Strategyproof Mean Estimation from Multiple-Choice Questions

Anson Kahng, Gregory Kehne, Ariel Procaccia
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:5042-5052, 2020.

Abstract

Given n values possessed by n agents, we study the problem of estimating the mean by truthfully eliciting agents’ answers to multiple-choice questions about their values. We consider two natural candidates for estimation error: mean squared error (MSE) and mean absolute error (MAE). We design a randomized estimator which is asymptotically optimal for both measures in the worst case. In the case where prior distributions over the agents’ values are known, we give an optimal, polynomial-time algorithm for MSE, and show that the task of computing an optimal estimate for MAE is #P-hard. Finally, we demonstrate empirically that knowledge of prior distributions gives a significant edge.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-kahng20a, title = {Strategyproof Mean Estimation from Multiple-Choice Questions}, author = {Kahng, Anson and Kehne, Gregory and Procaccia, Ariel}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {5042--5052}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/kahng20a/kahng20a.pdf}, url = { http://proceedings.mlr.press/v119/kahng20a.html }, abstract = {Given n values possessed by n agents, we study the problem of estimating the mean by truthfully eliciting agents’ answers to multiple-choice questions about their values. We consider two natural candidates for estimation error: mean squared error (MSE) and mean absolute error (MAE). We design a randomized estimator which is asymptotically optimal for both measures in the worst case. In the case where prior distributions over the agents’ values are known, we give an optimal, polynomial-time algorithm for MSE, and show that the task of computing an optimal estimate for MAE is #P-hard. Finally, we demonstrate empirically that knowledge of prior distributions gives a significant edge.} }
Endnote
%0 Conference Paper %T Strategyproof Mean Estimation from Multiple-Choice Questions %A Anson Kahng %A Gregory Kehne %A Ariel Procaccia %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-kahng20a %I PMLR %P 5042--5052 %U http://proceedings.mlr.press/v119/kahng20a.html %V 119 %X Given n values possessed by n agents, we study the problem of estimating the mean by truthfully eliciting agents’ answers to multiple-choice questions about their values. We consider two natural candidates for estimation error: mean squared error (MSE) and mean absolute error (MAE). We design a randomized estimator which is asymptotically optimal for both measures in the worst case. In the case where prior distributions over the agents’ values are known, we give an optimal, polynomial-time algorithm for MSE, and show that the task of computing an optimal estimate for MAE is #P-hard. Finally, we demonstrate empirically that knowledge of prior distributions gives a significant edge.
APA
Kahng, A., Kehne, G. & Procaccia, A.. (2020). Strategyproof Mean Estimation from Multiple-Choice Questions. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:5042-5052 Available from http://proceedings.mlr.press/v119/kahng20a.html .

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