Probability of inconsistencies in theory revision |
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Authors: | S Wenmackers D E P Vanpoucke I Douven |
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Institution: | (1) Faculty of Philosophy, University of Groningen, Oude Boteringestraat 52, 9712 GL Groningen, The Netherlands;(2) Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 – S3, 9000 Gent, Belgium |
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Abstract: | We present a model for studying communities of epistemically interacting agents who
update their belief states by averaging (in a specified way) the belief states of other
agents in the community. The agents in our model have a rich belief state, involving
multiple independent issues which are interrelated in such a way that they form a theory
of the world. Our main goal is to calculate the probability for an agent to end up in an
inconsistent belief state due to updating (in the given way). To that end, an analytical
expression is given and evaluated numerically, both exactly and using statistical
sampling. It is shown that, under the assumptions of our model, an agent always has a
probability of less than 2% of ending up in an inconsistent belief state. Moreover, this
probability can be made arbitrarily small by increasing the number of independent issues
the agents have to judge or by increasing the group size. A real-world situation to which
this model applies is a group of experts participating in a Delphi-study. |
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