Computing Voting Rules with Elicited Incomplete Votes (2402.11104v2)
Abstract: Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on specific instances of this problem, our paper fully characterizes the set of positional scoring rules that can be computed for any $1 \leq t < m$, which, notably, does not include plurality. We then extend this to show a similar impossibility result for single transferable vote (elimination voting). These negative results are information-theoretic and agnostic to the number of queries. Finally, for scoring rules that are computable with limited-sized queries, we give parameterized upper and lower bounds on the number of such queries a deterministic or randomized algorithm must make to determine the score-maximizing candidate. While there is no gap between our bounds for deterministic algorithms, identifying the exact query complexity for randomized algorithms is a challenging open problem, of which we solve one special case.
- M. Bentert and P. Skowron. 2020. Comparing election methods where each voter ranks only few candidates. In Proceedings of the 34th AAAI Conference on Artificial Intelligence (AAAI). 2218–2225.
- Handbook of Computational Social Choice. Cambridge University Press.
- C. M. Burnett and V. Kogan. 2015. Ballot (and voter) “exhaustion” under Instant Runoff Voting: An examination of four ranked-choice elections. Electoral Studies 37 (2015), 41–49.
- V. Conitzer and T. Sandholm. 2005. Communication Complexity of Common Voting Rules. In Proceedings of the 6th ACM Conference on Economics and Computation (EC). 78–87.
- Less is more: The paradox of choice in voting behavior. Electoral Studies 69 (2021), 102230.
- Too much of a good thing? Longer ballots reduce voter participation. Journal of Elections, Public Opinion and Parties (2023), 1–18.
- P. Dey and A. Bhattacharyya. 2015. Sample complexity for winner prediction in elections. In Proceedings of the 14th International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS). 1421–1430.
- FairVote. 2024. Research and data on RCV in practice. https://fairvote.org/resources/data-on-rcv/
- Y. Filmus and J. Oren. 2014. Efficient Voting via the Top-k𝑘kitalic_k Elicitation Scheme: A Probabilistic Approach. In Proceedings of the 15th ACM Conference on Economics and Computation (EC). 295–312.
- P. C. Fishburn. 1977. Condorcet Social Choice Functions. SIAM J. Appl. Math. 33, 3 (1977), 469–487.
- Representation with Incomplete Votes. In Proceedings of the 37th AAAI Conference on Artificial Intelligence (AAAI). 5657–5664.
- S. Hirano and J. M. Snyder Jr. 2019. Primary elections in the United States. Cambridge University Press.
- C. Horton. 2018. The simple but ingenious system Taiwan uses to crowdsource its laws. MIT Technology Review (2018).
- S. S. Iyengar and M. R. Lepper. 2000. When choice is demotivating: Can one desire too much of a good thing? Journal of personality and social psychology 79, 6 (2000), 995.
- K. Konczak and J. Lang. 2005. Voting Procedures with Incomplete Preferences. In Proceedings of the 2nd Multidisciplinary Workshop on Advances in Preference Handling (M-PREF).
- T. Lu and C. Boutilier. 2011. Robust Approximation and Incremental Elicitation in Voting Protocols. In Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI). 287–293.
- W. H. Mills and R. C. Mullin. 1995. Coverings and packings. In Contemporary Design Theory: A Collection of Surveys, J. H. Dinitz and D. R. Stinson (Eds.). Wiley, Chapter 9.
- Efficient vote elicitation under candidate uncertainty. In Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI). 309–316.
- A. D. Procaccia. 2008. A Note on the Query Complexity of the Condorcet Winner Problem. Inform. Process. Lett. 108, 6 (2008), 390–393.
- A. D. Procaccia and J. S. Rosenschein. 2006. The Distortion of Cardinal Preferences in Voting. In Proceedings of the 10th International Workshop on Cooperative Information Agents (CIA). 317–331.
- B. Schwartz. 2004. The paradox of choice: Why more is less. Harper Perennial.
- Polis: Scaling Deliberation by Mapping High Dimensional Opinion Spaces. Revista De Pensament I Anàlisi 26, 2 (2021).
- L. Xia and V. Conitzer. 2011. Determining Possible and Necessary Winners Given Partial Orders. Journal of Artificial Intelligence Research 41 (2011), 25–67.
- A. C. Yao. 1977. Probabilistic Computations: Towards a Unified Measure of Complexity. In Proceedings of the 17th Symposium on Foundations of Computer Science (FOCS). 222–227.
- H. P. Young. 1975. Social Choice Scoring Functions. SIAM Journal of Applied Mathematics 28, 4 (1975), 824–838.
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