Anonymous Social Influence
40 Pages Posted: 7 Jun 2013
Date Written: June 6, 2013
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: Suggested Citation