This paper poses a problem for Lewis’ Principal Principle in a subjective Bayesian framework: we show that, where chances inform degrees of belief, subjective Bayesianism fails to validate normal informal standards of what is reasonable. This problem points to a tension between the Principal Principle and the claim that conditional degrees of belief are conditional probabilities. However, one version of objective Bayesianism has a straightforward resolution to this problem, because it avoids this latter claim. The problem, then, offers some support (...) to this version of objective Bayesianism. (shrink)

This paper poses a problem for Lewis’ Principal Principle in a subjective Bayesian framework: we show that, where chances inform degrees of belief, subjective Bayesianism fails to validate normal informal standards of what is reasonable. This problem points to a tension between the Principal Principle and the claim that conditional degrees of belief are conditional probabilities. However, one version of objective Bayesianism has a straightforward resolution to this problem, because it avoids this latter claim. The problem, then, offers some support (...) to this version of objective Bayesianism. (shrink)

This paper explores the fact that linear opinion pooling can be represented as a Bayesian update on the opinions of others. It uses this fact to propose a new interpretation of the pooling weights. Relative to certain modelling assumptions the weights can be equated with the so-called truth-conduciveness known from the context of Condorcet's jury theorem. This suggests a novel way to elicit the weights.

In a series of papers over the past twenty years, and in a new book, Igor Douven has argued that Bayesians are too quick to reject versions of inference to the best explanation that cannot be accommodated within their framework. In this paper, I survey their worries and attempt to answer them using a series of pragmatic and purely epistemic arguments that I take to show that Bayes’ Rule really is the only rational way to respond to your evidence.

We often need to have beliefs about things on which we are not experts. Luckily, we often have access to expert judgements on such topics. But how should we form our beliefs on the basis of expert opinion when experts conflict in their judgments? This is the core of the novice/2-expert problem in social epistemology. A closely related question is important in the context of policy making: how should a policy maker use expert judgments when making policy in domains in (...) which she is not herself an expert? This question is more complex, given the messy and strategic nature of politics. In this paper we argue that the prediction with expert advice framework from machine learning provides helpful tools for addressing these problems. We outline conditions under which we should expert PWEA to be helpful and those under which we should not expect these methods to perform well. (shrink)

Bradley develops some theory of the linear opinion pool, in apparent contradiction to results of Dawid et al.. We investigate the sources of these contradictions, and in particular identify a mathematical error in Bradley that invalidates his main result.

Supra-Bayesianism is the Bayesian response to learning the opinions of others. Probability pooling constitutes an alternative response. One natural question is whether there are cases where probability pooling gives the supra-Bayesian result. This has been called the problem of Bayes-compatibility for pooling functions. It is known that in a common prior setting, under standard assumptions, linear pooling cannot be nontrivially Bayes-compatible. We show by contrast that geometric pooling can be nontrivially Bayes-compatible. Indeed, we show that, under certain assumptions, geometric and (...) Bayes-compatible pooling are equivalent. Granting supra-Bayesianism its usual normative status, one upshot of our study is thus that, in a certain class of epistemic contexts, geometric pooling enjoys a normative advantage over linear pooling as a social learning mechanism. We discuss the philosophical ramifications of this advantage, which we show to be robust to variations in our statement of the Bayes-compatibility problem. (shrink)

This paper contributes to the project of articulating and defending the supra-Bayesian approach to judgment aggregation. I discuss three cases where a person is disposed to defer to two different experts, and ask how they should respond when they learn about the opinion of each. The guiding principles are that this learning should go by conditionalisation, and that they should aim to update on the evidence that the expert had updated on. But this doesn’t settle how the update on pairs (...) of experts should go, because we also need to know how the experts are related. I work through three examples showing how the results change given different prior beliefs about this relationship. (shrink)

Dawid, DeGroot and Mortera showed, a quarter century ago, that any agent who regards a fellow agent as a peer--in particular, defers to the fellow agent's prior credences in the same way that she defers to her own--and updates by split-the-difference is prone to diachronic incoherence. On the other hand one may show that there are special scenarios in which Bayesian updating approximates difference splitting, so it remains an important question whether it remains a viable response to ``generic" peer update. (...) We look at arguments by two teams of philosophers against difference splitting. (shrink)