# Sociophysics: probability of inconsistency in opinion dynamics

Author
Organization
Abstract
Sociophysics is an interdisciplinary field which applies the methodology of physics to questions in sociology. In particular, opinion dynamics provides agent-based models to study processes of belief revision in societies. In the models for opinion dynamics, the agents update their current opinions by averaging the belief states of other agents in the community. When the agents hold opinions on logically related issues, the updating process may give rise to inconsistent belief states. We model the agents’ beliefs as ‘theories about the world’ and assume that each agent holds a consistent theory initially. This allows us to calculate the probability for an agent to end up in an inconsistent belief state due to updating [1]. To that end, an analytical expression is given and evaluated numerically. The simulations show 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 issues the agents have to judge or by increasing the group size. [1] S. Wenmackers, D.E.P. Vanpoucke, I. Douven. “Determining the Probability of Inconsistencies in Theory Updating under Bounded Confidence.” Submitted to J. Math. Soc. (2010).
Keywords
sociophysics, simulation, opinion dynamics

## Citation

Chicago
Wenmackers, Sylvia, Danny Vanpoucke, and Igor Douven. 2011. “Sociophysics: Probability of Inconsistency in Opinion Dynamics.” In Belgian Physical Society, Annual General Scientific Meeting, Abstracts. Belgian Physical Society (BPS).
APA
Wenmackers, Sylvia, Vanpoucke, D., & Douven, I. (2011). Sociophysics: probability of inconsistency in opinion dynamics. Belgian Physical Society, Annual general scientific meeting, Abstracts. Presented at the 2011 Annual general scientific meeting of the Belgian Physical Society (BPS 2011), Belgian Physical Society (BPS).
Vancouver
1.
Wenmackers S, Vanpoucke D, Douven I. Sociophysics: probability of inconsistency in opinion dynamics. Belgian Physical Society, Annual general scientific meeting, Abstracts. Belgian Physical Society (BPS); 2011.
MLA
Wenmackers, Sylvia, Danny Vanpoucke, and Igor Douven. “Sociophysics: Probability of Inconsistency in Opinion Dynamics.” Belgian Physical Society, Annual General Scientific Meeting, Abstracts. Belgian Physical Society (BPS), 2011. Print.
```@inproceedings{1887347,
abstract     = {Sociophysics is an interdisciplinary field which applies the
methodology of physics to questions in sociology. In particular, opinion dynamics provides agent-based models to study processes of belief revision in societies. In the models for opinion dynamics, the agents update their current opinions by averaging the belief states of other agents in the community.

When the agents hold opinions on logically related issues, the
updating process may give rise to inconsistent belief states. We model the agents{\textquoteright} beliefs as {\textquoteleft}theories about the world{\textquoteright} and assume that each agent holds a consistent theory initially. This allows us to calculate the probability for an agent to end up in an inconsistent belief state due to updating [1]. To that end, an analytical expression is given and evaluated numerically.

The simulations show 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 issues the agents have to judge or by increasing the group size.

[1] S. Wenmackers, D.E.P. Vanpoucke, I. Douven. {\textquotedblleft}Determining the Probability of Inconsistencies in Theory Updating under Bounded Confidence.{\textquotedblright} Submitted to J. Math. Soc. (2010).},
author       = {Wenmackers, Sylvia and Vanpoucke, Danny and Douven, Igor},
booktitle    = {Belgian Physical Society, Annual general scientific meeting, Abstracts},
isbn         = {9782870377178},
keyword      = {sociophysics,simulation,opinion dynamics},
language     = {eng},
location     = {Namur, Belgium},
publisher    = {Belgian Physical Society (BPS)},
title        = {Sociophysics: probability of inconsistency in opinion dynamics},
year         = {2011},
}

```