A relative interpretation of opinion formation
To what extent can an agent’s opinion be captured by a single (multi-dimensional) number? We bypass this question by defining an agent’s opinion relative to its society’s opinion. We propose a linear model, the relative opinion model (ROM), where opinion vectors which are related by an overall scaling factor are identified as equivalent. An agent’s opinion is represented by any number in R and develops according to positive and negative impacts resulting from the other agents. As a result of the relative interpretation, ROM exhibits nonlinear dynamics despite its DeGroot-like linear foundation. Even when agents are ‘well-connected’, ROM’s dynamics may lead to polarization, consensus formation and periodic behavior of the society’s opinion. For the 2-agent case, we provide an exhaustive description of ROM’s asymptotic behavior. Group dynamics have been explored as well. In particular, we provide a non-trivial condition under which groups act as a unity with respect to other groups.
Joint work by Danny Chan, Robert Duivenvoorden, Andreas Flache, and Michel Mandjes
Valentin Flietner (Tinbergen & Erasmus University Rottermdam) & Ines Lindner (Tinbergen and Free University Amsterdam)