Strategyproof Mean Estimation from Multiple-Choice Questions
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
Text
Kahng et al. "Strategyproof Mean Estimation from Multiple-Choice Questions." International Conference on Machine Learning, 2020.Markdown
[Kahng et al. "Strategyproof Mean Estimation from Multiple-Choice Questions." International Conference on Machine Learning, 2020.](https://mlanthology.org/icml/2020/kahng2020icml-strategyproof/)BibTeX
@inproceedings{kahng2020icml-strategyproof,
title = {{Strategyproof Mean Estimation from Multiple-Choice Questions}},
author = {Kahng, Anson and Kehne, Gregory and Procaccia, Ariel},
booktitle = {International Conference on Machine Learning},
year = {2020},
pages = {5042-5052},
volume = {119},
url = {https://mlanthology.org/icml/2020/kahng2020icml-strategyproof/}
}