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Subjective inference

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  • Andrew Mackenzie

Abstract

An agent observes a clue, and an analyst observes an inference: a ranking of events on the basis of how corroborated they are by the clue. We prove that if the inference satisfies the axioms of Villegas (1964) except for the classic qualitative probability axiom of monotonicity, then it has a unique normalized signed measure representation (Theorem 1). Moreover, if the inference also declares the largest event equivalent to the smallest event, then it can be represented as a difference between a posterior and a prior such that the former is the conditional probability of the latter with respect to an assessed event that is interpreted as a clue guess. Across these Bayesian representations, the posterior is unique, all guesses are in a suitable sense equivalent, and the prior is determined by the weight it assigns to each possible guess (Theorem 2). However, observation of a prior and posterior compatible with the inference could reveal that all of these guesses are wrong.

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  • Andrew Mackenzie, 2025. "Subjective inference," Papers 2511.00173, arXiv.org.
    • Handle: RePEc:arx:papers:2511.00173
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    References listed on IDEAS

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    1. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, July.
    2. Mackenzie, Andrew, 2019. "A foundation for probabilistic beliefs with or without atoms," Theoretical Economics, Econometric Society, vol. 14(2), May.
    3. K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(2), pages 91-96.
    4. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    5. Adam Brandenburger & Paolo Ghirardato & Daniele Pennesi & Lorenzo Stanca, 2024. "Event Valence and Subjective Probability," Carlo Alberto Notebooks 717 JEL Classification: D, Collegio Carlo Alberto.
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