AN ENERGY-BASED INTERACTION MODEL FOR POPULATION OPINION DYNAMICS WITH TOPIC COUPLING

Abstract

Thesis (Ph.D.), Mathematics, Washington State UniversityOpinion dynamics, also called the opinion game, has gained a great deal of attention during past several decades. It tries to model and explain the evolution of opinions of people in a society. How individuals learn, how ideas are spread out, the role of leaders and/or media in directing public opinion, co-existence of different ideas held by distinct groups and loss of cultures and languages in global village era are fascinating phenomena, attracting the attention of scientists. A new general variational model based on pairwise interaction potentials is introduced, where each agent can behave in its own unique way which can vary depending on the topic or even depending on whom it is interacting with. The model can be extended to the synchronous version in which an agent interacts with all of its neighbors at the same time. We observe interesting behavior emerges in the synchronous version of the game for simple potential functions such as a tent function. The model supports the concept of topic ``coupling'', allowing opinions held by individuals to be changed via indirect interaction with others on different subjects. As mentioned above, co-existence of different ideas are of interest. However, recent technological changes have increased connectivity between individuals around the world leading to higher frequency interactions between members of social groups that would be otherwise distant and disconnected. In Chapter 3, we examine the model of opinion dynamics in interacting groups and study how increasing interaction frequency affects the ability for groups to retain distinct identities versus falling into consensus or polarized states in which group identity is lost. We also study the effect (if any) of opinion noise related to a tendency for individuals to assert their individuality in homogenous populations.Washington State University, Mathematic