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Predicting the Unpredictable under Subjective Expected Utility

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  • Burkhard C. Schipper
Abstract
We consider a decision maker who is unaware of objects to be sampled and thus cannot form beliefs about the occurrence of particular objects. Ex ante she can form beliefs about the occurrence of novelty and the frequencies of yet to be known objects. Conditional on any sampled objects, she can also form beliefs about the next object being novel or being one of the previously sampled objects. We characterize behaviorally such beliefs under subjective expected utility. In doing so, we relate "reverse" Bayesianism, a central property in the literature on decision making under growing awareness, with exchangeable random partitions, the central property in the literature on the discovery of species problem and mutations in statistics, combinatorial probability theory, and population genetics. Partition exchangeable beliefs do not necessarily satisfy "reverse" Bayesianism. Yet, the most prominent models of exchangeable random partitions, the model by De Morgan (1838), the one parameter model of Ewens (1972), and the two parameter model of Pitman (1995) and Zabell (1997), do satisfy "reverse" Bayesianism.

Suggested Citation

  • Burkhard C. Schipper, 2024. "Predicting the Unpredictable under Subjective Expected Utility," Papers 2403.01421, arXiv.org.
    • Handle: RePEc:arx:papers:2403.01421
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    References listed on IDEAS

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

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    More about this item

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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