Strategyproof Mean Estimation from Multiple-Choice Questions

@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 = 	 {III, Hal Daumé and Singh, Aarti},
  volume = 	 {119},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {13--18 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v119/kahng20a/kahng20a.pdf},
  url = 	 {https://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.}
}