There are many things—call them ‘experts’—that you should defer to in forming your opinions. The trouble is, many experts are modest: they’re less than certain that they are worthy of deference. When this happens, the standard theories of deference break down: the most popular (“Reflection”-style) principles collapse to inconsistency, while their most popular (“New-Reflection”-style) variants allow you to defer to someone while regarding them as an anti-expert. We propose a middle way: deferring to someone involves preferring to make any decision (...) using their opinions instead of your own. In a slogan, deferring opinions is deferring decisions. Generalizing the proposal of Dorst (2020a), we first formulate a new principle that shows exactly how your opinions must relate to an expert’s for this to be so. We then build off the results of Levinstein (2019) and Campbell-Moore (2020) to show that this principle is also equivalent to the constraint that you must always expect the expert’s estimates to be more accurate than your own. Finally, we characterize the conditions an expert’s opinions must meet to be worthy of deference in this sense, showing how they sit naturally between the too-strong constraints of Reflection and the too-weak constraints of New Reflection. (shrink)

Good’s theorem is the apparent platitude that it is always rational to ‘look before you leap’: to gather information before making a decision when doing so is free. We argue that Good’s theorem is not platitudinous and may be false. And we argue that the correct advice is rather to ‘make your act depend on the answer to a question’. Looking before you leap is rational when, but only when, it is a way to do this.

In addition to purely practical values, cognitive values also figure into scientific deliberations. One way of introducing cognitive values is to consider the cognitive value that accrues to the act of accepting a hypothesis. Although such values may have a role to play, such a role does not exhaust the significance of cognitive values in scientific decision-making. This paper makes a plea for consideration of epistemic value —that is, value attaching to a state of belief—and defends the notion of cognitive (...) epistemic value against some criticisms that have been raised. A stability requirement for epistemic value functions is argued for on the basis of considerations of diachronic coherence. This stability requirement is sufficient to obtain the Value of Learning Theorem, which says that the expected utility of cost-free learning cannot be negative. This holds also for cognitive epistemic values, provided that the stability requirement is met. (shrink)

Does the philosophy of Radical Probabilism have enough structure to enable it to address fundamental epistemological questions? The requirement of dynamic coherence provides the structure for radical probabilist epistemology. This structure is sufficient to establish (i) the value of knowledge and (ii) long run convergence of degrees of belief.

We show there is only one consistent way to update a probability assignment, that given by Bayes's rule. The price of inconsistent updating is a loss of efficiency. The implications of this for the problem of induction are discussed.

Can you rationally double-check what you already know? In this paper, I argue that you can. Agents can know that something is true and rationally double-check it at the very same time. I defend my position by considering a wide variety of cases where agents double-check their beliefs to gain epistemic improvements beyond knowledge. These include certainty, epistemic resilience, and sensitivity to error. Although this phenomenon is widespread, my proposal faces two types of challenges. First, some have defended ignorance norms, (...) on which agents are only allowed to inquire about things they don't already know. Second – motivated by strong conceptions of belief or pragmatic encroachment – some have argued that double-checking destroys knowledge. I argue that these competing views fail to capture both the epistemic value of double-checking and the many reasons why agents might double-check. Moreover, they rely on overly strong assumptions about what inquiry, knowledge, or belief requires. Finally, I marshal linguistic data in favor of the compatibility of knowledge and double-checking. (shrink)

We explore the question of whether cost-free uncertain evidence is worth waiting for in advance of making a decision. A classical result in Bayesian decision theory, known as the value of evidence theorem, says that, under certain conditions, when you update your credences by conditionalizing on some cost-free and certain evidence, the subjective expected utility of obtaining this evidence is never less than the subjective expected utility of not obtaining it. We extend this result to a type of update method, (...) a variant of Judea Pearl’s virtual conditionalization, where uncertain evidence is represented as a set of likelihood ratios. Moreover, we argue that focusing on this method rather than on the widely accepted Jeffrey conditionalization enables us to show that, under a fairly plausible assumption, gathering uncertain evidence not only maximizes expected pragmatic utility, but also minimizes expected epistemic disutility. (shrink)

A "symptomatic act" is an act that is evidence for a state that it has no tendency to cause. In this paper I show that when the evidential value of a symptomatic act might influence subsequent choices, causal decision theory may initially recommend against its own use for those subsequent choices. And if one knows that one will nevertheless use causal decision theory to make those subsequent choices, causal decision theory may favor the one-box solution in Newcomb's problem, and may (...) recommend against making cost-free observations. But if one can control one's future choices, then causal decision theory never recommends against cost-free observation. (shrink)

Nobody's going to object to the advice "Do the right thing", but that doesn't mean everyone's always going to follow it. Sometimes this is because of our volitional limitations; we cannot always bring ourselves to make the sacrifices that right action requires. But sometimes this is because of our cognitive limitations; we cannot always be sure of what is right. Sometimes we can't be sure of what's right because we don't know the non-normative facts. But sometimes, even if we were (...) to know all of the non-normative facts, we'd still not be sure about what's right, because we're uncertain about the normative reasons those facts give us. In this dissertation, I attempt to answer the question of what we're to do when we must act under fundamentally normative uncertainty. It's tempting to think that, in such circumstances, we should do what we regard as most probably right. I argue that this view is mistaken, for it is insensitive to how degrees of actions' values compare across different normative hypotheses; if an action is probably right, but, if wrong, is terribly, terribly, wrong, it may be rational not to do that action. A better answer is that we should do the action with the highest expected value. I spend the first part of the dissertation providing arguments for and rebutting arguments against this view of action under normative uncertainty. I spend the next part of the dissertation explaining what degrees of value are, and showing how they can be compared across normative hypotheses. In the remaining parts of the dissertation, I consider two questions related to our primary question -- first, what is one required, or obligated, to do under normative uncertainty; and second, what is it rational for one to do when one is not only normatively uncertain in the way we've been discussing, but also uncertain about what it is rational to do under this sort of normative uncertainty. (shrink)

I.J. Good's ``On the Principle of Total Evidence" (1967) looms large in decision theory and Bayesian epistemology. Good proves that in Savage's (1954) decision theory, a coherent agent always prefers to collect, rather than ignore, free evidence. It is now well known that Good's result was prefigured in an unpublished note by Frank Ramsey (Skyrms 2006). The present paper highlights another early forerunner to Good's argument, appearing in Janina Hosiasson's ``Why do We Prefer Probabilities Relative to Many Data?" (1931), that (...) has been neglected in the literature. Section 1 reviews Good's argument and the problem it was meant to resolve; call this the \textit{value of evidence problem}. Section 2 offers a brief history of the value of evidence problem and provides biographical background to contextualize Hosiasson's contribution. Section 3 explicates the central argument of Hosiasson's paper and considers its relationship to Good's (1967). (shrink)

Generalized probabilistic learning takes place in a black-box where present probabilities lead to future probabilities by way of a hidden learning process. The idea that generalized learning can be partially characterized by saying that it doesn’t foreseeably lead to harmful decisions is explored. It is shown that a martingale principle follows for finite probability spaces.