# Logical dynamics of belief change in the community

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## Abstract

In this paper we explore the relationship between norms of belief revision that may be adopted by members of a community and the resulting dynamic properties of the distribution of beliefs across that community. We show that at a qualitative level many aspects of social belief change can be obtained from a very simple model, which we call ‘threshold influence’. In particular, we focus on the question of what makes the beliefs of a community stable under various dynamical situations. We also consider refinements and alternatives to the ‘threshold’ model, the most significant of which is to consider changes to plausibility judgements rather than mere beliefs. We show first that some such change is mandated by difficult problems with belief-based dynamics related to the need to decide on an order in which different beliefs are considered. Secondly, we show that the resulting plausibility-based account results in a deterministic dynamical system that is *non*-deterministic at the level of beliefs.

## Keywords

Belief revision Belief influence Community Plausibility judgement## Notes

### Acknowledgments

We would like to thank Frank Zenker and Carlo Proietti for their efforts in putting together this volum. A previous version of the paper was presented at the LOGICIC kick-off workshop: Belief Change in Social Context in Amsterdam, at the Centre for Mathematical Social Science seminar series in Auckland, New Zealand, and at the Workshop on Knowledge Representation and Reasoning in Guiyang, China. We would like to thank the participants of each event, and in particular Christian List, Zoé Christoff, Chenwei Shi, Shaun White and Mark C. Wilson for valuable comments and discussions. Finally, we would like to thank the anonymous referees for their useful comments. Fenrong Liu is supported by the Project of National Social Science Foundation of China (No.13AZX018) and Tsinghua University Initiative Scientific Research Program (20131089292).

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