To thine own self be untrue : a diagnosis of the cable guy paradox

Research output: Journal PublicationsJournal Article (refereed)

Abstract

Hájek has recently presented the following paradox. You are certain that a cable guy will visit you tomorrow between 8 a.m. and 4 p.m. but you have no further information about when. And you agree to a bet on whether he will come in the morning interval (8, 12] or in the afternoon interval (12, 4). At first, you have no reason to prefer one possibility rather than the other. But you soon realise that there will definitely be a future time at which you will (rationally) assign higher probability to an afternoon arrival than a morning one, due to time elapsing. You are also sure there may not be a future time at which you will (rationally) assign a higher probability to a morning arrival than an afternoon one. It would therefore appear that you ought to bet on an afternoon arrival. The paradox is based on the apparent incompatibility of the principle of expected utility and principles of diachronic rationality which are prima facie plausible. Hájek concludes that the latter are false, but doesn't provide a clear diagnosis as to why. We endeavour to further our understanding of the paradox by providing such a diagnosis.
Original languageEnglish
Pages (from-to)355-364
Number of pages10
JournalLogique et Analyse
Volume51
Issue number204
Publication statusPublished - 1 Jan 2008
Externally publishedYes

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Paradox
Rationality
Diachrony
Expected Utility

Cite this

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title = "To thine own self be untrue : a diagnosis of the cable guy paradox",
abstract = "H{\'a}jek has recently presented the following paradox. You are certain that a cable guy will visit you tomorrow between 8 a.m. and 4 p.m. but you have no further information about when. And you agree to a bet on whether he will come in the morning interval (8, 12] or in the afternoon interval (12, 4). At first, you have no reason to prefer one possibility rather than the other. But you soon realise that there will definitely be a future time at which you will (rationally) assign higher probability to an afternoon arrival than a morning one, due to time elapsing. You are also sure there may not be a future time at which you will (rationally) assign a higher probability to a morning arrival than an afternoon one. It would therefore appear that you ought to bet on an afternoon arrival. The paradox is based on the apparent incompatibility of the principle of expected utility and principles of diachronic rationality which are prima facie plausible. H{\'a}jek concludes that the latter are false, but doesn't provide a clear diagnosis as to why. We endeavour to further our understanding of the paradox by providing such a diagnosis.",
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To thine own self be untrue : a diagnosis of the cable guy paradox. / ROWBOTTOM, Darrell Patrick; BAUMANN, Peter.

In: Logique et Analyse, Vol. 51, No. 204, 01.01.2008, p. 355-364.

Research output: Journal PublicationsJournal Article (refereed)

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