IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2110.11399.html
   My bibliography  Save this paper

Algebraic Properties of Blackwell's Order and A Cardinal Measure of Informativeness

Author

Listed:
  • Andrew Kosenko

Abstract

I establish a translation invariance property of the Blackwell order over experiments, show that garbling experiments bring them closer together, and use these facts to define a cardinal measure of informativeness. Experiment $A$ is inf-norm more informative (INMI) than experiment $B$ if the infinity norm of the difference between a perfectly informative structure and $A$ is less than the corresponding difference for $B$. The better experiment is "closer" to the fully revealing experiment; distance from the identity matrix is interpreted as a measure of informativeness. This measure coincides with Blackwell's order whenever possible, is complete, order invariant, and prior-independent, making it an attractive and computationally simple extension of the Blackwell order to economic contexts.

Suggested Citation

  • Andrew Kosenko, 2021. "Algebraic Properties of Blackwell's Order and A Cardinal Measure of Informativeness," Papers 2110.11399, arXiv.org.
    • Handle: RePEc:arx:papers:2110.11399
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2110.11399
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2013. "Entropy and the Value of Information for Investors," American Economic Review, American Economic Association, vol. 103(1), pages 360-377, February.
    2. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again," Econometrica, Econometric Society, vol. 89(1), pages 475-506, January.
    3. Cabrales, Antonio & Gossner, Olivier & Serrano, Roberto, 2017. "A normalized value for information purchases," Journal of Economic Theory, Elsevier, vol. 170(C), pages 266-288.
    4. Peski, Marcin, 2008. "Comparison of information structures in zero-sum games," Games and Economic Behavior, Elsevier, vol. 62(2), pages 732-735, March.
    5. de Oliveira, Henrique, 2018. "Blackwell's informativeness theorem using diagrams," Games and Economic Behavior, Elsevier, vol. 109(C), pages 126-131.
    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. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again," Econometrica, Econometric Society, vol. 89(1), pages 475-506, January.
    2. Arrondel, Luc & Calvo-Pardo, Hector & Giannitsarou, Chryssi & Haliassos, Michael, 2022. "Informative social interactions," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 246-263.
    3. Luciano Pomatto & Philipp Strack & Omer Tamuz, 2018. "The Cost of Information: The Case of Constant Marginal Costs," Papers 1812.04211, arXiv.org, revised Feb 2023.
    4. Michel De Lara & Olivier Gossner, 2017. "An instrumental approach to the value of information," Working Papers 2017-49, Center for Research in Economics and Statistics.
    5. Michel de Lara & Olivier Gossner, 2020. "Payoffs-Beliefs Duality and the Value of Information," Post-Print hal-01941006, HAL.
    6. Chady Jabbour & Anis Hoayek & Jean-Michel Salles, 2022. "Formalizing a Two-Step Decision-Making Process in Land Use: Evidence from Controlling Forest Clearcutting Using Spatial Information," Land, MDPI, vol. 12(1), pages 1-17, December.
    7. Jaehyuk Choi & Lan Ju & Jian Li & Zhiyong Tu, 2023. "Information extraction and artwork pricing," Papers 2302.08167, arXiv.org.
    8. Lindbeck, Assar & Weibull, Jörgen, 2020. "Delegation of investment decisions, and optimal remuneration of agents," European Economic Review, Elsevier, vol. 129(C).
    9. Kyungmin Kim & Benjamin Lester & Braz Camargo, 2012. "Subsidizing Price Discovery," 2012 Meeting Papers 338, Society for Economic Dynamics.
    10. Dillenberger, David & Krishna, R. Vijay & Sadowski, Philipp, 2023. "Subjective information choice processes," Theoretical Economics, Econometric Society, vol. 18(2), May.
    11. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Working Papers 2012-13, Brown University, Department of Economics.
    12. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2022. "Counterfactuals with Latent Information," American Economic Review, American Economic Association, vol. 112(1), pages 343-368, January.
    13. Akisik, Orhan & Gal, Graham, 2023. "IFRS, financial development and income inequality: An empirical study using mediation analysis," Economic Systems, Elsevier, vol. 47(2).
    14. Taneva, Ina A, 2015. "Information Design," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-50, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    15. Alexander M. Jakobsen, 2021. "An Axiomatic Model of Persuasion," Econometrica, Econometric Society, vol. 89(5), pages 2081-2116, September.
    16. Áron Tóbiás, 2023. "Cognitive limits and preferences for information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 221-253, June.
    17. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Learning Efficiency of Multi-Agent Information Structures," Cowles Foundation Discussion Papers 2299R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.
    18. Antonio Jiménez-Martínez, 2015. "A model of belief influence in large social networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 21-59, May.
    19. Taneva, Ina A, 2015. "Information Design," SIRE Discussion Papers 2015-50, Scottish Institute for Research in Economics (SIRE).
    20. Agostino Manduchi, 2013. "Non-neutral information costs with match-value uncertainty," Journal of Economics, Springer, vol. 109(1), pages 1-25, May.

    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:2110.11399. 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.