IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2203.07469.html
   My bibliography  Save this paper

Quantum Information Elicitation

Author

Listed:
  • Rafael Frongillo

Abstract

In the classic scoring rule setting, a principal incentivizes an agent to truthfully report their probabilistic belief about some future outcome. This paper addresses the situation when this private belief, rather than a classical probability distribution, is instead a quantum mixed state. In the resulting quantum scoring rule setting, the principal chooses both a scoring function and a measurement function, and the agent responds with their reported density matrix. Several characterizations of quantum scoring rules are presented, which reveal a familiar structure based on convex analysis. Spectral scores, where the measurement function is given by the spectral decomposition of the reported density matrix, have particularly elegant structure and connect to quantum information theory. Turning to property elicitation, eigenvectors of the belief are elicitable, whereas eigenvalues and entropy have maximal elicitation complexity. The paper concludes with a discussion of other quantum information elicitation settings and connections to the literature.

Suggested Citation

  • Rafael Frongillo, 2022. "Quantum Information Elicitation," Papers 2203.07469, arXiv.org.
    • Handle: RePEc:arx:papers:2203.07469
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2203.07469
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    2. Rafael Frongillo & Ian A. Kash, 2015. "Elicitation Complexity of Statistical Properties," Papers 1506.07212, arXiv.org, revised Aug 2020.
    3. Robin Hanson, 2007. "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation," Journal of Prediction Markets, University of Buckingham Press, vol. 1(1), pages 3-15, February.
    4. Lambert, Nicolas S. & Langford, John & Wortman Vaughan, Jennifer & Chen, Yiling & Reeves, Daniel M. & Shoham, Yoav & Pennock, David M., 2015. "An axiomatic characterization of wagering mechanisms," Journal of Economic Theory, Elsevier, vol. 156(C), pages 389-416.
    5. Frongillo, Rafael M. & Kash, Ian A., 2021. "General truthfulness characterizations via convex analysis," Games and Economic Behavior, Elsevier, vol. 130(C), pages 636-662.
    6. 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.
    7. Robin Hanson, 2003. "Combinatorial Information Market Design," Information Systems Frontiers, Springer, vol. 5(1), pages 107-119, January.
    Full references (including those not matched with items on IDEAS)

    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. Karimi, Majid & Zaerpour, Nima, 2022. "Put your money where your forecast is: Supply chain collaborative forecasting with cost-function-based prediction markets," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1035-1049.
    2. Bergemann, Dirk & Ottaviani, Marco, 2021. "Information Markets and Nonmarkets," CEPR Discussion Papers 16459, C.E.P.R. Discussion Papers.
    3. Yiling Chen & Mike Ruberry & Jennifer Wortman Vaughan, 2012. "Designing Informative Securities," Papers 1210.4837, arXiv.org.
    4. Fissler Tobias & Ziegel Johanna F., 2021. "On the elicitability of range value at risk," Statistics & Risk Modeling, De Gruyter, vol. 38(1-2), pages 25-46, January.
    5. Robert L. Winkler & Yael Grushka-Cockayne & Kenneth C. Lichtendahl Jr. & Victor Richmond R. Jose, 2019. "Probability Forecasts and Their Combination: A Research Perspective," Decision Analysis, INFORMS, vol. 16(4), pages 239-260, December.
    6. Lambert, Nicolas S. & Langford, John & Wortman Vaughan, Jennifer & Chen, Yiling & Reeves, Daniel M. & Shoham, Yoav & Pennock, David M., 2015. "An axiomatic characterization of wagering mechanisms," Journal of Economic Theory, Elsevier, vol. 156(C), pages 389-416.
    7. Forsell, Eskil & Viganola, Domenico & Pfeiffer, Thomas & Almenberg, Johan & Wilson, Brad & Chen, Yiling & Nosek, Brian A. & Johannesson, Magnus & Dreber, Anna, 2019. "Predicting replication outcomes in the Many Labs 2 study," Journal of Economic Psychology, Elsevier, vol. 75(PA).
    8. Florian Teschner & David Rothschild & Henner Gimpel, 2017. "Manipulation in Conditional Decision Markets," Group Decision and Negotiation, Springer, vol. 26(5), pages 953-971, September.
    9. Frongillo, Rafael M. & Kash, Ian A., 2021. "General truthfulness characterizations via convex analysis," Games and Economic Behavior, Elsevier, vol. 130(C), pages 636-662.
    10. Mueller-Frank, Manuel, 2014. "Does one Bayesian make a difference?," Journal of Economic Theory, Elsevier, vol. 154(C), pages 423-452.
    11. Armantier, Olivier & Treich, Nicolas, 2013. "Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging," European Economic Review, Elsevier, vol. 62(C), pages 17-40.
    12. Lahiri, Kajal & Yang, Liu, 2013. "Forecasting Binary Outcomes," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1025-1106, Elsevier.
    13. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    14. Alexander Henzi & Johanna F Ziegel, 2022. "Valid sequential inference on probability forecast performance [A comparison of the ECMWF, MSC, and NCEP global ensemble prediction systems]," Biometrika, Biometrika Trust, vol. 109(3), pages 647-663.
    15. Galanis, S. & Ioannou, C. & Kotronis, S., 2019. "Information Aggregation Under Ambiguity: Theory and Experimental Evidence," Working Papers 20/05, Department of Economics, City University London.
    16. Tobias Fissler & Silvana M. Pesenti, 2022. "Sensitivity Measures Based on Scoring Functions," Papers 2203.00460, arXiv.org, revised Jul 2022.
    17. Knüppel, Malte & Schultefrankenfeld, Guido, 2019. "Assessing the uncertainty in central banks’ inflation outlooks," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1748-1769.
    18. Mikuláš Gangur & Miroslav Plevný, 2014. "Tools for Consumer Rights Protection in the Prediction of Electronic Virtual Market and Technological Changes," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 16(36), pages 578-578, May.
    19. Costa, Alexandre Bonnet R. & Ferreira, Pedro Cavalcanti G. & Gaglianone, Wagner P. & Guillén, Osmani Teixeira C. & Issler, João Victor & Lin, Yihao, 2021. "Machine learning and oil price point and density forecasting," Energy Economics, Elsevier, vol. 102(C).
    20. Tsakas, Elias, 2020. "Robust scoring rules," Theoretical Economics, Econometric Society, vol. 15(3), July.

    More about this item

    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:2203.07469. 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.