An impossibility result for strongly group-strategyproof multi-winner approval-based voting (2402.08746v1)
Abstract: Multi-winner approval-based voting has received considerable attention recently. A voting rule in this setting takes as input ballots in which each agent approves a subset of the available alternatives and outputs a committee of alternatives of given size $k$. We consider the scenario when a coalition of agents can act strategically and alter their ballots so that the new outcome is strictly better for a coalition member and at least as good for anyone else in the coalition. Voting rules that are robust against this strategic behaviour are called strongly group-strategyproof. We prove that, for $k\in {1,2, ..., m-2}$, strongly group-strategyproof multi-winner approval-based voting rules which furthermore satisfy the minimum efficiency requirement of unanimity do not exist, where $m$ is the number of available alternatives. Our proof builds a connection to single-winner voting with ranking-based ballots and exploits the infamous Gibbard-Satterthwaite theorem to reach the desired impossibility result. Our result has implications for paradigmatic problems from the area of approximate mechanism design without money and indicates that strongly group-strategyproof mechanisms for minimax approval voting, variants of facility location, and classification can only have an unbounded approximation ratio.
- Strategyproof approximation of the minimax on networks. Mathematics of Operations Research 35, 3 (2010), 513–526.
- Haris Aziz and Nisarg Shah. 2021. Participatory budgeting: Models and approaches. In Pathways Between Social Science and Computational Social Science: Theories, Methods, and Interpretations, Tamás Rudas and Gábor Péli (Eds.). Springer International Publishing, 215–236.
- Individual versus group strategy-proofness: When do they coincide? Journal of Economic Theory 145, 5 (2010), 1648–1674.
- Group strategy-proof social choice functions with binary ranges and arbitrary domains: Characterization results. International Journal of Game Theory 41 (2011), 791–808.
- Generalized median voter schemes and committees. Journal of Economic Theory 61, 2 (1993), 262–289.
- Avraham Beja. 1993. Arrow and Gibbard-Satterthwaite revisited: Extended domains and shorter proofs. Mathematical Social Sciences 25, 3 (1993), 281–286.
- A minimax procedure for electing committees. Public Choice 132, 3/4 (2007), 401–420.
- Jaroslaw Byrka and Krzysztof Sornat. 2014. PTAS for minimax approval voting. In Proceedings of the 10th International Conference on Web and Internet Economics (WINE). 203–217.
- Approximation algorithms and mechanism design for minimax approval voting. In Proceedings of the 24th AAAI Conference on Artificial Intelligence (AAAI). 737–742.
- Facility location with double-peaked preferences. Autonomous Agents & Multi Agent Systems 31, 6 (2017), 1209–1235.
- Allan Gibbard. 1973. Manipulation of voting schemes. Econometrica 41, 4 (1973), 587–602.
- Mechanism design for constrained heterogeneous facility location. In Proceedings of the 12th International Symposium on Algorithmic Game Theory (SAGT). 63–76.
- Martin Lackner and Piotr Skowron. 2023. Multi-Winner Voting with Approval Preferences. Springer.
- Michel Le Breton and Vera Zaporozhets. 2009. On the equivalence of coalitional and individual strategy-proofness properties. Social Choice and Welfare 33, 2 (2009), 287–309.
- Some results on approximating the minimax solution in approval voting. In Proceedings of the 6th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS). 1193–1195.
- Asymptotically optimal strategy-proof mechanisms for two-facility games. In Proceedings 11th ACM Conference on Electronic Commerce (EC). 315–324.
- Vikram Manjunath. 2012. Group strategy-proofness and voting between two alternatives. Mathematical Social Sciences 63, 3 (2012), 239–242.
- Tight bounds for strategyproof classification. In Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS). 319–326.
- Algorithms for strategyproof classification. Artificial Intelligence 186 (2012), 123–156.
- Herve Moulin. 1980. On strategy-proofness and single peakedness. Public Choice 35, 4 (1980), 437–455.
- Ariel D. Procaccia and Moshe Tennenholtz. 2013. Approximate mechanism design without money. ACM Transactions on Economics and Computation 1, 4 (2013), 18:1–18:26.
- Simon Rey and Jan Maly. 2023. The (computational) social choice take on indivisible participatory budgeting. CoRR abs/2303.00621 (2023).
- Mark Allen Satterthwaite. 1975. Strategy-proofness and Arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory 10, 2 (1975), 187–217.
- James Schummer and Rakesh V. Vohra. 2002. Strategy-proof location on a network. Journal of Economic Theory 104, 2 (2002), 405–428.
- Xin Sui and Craig Boutilier. 2015. Approximately strategy-proof mechanisms for (constrained) facility location. In Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems (AAMAS). 605–613.
- Nimrod Talmon. 2023. Social choice around decentralized autonomous organizations: On the computational social choice of digital communities. In Proceedings of the 22nd International Conference on Autonomous Agents and Multiagent Systems (AAMAS). 1768–1773.
- Toby Walsh. 2021. Strategy proof mechanisms for facility location at limited locations. In Proceedings of the 18th Pacific Rim International Conference on Artificial Intelligence (PRICAI). 113–124.