Synthese 194 (6):2025-2051 (2017)

Authors
Paul D. Thorn
Heinrich Heine University Düsseldorf
Abstract
In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency information for more specific reference classes yields personal probabilities whose accuracy is optimal, according to all proper scoring rules, in situations where all of the relevant frequency information is point-valued. Assuming that frequency information for narrower reference classes is preferred, when the relevant frequency statements are point-valued, a dilemma arises when choosing whether to make a direct inference based upon relatively precise-valued frequency information for a broad reference class, R, or upon relatively imprecise-valued frequency information for a more specific reference class, R*. I address such cases, by showing that it is often possible to make a precise-valued frequency judgment regarding R* based on precise-valued frequency information for R, using standard principles of direct inference. Having made such a frequency judgment, the dilemma of choosing between and is removed, and one may proceed by using the precise-valued frequency estimate for the more specific reference class as a premise for direct inference.
Keywords Direct inference  Statistical syllogism  Specificity  Scoring rules   The reference class problem  Imprecise probabilities  The principle of indifference
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DOI 10.1007/s11229-016-1035-y
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[Introduction].O. H. Mitchell & J. Venn - 1884 - Mind 9 (34):321-322.

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Citations of this work BETA

A Bayesian Solution to the Conflict of Narrowness and Precision in Direct Inference.Christian Wallmann - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (3):485-500.
An Argument for the Principle of Indifference and Against the Wide Interval View.John E. Wilcox - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (1):65-87.
An Argument for the Principle of Indifference and Against the Wide Interval View.John E. Wilcox - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (1):65-87.

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