Senior Honors Thesis: "Group Decision-Making with Negative Influence Actors"

Abstract:  When a group makes a decision, the consensus—if one exists—is determined by the agents’ initial opinions and the extent to which the agents are able to influence one another during the decision-making process. Many mathematical representations exist that model this process and determine under what conditions a group will reach a consensus. All practical models assume that decision-makers try to influence each other’s opinions regarding the issue and that the decision-making process defines restrictions and opportunities for said influence. The classical model and its variations additionally assume that the agents act simultaneously and in discrete time. Most of these models are linear, for simplicity. Most models additionally assume that an agent’s influence on another agent is a nonnegative, real number in the interval [0, 1] and that every decision-maker is aware of the opinions of the other actors, even if he or she chooses to ignore some of them. In these models, an agent’s opinion is non-decreasing over time due to the nonnegative constraint. In this paper, I explore a regular opinion function adapted from the classical model that allows decision-makers with conflicting opinions or personalities to negatively influence each other. That is, given two agents i and j such that j has negative influence on i, i ’s opinion decreases under j ’s influence. I explain why this allowance complicates the classical model and define under what new conditions a group will reach a consensus. These questions have, to the best of my knowledge, not been investigated. in the literature of opinion dynamics thus far.

Advisor: John Shareshian