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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 36 / No. 5: AAAI-22 Technical Tracks 5

Dimensionality and Coordination in Voting: The Distortion of STV

February 1, 2023

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Authors

Ioannis Anagnostides

Carnegie Mellon University


Dimitris Fotakis

National Technical University of Athens


Panagiotis Patsilinakos

National Technical University of Athens


DOI:

10.1609/aaai.v36i5.20404


Abstract:

We study the performance of voting mechanisms from a utilitarian standpoint, under the recently introduced framework of metric-distortion, offering new insights along two main lines. First, if d represents the doubling dimension of the metric space, we show that the distortion of STV is O(d log log m), where m represents the number of candidates. For doubling metrics this implies an exponential improvement over the lower bound for general metrics, and as a special case it effectively answers a question left open by Skowron and Elkind (AAAI '17) regarding the distortion of STV under low-dimensional Euclidean spaces. More broadly, this constitutes the first nexus between the performance of any voting rule and the ``intrinsic dimensionality'' of the underlying metric space. We also establish a nearly-matching lower bound, refining the construction of Skowron and Elkind. Moreover, motivated by the efficiency of STV, we investigate whether natural learning rules can lead to low-distortion outcomes. Specifically, we introduce simple, deterministic and decentralized exploration/exploitation dynamics, and we show that they converge to a candidate with O(1) distortion.

Topics: AAAI

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HOW TO CITE:

Ioannis Anagnostides||Dimitris Fotakis||Panagiotis Patsilinakos Dimensionality and Coordination in Voting: The Distortion of STV Proceedings of the AAAI Conference on Artificial Intelligence (2022) 4776-4784.

Ioannis Anagnostides||Dimitris Fotakis||Panagiotis Patsilinakos Dimensionality and Coordination in Voting: The Distortion of STV AAAI 2022, 4776-4784.

Ioannis Anagnostides||Dimitris Fotakis||Panagiotis Patsilinakos (2022). Dimensionality and Coordination in Voting: The Distortion of STV. Proceedings of the AAAI Conference on Artificial Intelligence, 4776-4784.

Ioannis Anagnostides||Dimitris Fotakis||Panagiotis Patsilinakos. Dimensionality and Coordination in Voting: The Distortion of STV. Proceedings of the AAAI Conference on Artificial Intelligence 2022 p.4776-4784.

Ioannis Anagnostides||Dimitris Fotakis||Panagiotis Patsilinakos. 2022. Dimensionality and Coordination in Voting: The Distortion of STV. "Proceedings of the AAAI Conference on Artificial Intelligence". 4776-4784.

Ioannis Anagnostides||Dimitris Fotakis||Panagiotis Patsilinakos. (2022) "Dimensionality and Coordination in Voting: The Distortion of STV", Proceedings of the AAAI Conference on Artificial Intelligence, p.4776-4784

Ioannis Anagnostides||Dimitris Fotakis||Panagiotis Patsilinakos, "Dimensionality and Coordination in Voting: The Distortion of STV", AAAI, p.4776-4784, 2022.

Ioannis Anagnostides||Dimitris Fotakis||Panagiotis Patsilinakos. "Dimensionality and Coordination in Voting: The Distortion of STV". Proceedings of the AAAI Conference on Artificial Intelligence, 2022, p.4776-4784.

Ioannis Anagnostides||Dimitris Fotakis||Panagiotis Patsilinakos. "Dimensionality and Coordination in Voting: The Distortion of STV". Proceedings of the AAAI Conference on Artificial Intelligence, (2022): 4776-4784.

Ioannis Anagnostides||Dimitris Fotakis||Panagiotis Patsilinakos. Dimensionality and Coordination in Voting: The Distortion of STV. AAAI[Internet]. 2022[cited 2023]; 4776-4784.


ISSN: 2374-3468


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Copyright 2022, Association for the Advancement of
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