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Strategyproof Mean Estimation from Multiple-Choice Questions
Anson Kahng · Gregory Kehne · Ariel Procaccia

Tue Jul 14 08:00 AM -- 08:45 AM & Tue Jul 14 07:00 PM -- 07:45 PM (PDT) @

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.

Author Information

Anson Kahng (Carnegie Mellon University)
Gregory Kehne (Carnegie Mellon University)
Ariel Procaccia (Harvard University)

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