A pragmatic characterisation of linear pooling
How we should determine a group’s collective probabilistic judgments, given the probabilistic judgments of the individuals in the group? A standard answer is given by this condition: The group probability distribution over the propositions should be a weighted average of the individual probability distributions. Call this Linear Pooling. We provide a condition on aggregates that characterises linear pooling: Given a utility function shared by all members of the group, if each individual in the group expects one act to have greater utility than another, then the group expects the first act to have greater utility than the second. Call this Pareto. We prove that Linear Pooling and Pareto are equivalent.
Aggregating incoherent agents who disagree
In this paper, we explore how we should aggregate the degrees of belief of a group of agents to give a single coherent set of degrees of belief, when at least some of those agents might be probabilistically incoherent. There are a number of way of aggregating degrees of belief, and there are a number of ways of fixing incoherent degrees of belief. When we have picked one of each, should we aggregate first and then fix, or fix first and then aggregate? Or should we try to do both at once? And when do these different procedures agree with one another? In this paper, we focus particularly on the final question.
On the accuracy of group credences
in Szabó Gendler, T. & J. Hawthorne (eds.) Oxford Studies in Epistemology volume 6
We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And how do they relate to the individual credences assigned by the members of the particular group in question? According to the credal judgment aggregation principle, Linear Pooling, the credence function of a group should be a weighted average or linear pool of the credence functions of the individuals in the group. In this paper, I give an argument for Linear Pooling based on considerations of accuracy. And I respond to two standard objections to the aggregation principle.
Deference done right (with Mike Titelbaum)
Philosophers’ Imprint 14(35):1-19
There are many kinds of epistemic experts to which we might wish to defer in setting our credences. These include: highly rational agents, objective chances, our own future credences, our own current credences, and evidential (or logical) probabilities. But how, precisely, ought we defer to these experts? Exactly what constraint does a deference requirement place on an agent’s credences at a particular time?
In this paper we consider three possible answers, inspired by three different principles that have been proposed for deference to objective chances. We consider how these options fare when applied to the other kinds of epistemic experts mentioned above. Besides assuming a baseline probabilism about rational credences, we are particularly interested in the following two desiderata:
- A deference principle should be consistent with both the agent’s and the experts’ updating by Conditionalization.
- A deference principle should permit agents to have various kinds of doubts about what’s rationally required.
Of the three deference principles we consider, we argue that two of the options face insuperable difficulties meeting these desiderata. The third, on the other hand, fares well — at least when it is applied in a particular way.