Probability of Inconsistencies in Theory Revision: A multi-agent model for updating logically interconnected beliefs under bounded confidence

TL;DR

This paper models how communities of agents update their interconnected beliefs and calculates the low probability of inconsistency arising from such updates, with implications for expert group decision-making.

Contribution

It introduces a novel multi-agent model analyzing belief updates on interconnected issues and derives an analytical expression for inconsistency probability.

Findings

Probability of inconsistency is less than 2% under the model.

Increasing issues or group size reduces inconsistency probability.

Model applies to expert Delphi-studies.

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.