IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2206.08149.html
   My bibliography  Save this paper

A Truthful Owner-Assisted Scoring Mechanism

Author

Listed:
  • 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.

Suggested Citation

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

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2206.08149
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yuling Yan & Weijie J. Su & Jianqing Fan, 2023. "The Isotonic Mechanism for Exponential Family Estimation," Papers 2304.11160, arXiv.org, revised Oct 2023.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tino Werner, 2022. "Elicitability of Instance and Object Ranking," Decision Analysis, INFORMS, vol. 19(2), pages 123-140, June.
    2. Dipankar Das, 2023. "A Model of Competitive Assortment Planning Algorithm," Papers 2307.09479, arXiv.org.
    3. Christis Katsouris, 2023. "Statistical Estimation for Covariance Structures with Tail Estimates using Nodewise Quantile Predictive Regression Models," Papers 2305.11282, arXiv.org, revised Jul 2023.
    4. Frongillo, Rafael M. & Kash, Ian A., 2021. "General truthfulness characterizations via convex analysis," Games and Economic Behavior, Elsevier, vol. 130(C), pages 636-662.
    5. Yangming Zhou & Jin-Kao Hao & Zhen Li, 2024. "Heuristic Search for Rank Aggregation with Application to Label Ranking," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 308-326, March.
    6. Alwyn Lim & Shawn Pope, 2022. "What drives companies to do good? A “universal” ordering of corporate social responsibility motivations," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 29(1), pages 233-255, January.
    7. Carrizosa, Emilio & Guerrero, Vanesa & Romero Morales, Dolores, 2019. "Visualization of complex dynamic datasets by means of mathematical optimization," Omega, Elsevier, vol. 86(C), pages 125-136.
    8. Christopher P. Chambers & Nicolas S. Lambert, 2021. "Dynamic Belief Elicitation," Econometrica, Econometric Society, vol. 89(1), pages 375-414, January.
    9. Azar, Pablo D. & Micali, Silvio, 2018. "Computational principal agent problems," Theoretical Economics, Econometric Society, vol. 13(2), May.
    10. Angelica Gianfreda & Francesco Ravazzolo & Luca Rossini, 2023. "Large Time‐Varying Volatility Models for Hourly Electricity Prices," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 545-573, June.
    11. Koessler, Frédéric & Skreta, Vasiliki, 2016. "Informed seller with taste heterogeneity," Journal of Economic Theory, Elsevier, vol. 165(C), pages 456-471.
    12. Tobias Fissler & Yannick Hoga, 2024. "How to Compare Copula Forecasts?," Papers 2410.04165, arXiv.org.
    13. Davide Pettenuzzo & Francesco Ravazzolo, 2016. "Optimal Portfolio Choice Under Decision‐Based Model Combinations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1312-1332, November.
    14. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    15. Hwang, Eunju, 2022. "Prediction intervals of the COVID-19 cases by HAR models with growth rates and vaccination rates in top eight affected countries: Bootstrap improvement," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    16. R de Fondeville & A C Davison, 2018. "High-dimensional peaks-over-threshold inference," Biometrika, Biometrika Trust, vol. 105(3), pages 575-592.
    17. Armantier, Olivier & Treich, Nicolas, 2013. "Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging," European Economic Review, Elsevier, vol. 62(C), pages 17-40.
    18. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    19. Finn Lindgren, 2015. "Comments on: Comparing and selecting spatial predictors using local criteria," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 35-44, March.
    20. Chuliá, Helena & Garrón, Ignacio & Uribe, Jorge M., 2024. "Daily growth at risk: Financial or real drivers? The answer is not always the same," International Journal of Forecasting, Elsevier, vol. 40(2), pages 762-776.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2206.08149. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.