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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 29 / No.1: The Twenty-Ninth Conference on Artificial Intelligence

Approximating Optimal Social Choice under Metric Preferences

March 8, 2023

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Abstract:

We examine the quality of social choice mechanisms using a utilitarian view, in which all of the agents have costs for each of the possible alternatives. While these underlying costs determine what the optimal alternative is, they may be unknown to the social choice mechanism; instead the mechanism must decide on a good alternative based only on the ordinal preferences of the agents which are induced by the underlying costs. Due to its limited information, such a social choice mechanism cannot simply select the alternative that minimizes the total social cost (or minimizes some other objective function). Thus, we seek to bound the distortion: the worst-case ratio between the social cost of the alternative selected and the optimal alternative. Distortion measures how good a mechanism is at approximating the alternative with minimum social cost, while using only ordinal preference information. The underlying costs can be arbitrary, implicit, and unknown; our only assumption is that the agent costs form a metric space, which is a natural assumption in many settings. We quantify the distortion of many well-known social choice mechanisms. We show that for both total social cost and median agent cost, many positional scoring rules have large distortion, while on the other hand Copeland and similar mechanisms perform optimally or near-optimally, always obtaining a distortion of at most 5. We also give lower bounds on the distortion that could be obtained by any deterministic social choice mechanism, and extend our results on median agent cost to more general objective functions.

Authors

Elliot Anshelevich

Rensselaer Polytechnic Institute


Onkar Bhardwaj

Rensselaer Polytechnic Institute


John Postl

Rensselaer Polytechnic Institute


DOI:

10.1609/aaai.v29i1.9308


Topics: AAAI

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HOW TO CITE:

Elliot Anshelevich|| Onkar Bhardwaj|| John Postl Approximating Optimal Social Choice under Metric Preferences Proceedings of the AAAI Conference on Artificial Intelligence, 29 (2015) .

Elliot Anshelevich|| Onkar Bhardwaj|| John Postl Approximating Optimal Social Choice under Metric Preferences AAAI 2015, .

Elliot Anshelevich|| Onkar Bhardwaj|| John Postl (2015). Approximating Optimal Social Choice under Metric Preferences. Proceedings of the AAAI Conference on Artificial Intelligence, 29, .

Elliot Anshelevich|| Onkar Bhardwaj|| John Postl. Approximating Optimal Social Choice under Metric Preferences. Proceedings of the AAAI Conference on Artificial Intelligence, 29 2015 p..

Elliot Anshelevich|| Onkar Bhardwaj|| John Postl. 2015. Approximating Optimal Social Choice under Metric Preferences. "Proceedings of the AAAI Conference on Artificial Intelligence, 29". .

Elliot Anshelevich|| Onkar Bhardwaj|| John Postl. (2015) "Approximating Optimal Social Choice under Metric Preferences", Proceedings of the AAAI Conference on Artificial Intelligence, 29, p.

Elliot Anshelevich|| Onkar Bhardwaj|| John Postl, "Approximating Optimal Social Choice under Metric Preferences", AAAI, p., 2015.

Elliot Anshelevich|| Onkar Bhardwaj|| John Postl. "Approximating Optimal Social Choice under Metric Preferences". Proceedings of the AAAI Conference on Artificial Intelligence, 29, 2015, p..

Elliot Anshelevich|| Onkar Bhardwaj|| John Postl. "Approximating Optimal Social Choice under Metric Preferences". Proceedings of the AAAI Conference on Artificial Intelligence, 29, (2015): .

Elliot Anshelevich|| Onkar Bhardwaj|| John Postl. Approximating Optimal Social Choice under Metric Preferences. AAAI[Internet]. 2015[cited 2023]; .


ISSN: 2374-3468


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