Strategyproof Mean Estimation from Multiple-Choice Questions

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

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Anson Kahng, Gregory Kehne, Ariel Procaccia


<p>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.</p>