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

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  • 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.

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Itai Arieli & Yakov Babichenko & Dima Shaiderman & Xianwen Shi, 2025. "Persuading while Learning," Working Papers tecipa-791, University of Toronto, Department of Economics.

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