Anonymous Social Influence

40 Pages Posted: 7 Jun 2013

See all articles by Manuel Foerster

Manuel Foerster

University of Hamburg - Department of Economics

Michel Grabisch

Université Paris I Panthéon-Sorbonne - CERMSEM

Agnieszka Rusinowska

CNRS - Paris School of Economics

Date Written: June 6, 2013

Abstract

We study a stochastic model of influence where agents have “yes” or “no” inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ordered weighted averaging operators, which are anonymous: they only depend on how many agents share an opinion. For instance, this allows to study situations where the influence process is based on majorities, which are not covered by the classical approach of weighted averaging aggregation. We find a necessary and sufficient condition for convergence to consensus and characterize outcomes where the society ends up polarized. Our results can also be used to understand more general situations, where ordered weighted averaging operators are only used to some extent. We provide an analysis of the speed of convergence and the possible outcomes of the process. Furthermore, we apply our results to fuzzy linguistic quantifiers, i.e., expressions like “most” or “at least a few”.

Keywords: Influence, Anonymity, Ordered Weighted Averaging Operator, Convergence, Consensus, Speed Of Convergence, Fuzzy Linguistic Quantifier

JEL Classification: C7, D7, D85

Suggested Citation

Foerster, Manuel and Grabisch, Michel and Rusinowska, Agnieszka, Anonymous Social Influence (June 6, 2013). FEEM Working Paper No. 51.2013. Available at SSRN: https://ssrn.com/abstract=2275236 or http://dx.doi.org/10.2139/ssrn.2275236

Manuel Foerster (Contact Author)

University of Hamburg - Department of Economics ( email )

Von-Melle-Park 5
room 2128 C rise
Hamburg, 20146
Germany

Michel Grabisch

Université Paris I Panthéon-Sorbonne - CERMSEM ( email )

106-112, Boulevard de l'Hôpital
Paris, 75647
France

Agnieszka Rusinowska

CNRS - Paris School of Economics ( email )

3, rue Michel-Ange
106-112 Boulevard de l'Hôpital
Paris cedex 16, 75794
France

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