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Second-order Inductive Inference: an axiomatic approach

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  • Patrick H. O'Callaghan

Abstract

Consider a predictor who ranks eventualities on the basis of past cases: for instance a search engine ranking webpages given past searches. Resampling past cases leads to different rankings and the extraction of deeper information. Yet a rich database, with sufficiently diverse rankings, is often beyond reach. Inexperience demands either "on the fly" learning-by-doing or prudence: the arrival of a novel case does not force (i) a revision of current rankings, (ii) dogmatism towards new rankings, or (iii) intransitivity. For this higher-order framework of inductive inference, we derive a suitably unique numerical representation of these rankings via a matrix on eventualities x cases and describe a robust test of prudence. Applications include: the success/failure of startups; the veracity of fake news; and novel conditions for the existence of a yield curve that is robustly arbitrage-free.

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  • Patrick H. O'Callaghan, 2019. "Second-order Inductive Inference: an axiomatic approach," Papers 1904.02934, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:1904.02934
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    References listed on IDEAS

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    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
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    7. Halpern, Joseph Y. & Rêgo, Leandro C., 2009. "Reasoning about knowledge of unawareness," Games and Economic Behavior, Elsevier, vol. 67(2), pages 503-525, November.
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