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Evaluating Test Cases for Probabilistic Measures of Coherence

Abstract

How can we determine the adequacy of a probabilistic coherence measure? A widely accepted approach to this question besides formulating adequacy constraints is to employ paradigmatic test cases consisting of a scenario providing a joint probability distribution over some specified set of propositions coupled with a normative coherence assessment for this set. However, despite the popularity of the test case approach, a systematic evaluation of the proposed test cases is still missing. This paper’s aim is to change this. Using a custom written computer program for the necessary probabilistic calculations a large number of coherence measures in an extensive collection of test cases is examined. The result is a detailed overview of the test case performance of any probabilistic coherence measures proposed so far. It turns out that none of the popular coherence measures such as Shogenji’s, Glass’ and Olsson’s, Fitelson’s or Douven and Meijs’ but two rather unnoticed measures perform best. This, however, does not mean that the other measures can be rejected straightforwardly. Instead, the results presented here are to be understood as a contribution among others to the project of finding adequate probabilistic coherence measures.

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Acknowledgments

I would like to thank Michael Schippers and Mark Siebel for helpful comments or discussion. This work was supported by grant SI 1731/1-1 to Mark Siebel from the Deutsche Forschungsgemeinschaft (DFG) as part of the priority program “New Frameworks of Rationality” (SPP 1516).

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Correspondence to Jakob Koscholke.

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Koscholke, J. Evaluating Test Cases for Probabilistic Measures of Coherence. Erkenn 81, 155–181 (2016). https://doi.org/10.1007/s10670-015-9734-1

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  • DOI: https://doi.org/10.1007/s10670-015-9734-1

Keywords

  • Support Measure
  • Joint Probability Distribution
  • Coherence Measure
  • Relative Score
  • Alternative Generalization