Munich Center for Mathematical Philosophy (MCMP)

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Zoom Talk: Name Jan-Willem Romeijn (University of Groningen)

Meeting-ID: 950 1039 5841

19.01.2022 at 16:15 

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Extremizing: Social Learning, Meta-analysis, and Inductive Logic

Joint work with Simon Huttegger (UC Irvine)


This paper is concerned with methods for aggregating expert opinions, more in particular the aggregation of statistical results. Topics from social epistemology are thereby connected to statistical meta-analysis. The primary topic is a phenomenon known as “extremizing”: in some cases it is rational to have the aggregated estimate lie outside the convex hull of input estimations. This phenomenon can be connected to the “risky shift” observed in social psychology, where agents irrationally amplify each others’ opinions, but also to successful forecasting methods and to the correction of biases described in Kahneman’s prospect theory. All in all, the paper offers new ways of thinking about meta-analysis by combining insights from inductive logic and social epistemology.

Concretely, we will present three models in which extremizing can be rationalized. The first and simplest of these relies on multiplicative pooling. We show how this model connects to the Bayesian version of Condorcet’s Jury Theorem. A further model represents expert opinions in terms of Carnapian predictive systems, which allows us to capture the information overlap among experts as well as the biases described in prospect theory. A third model, finally, substantially generalizes the second model by framing it in terms of non-parametric Bayesian inference. A connection to inductive logic is provided by Blackwell-McQueen processes and Ferguson distributions, the natural generalization of Carnapian predictive systems to continuous attribute spaces.