell. Res. 58, 797–827 (2017)
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)
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)
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)
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)
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)
Caragiannis, I., Nath, S., Procaccia, A.D., Shah, N.: Subset selection via implicit utilitarian voting. J. Artif. Intell. Res. 58, 123–152 (2017)
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)
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). https://doi.org/10.1007/978-3-319-23114-3_24
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)
Filos-Ratsikas, A., Micha, E., Voudouris, A.A.: The distortion of distributed voting. CoRR abs/1905.01882 (2019)
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). https://doi.org/10.1007/978-3-319-13129-0_13
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)
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)
Goldberg, K., Roeder, T., Gupta, D., Perkins, C.: Eigentaste: a constant time collaborative filtering algorithm. Inf. Retrieval 4, 133–151 (2001)
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)
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)
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)
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)
Pierczynski, G., Skowron, P.: Approval-based elections and distortion of voting rules. CoRR abs/1901.06709 (2019)
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). https://doi.org/10.1007/11839354_23
Schuck, P.H.: The thickest thicket: partisan gerrymandering and judicial regulation of politics. Columbia Law Rev. 87(7), 1325–1384 (1987)
Wikipedia: 2016 United States presidential election (2016). https://en.wikipedia.org/wiki/2016_United_States_presidential_election
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Filos-Ratsikas, A., Micha, E., Voudouris, A.A. (2019). The Distortion of Distributed Voting. In: Fotakis, D., Markakis, E. (eds) Algorithmic Game Theory. SAGT 2019. Lecture Notes in Computer Science(), vol 11801. Springer, Cham. https://doi.org/10.1007/978-3-030-30473-7_21
Download citation
DOI: https://doi.org/10.1007/978-3-030-30473-7_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-30472-0
Online ISBN: 978-3-030-30473-7
eBook Packages: Computer ScienceComputer Science (R0)