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<p>How should rational agents revise their opinions given the opinions of multiple experts? One attractive answer is linear averaging: upon learning multiple experts’ opinions about a proposition <i>A</i>, one’s own probability of <i>A</i> should equal a linear average of the experts’ opinions about <i>A</i>. However, this answer has a well-known problem: it is compatible with Bayesian conditionalization only when the agent is certain that the experts assign the exact same probability to <i>A</i> (Dawid et al. in TEST, 4(2):263–313, 1995, Ranjan and Gneiting in J Royal Stat Soc Ser B Stat Methodol 72(1):71–91, 2010, Bradley in Theory Decis 85(1):5-20, 2018, Gallow in Philos Stud 175(10):2389–2398, 2018). This paper shows that, for priors of finite domains, a similar result holds for the much weaker norm of <i>strict convexity</i>. To this extent, the triviality phenomenon is more widespread than it has been previously appreciated.</p>

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Coherent combination of experts’ opinions: another impossibility result

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月27日

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  • Snow Zhang

摘要

How should rational agents revise their opinions given the opinions of multiple experts? One attractive answer is linear averaging: upon learning multiple experts’ opinions about a proposition A, one’s own probability of A should equal a linear average of the experts’ opinions about A. However, this answer has a well-known problem: it is compatible with Bayesian conditionalization only when the agent is certain that the experts assign the exact same probability to A (Dawid et al. in TEST, 4(2):263–313, 1995, Ranjan and Gneiting in J Royal Stat Soc Ser B Stat Methodol 72(1):71–91, 2010, Bradley in Theory Decis 85(1):5-20, 2018, Gallow in Philos Stud 175(10):2389–2398, 2018). This paper shows that, for priors of finite domains, a similar result holds for the much weaker norm of strict convexity. To this extent, the triviality phenomenon is more widespread than it has been previously appreciated.