How to quantify the coherence of a set of beliefs

Rowan Hess; Lionel Levine

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arXiv · 2412.02777

How to quantify the coherence of a set of beliefs

Rowan Hess·Lionel Levine

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Abstract

Given conflicting probability estimates for a set of events, how can we quantify how much they conflict? How can we find a single probability distribution that best encapsulates the given estimates? One approach is to minimize a loss function such as binary KL-divergence that quantifies the dissimilarity between the given estimates and the candidate probability distribution. Given a set of events, we characterize the facets of the polytope of coherent probability estimates about those events. We explore two applications of these ideas: eliciting the beliefs of large language models, and merging expert forecasts into a single coherent forecast.

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BibTeX RIS

Rowan Hess, Lionel Levine. 2024-12-03. How to quantify the coherence of a set of beliefs. https://arxiv.org/abs/2412.02777

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