We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem recapitulates insights achieved by other investigators, and clarifi es the connection of coherence and proper scoring rules to Bregman divergence.

The most immediately appealing model for formal constraints on degrees of belief is provided by probability theory, which tells us, for instance, that the probability of P can never be greater than that of (P v Q). But while this model has much intuitive appeal, many have been concerned to provide arguments showing that ideally rational degrees of belief would conform to the calculus of probabilities. The arguments most frequently used to make this claim plausible are the so-called "Dutch Book" (...) arguments. (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.

In Bayesian epistemology, the problem of the priors is this: How should we set our credences (or degrees of belief) in the absence of evidence? That is, how should we set our prior or initial credences, the credences with which we begin our credal life? David Lewis liked to call an agent at the beginning of her credal journey a superbaby. The problem of the priors asks for the norms that govern these superbabies. -/- The Principle of Indifference gives a (...) very restrictive answer. It demands that such an agent divide her credences equally over all possibilities. That is, according to the Principle of Indifference, only one initial credence function is permissible, namely, the uniform distribution. In this paper, we offer a novel argument for the Principle of Indifference. I call it the Argument from Accuracy. (shrink)

According to Bayesian epistemology, the epistemically rational agent updates her beliefs by conditionalization: that is, her posterior subjective probability after taking account of evidence X, pnew, is to be set equal to her prior conditional probability pold(·|X). Bayesians can be challenged to provide a justification for their claim that conditionalization is recommended by rationality—whence the normative force of the injunction to conditionalize? There are several existing justifications for conditionalization, but none directly addresses the idea that conditionalization will be epistemically rational (...) if and only if it can reasonably be expected to lead to epistemically good outcomes. We apply the approach of cognitive decision theory to provide a justification for conditionalization using precisely that idea. We assign epistemic utility functions to epistemically rational agents; an agent’s epistemic utility is to depend both upon the actual state of the world and on the agent’s credence distribution over possible states. We prove that, under independently motivated conditions, conditionalization is the unique updating rule that maximizes expected epistemic utility. (shrink)

Is there a rational requirement enjoining continence over time in the intentions one has formed, such that anyone going in for a certain form of agency has standing reason to conform to such a requirement? This paper suggests that there is not. I argue that Michael Bratman’s defense of such a requirement succeeds in showing that many agents have a reason favoring default intention continence much of the time, but does not establish that all planning agents have such a reason (...) in every case of intending. I then defend an account on which such a reason is grounded in the need to maintain the capacity to commit oneself to a practical option. But although I think this applies more widely than Bratman’s account, it is also not a reason that any planning agent has in every case. I tentatively conclude that although we have many good reasons to stick with our intentions once we have formed them, it is not required by rationality. (shrink)

Believing rationally is epistemically valuable, or so we tend to think. It’s something we strive for in our own beliefs, and we criticize others for falling short of it. We theorize about rationality, in part, because we want to be rational. But why? I argue that how we answer this question depends on how permissive our theory of rationality is. Impermissive and extremely permissive views can give good answers; moderately permissive views cannot.

Jim Joyce has presented an argument for Probabilism based on considerations of epistemic utility [Joyce, 1998]. In a recent paper, I adapted this argument to give an argument for Probablism and the Principal Principle based on similar considerations [Pettigrew, 2012]. Joyce’s argument assumes that a credence in a true proposition is better the closer it is to maximal credence, whilst a credence in a false proposition is better the closer it is to minimal credence. By contrast, my argument in that (...) paper assumed (roughly) that a credence in a proposition is better the closer it is to the objective chance of that proposition. In this paper, I present an epistemic utility argument for Probabilism and the Principal Principle that retains Joyce’s assumption rather than the alternative I endorsed in the earlier paper. I argue that this results in a superior argument for these norms. (shrink)

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its prequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism (...) follow from the norm, while the characteristic claim of the Objectivist Bayesian follows from the norm along with an extra assumption. Finally, we consider Richard Jeffrey’s proposed generalization of conditionalization. We show not only that his rule cannot be derived from the norm, unless the requirement of Rigidity is imposed from the start, but further that the norm reveals it to be illegitimate. We end by deriving an alternative updating rule for those cases in which Jeffrey’s is usually supposed to apply. (shrink)

Expected accuracy arguments have been used by several authors (Leitgeb and Pettigrew, and Greaves and Wallace) to support the diachronic principle of conditionalization, in updates where there are only finitely many possible propositions to learn. I show that these arguments can be extended to infinite cases, giving an argument not just for conditionalization but also for principles known as ‘conglomerability’ and ‘reflection’. This shows that the expected accuracy approach is stronger than has been realized. I also argue that we should (...) be careful to distinguish diachronic update principles from related synchronic principles for conditional probability. (shrink)