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Cautious Belief Formation

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  • Bleile, Jörg

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We provide an axiomatic approach to a belief formation process in an informational environment characterized by limited, heterogenous and differently precise information. For a list of previously observed cases an agent needs to express her belief by assigning probabilities to possible outcomes. Different numbers of observations of a particular case give rise to varying precision levels associated to the pieces of information. Different precise information affects the cautiousness and confidence with which agents form estimations. We modify the Concatenation axiom introduced in Billot, Gilboa, Samet and Schmeidler (BGSS) (Econometrica, 2005) in a way to capture the impact of precision and its related perceptional effects, while still keeping its normative appealing spirit. We obtain a representation of a belief as a weighted sum of estimates induced by past cases. The estimates are affected by cautiousness and confidence considerations depending on the precision of the underlying observed information, which generalizes BGSS. The weights are determined by frequencies of the observed cases and their similarities with the problem under consideration.

Suggested Citation

  • Bleile, Jörg, 2016. "Cautious Belief Formation," Center for Mathematical Economics Working Papers 507, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:507
    as

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    File URL: https://pub.uni-bielefeld.de/download/2901523/2902028
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    References listed on IDEAS

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    Keywords

    Belief formation; prior; relative frequencies; case-based reasoning; similarity precision; ambiguity; learning; imagination; con dence; cautiousness.;
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