Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice
| Autor: | Kamesh Munagala, Nina Prabhu, Brandon Fain, Ashish Goel |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
FOS: Computer and information sciences
050101 languages & linguistics Mathematical optimization Computer science Computer Science - Artificial Intelligence 02 engineering and technology Measure (mathematics) Square (algebra) Computer Science - Computer Science and Game Theory Distortion 0202 electrical engineering electronic engineering information engineering 0501 psychology and cognitive sciences Computer Science - Multiagent Systems 05 social sciences General Medicine Variance (accounting) 16. Peace & justice Constraint (information theory) Metric space Artificial Intelligence (cs.AI) Metric (mathematics) Ordinal number 020201 artificial intelligence & image processing Constant (mathematics) Social choice theory Computer Science and Game Theory (cs.GT) Multiagent Systems (cs.MA) |
| Zdroj: | AAAI |
| Popis: | We study social choice mechanisms in an implicit utilitarian framework with a metric constraint, where the goal is to minimize \textit{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 \textit{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. Conference version Published in AAAI 2019 (https://aaai.org/Conferences/AAAI-19/) |
| Databáze: | OpenAIRE |
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