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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence / EAAI-20

Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice

February 1, 2023

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Authors

Brandon Fain

Duke University


Ashish Goel

Stanford University


Kamesh Munagala

Duke University


Nina Prabhu

North Carolina School of Science and Mathematics


DOI:

10.1609/aaai.v33i01.33011893


Abstract:

We study social choice mechanisms in an implicit utilitarian framework with a metric constraint, where the goal is to minimize Distortion, the worst case social cost of an ordinal mechanism relative to underlying cardinal utilities. We consider two additional desiderata: Constant sample complexity and Squared Distortion. Constant sample complexity means that the mechanism (potentially randomized) only uses a constant number of ordinal queries regardless of the number of voters and alternatives. Squared Distortion is a measure of variance of the Distortion of a randomized mechanism.Our primary contribution is the first social choice mechanism with constant sample complexity and constant Squared Distortion (which also implies constant Distortion). We call the mechanism Random Referee, because it uses a random agent to compare two alternatives that are the favorites of two other random agents. We prove that the use of a comparison query is necessary: no mechanism that only elicits the top-k preferred alternatives of voters (for constant k) can have Squared Distortion that is sublinear in the number of alternatives. We also prove that unlike any top-k only mechanism, the Distortion of Random Referee meaningfully improves on benign metric spaces, using the Euclidean plane as a canonical example. Finally, among top-1 only mechanisms, we introduce Random Oligarchy. The mechanism asks just 3 queries and is essentially optimal among the class of such mechanisms with respect to Distortion.In summary, we demonstrate the surprising power of constant sample complexity mechanisms generally, and just three random voters in particular, to provide some of the best known results in the implicit utilitarian framework.

Topics: AAAI

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HOW TO CITE:

Brandon Fain||Ashish Goel||Kamesh Munagala||Nina Prabhu Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice Proceedings of the AAAI Conference on Artificial Intelligence (2019) 1893-1900.

Brandon Fain||Ashish Goel||Kamesh Munagala||Nina Prabhu Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice AAAI 2019, 1893-1900.

Brandon Fain||Ashish Goel||Kamesh Munagala||Nina Prabhu (2019). Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice. Proceedings of the AAAI Conference on Artificial Intelligence, 1893-1900.

Brandon Fain||Ashish Goel||Kamesh Munagala||Nina Prabhu. Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice. Proceedings of the AAAI Conference on Artificial Intelligence 2019 p.1893-1900.

Brandon Fain||Ashish Goel||Kamesh Munagala||Nina Prabhu. 2019. Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice. "Proceedings of the AAAI Conference on Artificial Intelligence". 1893-1900.

Brandon Fain||Ashish Goel||Kamesh Munagala||Nina Prabhu. (2019) "Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice", Proceedings of the AAAI Conference on Artificial Intelligence, p.1893-1900

Brandon Fain||Ashish Goel||Kamesh Munagala||Nina Prabhu, "Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice", AAAI, p.1893-1900, 2019.

Brandon Fain||Ashish Goel||Kamesh Munagala||Nina Prabhu. "Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice". Proceedings of the AAAI Conference on Artificial Intelligence, 2019, p.1893-1900.

Brandon Fain||Ashish Goel||Kamesh Munagala||Nina Prabhu. "Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice". Proceedings of the AAAI Conference on Artificial Intelligence, (2019): 1893-1900.

Brandon Fain||Ashish Goel||Kamesh Munagala||Nina Prabhu. Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice. AAAI[Internet]. 2019[cited 2023]; 1893-1900.


ISSN: 2374-3468


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