TRUST MODELING: A PROBABILITY APPROACH

Abstract

The work is devoted to describing an application of the DeGroot model in the following analysis: is it possible to establish a consensus of opinions of members in a social group (a society). This model describes the process of changing the agents’ opinion about a certain event or statement, factoring in the effect of interpersonal trust between agents, which is modelled by Markov chains. Agents’ opinions are represented by the probability of them showing their support to a given statement (event). The interpretation of the DeGroot model is quite broad. It includes, in particular, the study of economic decision-making, the influence of public opinion on people and the fact of achieving a consensus. The paper considers the conditions under which the process of updating the opinions of agents, belonging to a social group (network), converges to a certain limit value - a consensus, i.e. a case when all agents in a social group have the same opinion on a particular issue. We also show some generalizations of the DeGroot model, namely those that concern adding time dependency to the rules of updating the opinions of agents. To test the DeGroot model, we implemented the two-dimensional case as a dynamic Microsoft Excel workbook. The paper describes 2 types of problems related to reaching a consensus, solved with the model. The first kind of problem constitutes an analysis of possibilities of obtaining the desired consensus with a given matrix of trust (interpersonal trust of agents), whilst changing the initial group members’ opinions vector about an event (statement). We also discuss a solution of the inverse problem: find the trust matrix such that the iterative opinion update process converges to the desired consensus with a given initial vector of opinions. The results we obtained may be used for analyzing the process of managing public (collective) opinion concerning certain economic decisions in a social group (network).