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Reasonable Doubt and Alternative Hypotheses: A Bayesian Analysis

Hahn, Ulrike and Hartmann, Stephan (2020) Reasonable Doubt and Alternative Hypotheses: A Bayesian Analysis. [Preprint]

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Abstract

A longstanding question is the extent to which "reasonable doubt" may be expressed simply in terms of a threshold degree of belief. In this context, we examine the extent to which learning about possible alternatives may alter one's beliefs about a target hypothesis, even when no new "evidence" linking them to the hypothesis is acquired. Imagine the following scenario: a crime has been committed and Alice, the police's main suspect has been brought to trial. There are several pieces of evidence that raise the probability that Alice committed the crime. Her attorney's defense strategy is not to challenge this evidence, but instead to provide personal details about Alice's neighbour, Jane. While Jane is one of many people the police spoke to, they saw no reason to investigate her further. You now learn that Jane, too, had access to the shed where the murder weapon was stored, just like Alice. To what extent should this alter your beliefs about Alice's guilt? In this paper, we provide a formal description of the problem and a solution indicating circumstances under which learning about Jane will more or less impact beliefs about Alice.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Hahn, Ulrikeu.hahn@bbk.ac.uk
Hartmann, Stephans.hartmann@lmu.de0000-0001-8676-2177
Keywords: Reasonable doubt, Bayesian epistemology, catch-all alternative
Subjects: General Issues > Confirmation/Induction
Specific Sciences > Probability/Statistics
Depositing User: Stephan Hartmann
Date Deposited: 01 Dec 2020 18:52
Last Modified: 01 Dec 2020 18:52
Item ID: 18472
Subjects: General Issues > Confirmation/Induction
Specific Sciences > Probability/Statistics
Date: 1 December 2020
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/18472

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