The Interference Problem for the Betting Interpretetation

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Abstract

Abstract in Undetermined
On an influential interpretation, the agent's degrees of belief asr identified with her betting rates. However, being placed in a betting situation can itself change one’s degree of belief in the proposition in question. The problem as such isn’t new. Ramsey, for example, was right on to this idea when he wrote:
"… the proposal of a bet may inevitably alter [one’s] state of opinion; just as we could not always measure electric intensity by actually introducing a charge and seeing what force it was subject to, because the introduction of the charge would change the distribution to be measured." (Ramsey 1931 [1926], p. 172)
This ‘interference problem’ for the betting interpretation can best be put in the following way: The bets we are disposed to accept do not manifest our current unconditional degrees of belief in various propositions. Whether a bet on A would be accepted or not does not depend on the agent’s degree of belief in A but rather on the degree of belief she would have if she were confronted with this bet proposal, or – more generally – the degree of belief she would have if she were in a position to bet on A. Assuming the conditionalization model for belief change, this means that whether the agent would be willing to bet depends on her current conditional beliefs concerning A on the hypothetical supposition that she has an opportunity to make this bet. Furthermore, her disposition to bet also depends on the expected effects the act of betting would have on the truth of the proposition to be betted on. Both these phenomena imply that finding oneself in a betting situation might alter one’s expectations in important ways. Consequently, the identification of (unconditional) degrees of belief with betting rates is a mistake. We show that this problem comes up in several different versions, or – equivalently – that different kinds of arguments against the betting interpretation stem from the same source.

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Subject classification (UKÄ) – MANDATORY

  • Philosophy

Keywords

  • belief, probabilities, bets, betting, decision theory, Levi, Spohn, Ramsey, de Finetti
Original languageEnglish
JournalSynthese
Volumepublished on-line
Publication statusSubmitted - 2012
Publication categoryResearch
Peer-reviewedYes

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