The paper’s target is the historically influential betting interpretation of subjective probabilities due to Ramsey and de Finetti. While there are several classical and well-known objections to this interpretation, the paper focuses on just one fundamental problem: There is a sense in which degrees of belief cannot be interpreted as betting rates. The reasons differ in different cases, but there’s one crucial feature that all these cases have in common: The agent’s degree of belief in a proposition A does not (...) coincide with her degree of belief in a conditional that A would be the case if she were to bet on A, where the belief in this conditional itself is conditioned on the supposition that the agent will have an opportunity to make such a bet. Even though the two degrees of belief sometimes can coincide (they will coincide in those cases when the bet has no expected causal bearings on the proposition A and the opportunity to bet have no evidential bearings on that proposition), it is the latter belief rather than the former that guides the agent’s rational betting behaviour. The reason is that this latter belief takes into consideration potential interferences that bet opportunities and betting itself might create with regard to the proposition to be betted on. It is because of this interference problem that the agent’s degree of belief in A cannot be interpreted as her betting rate for A. (shrink)

A critical examination of the Reflection principle in Bayesian epistemology, and of the diachronic Dutch-book-style arguments that have been invoked to support Reflection and Conditionalization.

The Puzzle of the Hats is a betting arrangement which seems to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players’ rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences and (...) betting rates diverge. Second, there is an analogy between ways of dealing with situations of this kind and different policies for sequential choice. Third, there is an analogy with strategic voting, showing that the common interest is not always served by expressing how things seem to you in social decision-making. And fourth, our analysis of the Puzzle of the Hats casts light on a recent controversy about the Dutch book argument for the Sleeping Beauty. (shrink)

I provide a taxonomy of the various circumstances under which one might reasonably say "P and I will believe that not-P" or violate the Reflection Principle.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

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." 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 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. (shrink)

The Puzzle of the Hats is a betting arrangement which seems to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players’ rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences and (...) betting rates diverge. Second, there is an analogy between ways of dealing with situations of this kind and different policies for sequential choice. Third, there is an analogy with strategic voting, showing that the common interest is not always served by expressing how things seem to you in social decision-making. (shrink)

My focus is on pragmatic arguments for various rationality constraints on a decision maker’s state of mind: on his beliefs or preferences. An argument of this kind purports to show that a violator of a given constraint can be exposed to a decision problem in which she will act to her guaranteed disadvantage. Dramatically put, she can be exploited by a clever bookie who doesn’t know more than the agent himself. Examples of pragmatic arguments of this kind are synchronic Dutch (...) Books, for the standard probability axioms, diachronic Dutch Books, for the more controversial principles of reflection and conditionalization, and Money Pumps, for the transitivity requirement on preferences. It is suggested that the proposed exploitation set-ups share a common feature. If the violator of a given constraint is logically and mathematically competent, she can be exploited only if she is disunified in his decision-making, i.e., only if she makes decisions on various issues she confronts separately rather than jointly. In other words, exploitation is possible only if the decision problem has been framed in a certain way. Unification in decision making is relatively unproblematic in synchronic contexts, but it may be quite costly and inconvenient diachronically, especially when the issues under consideration are widely spread over time. On my view, therefore, pragmatic arguments should be seen as delivering conditional recommendations: If you want to afford disunification, then you’d better satisfy these constraints. The arguments of this kind fail to establish the inherent rationality of the constraints under consideration. Isaac Levis view of the status of pragmatic arguments is diametrically opposed to mine. According to him, only synchronic pragmatic arguments are valid. The diachronic ones, he argues, lack any validity at all. This line of reasoning is questioned in my paper. (shrink)

The Puzzle of the Hats is a betting arrangement which seems to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players’ rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences and (...) betting rates diverge. Second, there is an analogy between ways of dealing with situations of this kind and different policies for sequential choice. Third, there is an analogy with strategic voting, showing that the common interest is not always served by expressing how things seem to you in social decision-making. And fourth, our analysis of the Puzzle of the Hats casts light on a recent controversy about the Dutch book argument for the Sleeping Beauty. (shrink)

My focus is on pragmatic arguments for various rationality constraints on a decision maker’s state of mind: on his beliefs or preferences. An argument of this kind purports to show that a violator of a given constraint can be exposed to a decision problem in which she will act to her guaranteed disadvantage. Dramatically put, she can be exploited by a clever bookie who doesn’t know more than the agent himself. Examples of pragmatic arguments of this kind are synchronic Dutch (...) Books, for the standard probability axioms, diachronic Dutch Books, for the more controversial principles of reflection and conditionalization, and Money Pumps, for the transitivity requirement on preferences. It is suggested that the proposed exploitation set-ups share a common feature. If the violator of a given constraint is logically and mathematically competent, she can be exploited only if she is disunified in his decision-making, i.e., only if she makes decisions on various issues she confronts separately rather than jointly. In other words, exploitation is possible only if the decision problem has been framed in a certain way. Unification in decision making is relatively unproblematic in synchronic contexts, but it may be quite costly and inconvenient diachronically, especially when the issues under consideration are widely spread over time. On my view, therefore, pragmatic arguments should be seen as delivering conditional recommendations: If you want to afford disunification, then you’d better satisfy these constraints. The arguments of this kind fail to establish the inherent rationality of the constraints under consideration. Isaac Levis view of the status of pragmatic arguments is diametrically opposed to mine. According to him, only synchronic pragmatic arguments are valid. The diachronic ones, he argues, lack any validity at all. This line of reasoning is questioned in my paper. (shrink)