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A Truthful Owner-Assisted Scoring Mechanism

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  • Weijie J. Su

Abstract

Alice (owner) has knowledge of the underlying quality of her items measured in grades. Given the noisy grades provided by an independent party, can Bob (appraiser) obtain accurate estimates of the ground-truth grades of the items by asking Alice a question about the grades? We address this when the payoff to Alice is additive convex utility over all her items. We establish that if Alice has to truthfully answer the question so that her payoff is maximized, the question must be formulated as pairwise comparisons between her items. Next, we prove that if Alice is required to provide a ranking of her items, which is the most fine-grained question via pairwise comparisons, she would be truthful. By incorporating the ground-truth ranking, we show that Bob can obtain an estimator with the optimal squared error in certain regimes based on any possible way of truthful information elicitation. Moreover, the estimated grades are substantially more accurate than the raw grades when the number of items is large and the raw grades are very noisy. Finally, we conclude the paper with several extensions and some refinements for practical considerations.

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  • Weijie J. Su, 2022. "A Truthful Owner-Assisted Scoring Mechanism," Papers 2206.08149, arXiv.org.
    • Handle: RePEc:arx:papers:2206.08149
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    References listed on IDEAS

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    1. Sahand Negahban & Sewoong Oh & Devavrat Shah, 2017. "Rank Centrality: Ranking from Pairwise Comparisons," Operations Research, INFORMS, vol. 65(1), pages 266-287, February.
    2. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
    3. Sahand Negahban & Sewoong Oh & Devavrat Shah, 2017. "Rank Centrality: Ranking from Pairwise Comparisons," Operations Research, INFORMS, vol. 65(1), pages 266-287, February.
    4. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    5. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-1119, July.
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    Cited by:

    1. Jibang Wu & Haifeng Xu & Yifan Guo & Weijie Su, 2023. "A Truth Serum for Eliciting Self-Evaluations in Scientific Reviews," Papers 2306.11154, arXiv.org, revised Feb 2024.
    2. Yuling Yan & Weijie J. Su & Jianqing Fan, 2023. "The Isotonic Mechanism for Exponential Family Estimation," Papers 2304.11160, arXiv.org, revised Oct 2023.

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