TY - GEN

T1 - Testing preferential domains using sampling

AU - Dey, Palash

AU - Nath, Swaprava

AU - Shakya, Garima

N1 - Publisher Copyright:
© 2019 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org) Ail rights reserved.

PY - 2019

Y1 - 2019

N2 - A preferential domain is a collection of sets of preferences which are linear orders over a set of alternatives These domains have been studied extensively in social choice theory due to both its practical importance and theoretical elegance Examples of some extensively studied preferential domains include single peaked, single crossing Euclidean, etc In this paper, we study the sample complexity of testing whether a given preference profile is close to some specific domain We consider two notions of closeness: (a) closeness via preferences, and (b) closeness via alternatives We further explore the effect of assuming that the outlier preferences/alternatives to be random (instead of arbitrary) on the sample complexity of the testing problem In most cases, we show that the above testing problem can be solved with high probability for all commonly used domains by observing only a small number of samples (independent of the number of preferences, n, and often the number of alternatives, m) In the remaining few cases, we prove either impossibility results or fl(n) lower bound on the sample complexity We complement our theoretical findings with extensive simulations to figure out the actual constant factors of our asymptotic sample complexity bounds.

AB - A preferential domain is a collection of sets of preferences which are linear orders over a set of alternatives These domains have been studied extensively in social choice theory due to both its practical importance and theoretical elegance Examples of some extensively studied preferential domains include single peaked, single crossing Euclidean, etc In this paper, we study the sample complexity of testing whether a given preference profile is close to some specific domain We consider two notions of closeness: (a) closeness via preferences, and (b) closeness via alternatives We further explore the effect of assuming that the outlier preferences/alternatives to be random (instead of arbitrary) on the sample complexity of the testing problem In most cases, we show that the above testing problem can be solved with high probability for all commonly used domains by observing only a small number of samples (independent of the number of preferences, n, and often the number of alternatives, m) In the remaining few cases, we prove either impossibility results or fl(n) lower bound on the sample complexity We complement our theoretical findings with extensive simulations to figure out the actual constant factors of our asymptotic sample complexity bounds.

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M3 - Conference contribution

AN - SCOPUS:85076950420

T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS

SP - 855

EP - 863

BT - 18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019

PB - International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)

T2 - 18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019

Y2 - 13 May 2019 through 17 May 2019

ER -