The Shooting-Room Paradox and Conditionalizing on Measurably Challenged Sets View Full Text


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Article Info

DATE

1999-03

AUTHORS

Paul Bartha, Christopher Hitchcock

ABSTRACT

We provide a solution to the well-known “Shooting-Room” paradox, developed by John Leslie in connection with his Doomsday Argument. In the “Shooting-Room” paradox, the death of an individual is contingent upon an event that has a 1/36 chance of occurring, yet the relative frequency of death in the relevant population is 0.9. There are two intuitively plausible arguments, one concluding that the appropriate subjective probability of death is 1/36, the other that this probability is 0.9. How are these two values to be reconciled? We show that only the first argument is valid for a standard, countably additive probability distribution. However, both lines of reasoning are legitimate if probabilities are non-standard. The subjective probability of death rises from 1/36 to 0.9 by conditionalizing on an event that is not measurable, or whose probability is zero. Thus we can sometimes meaningfully ascribe conditional probabilities even when the event conditionalized upon is not of positive finite (or even infinitesimal) measure. More... »

PAGES

403-437

References to SciGraph publications

Journal

TITLE

Synthese

ISSUE

3

VOLUME

118

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1005100407551

DOI

http://dx.doi.org/10.1023/a:1005100407551

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1051188931


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