Bounded Confidence Opinion Dynamics in a Social Network of Bayesian Decision Makers

Abstract

Bounded confidence opinion dynamics model the propagation of information in social networks. However in the existing literature, opinions are only viewed as abstract quantities without semantics rather than as part of a decision-making system. In this work, opinion dynamics are examined when agents are Bayesian decision makers that perform hypothesis testing or signal detection, and the dynamics are applied to prior probabilities of hypotheses. Bounded confidence is defined on prior probabilities through Bayes risk error divergence, the appropriate measure between priors in hypothesis testing. This definition contrasts with the measure used between opinions in standard models: absolute error. It is shown that the rapid convergence of prior probabilities to a small number of limiting values is similar to that seen in the standard Krause-Hegselmann model. The most interesting finding in this work is that the number of these limiting values and the time to convergence changes with the signal-to-noise ratio in the detection task. The number of final values or clusters is maximal at intermediate signal-to-noise ratios, suggesting that the most contentious issues lead to the largest number of factions. It is at these same intermediate signal-to-noise ratios at which the degradation in detection performance of the aggregate vote of the decision makers is greatest in comparison to the Bayes optimal detection performance. ). 1 In all of these questions, one of the hypotheses is true and the other one is false.

Belief Dynamics in Social Networks: A Fluid-Based Analysis

“…2 is based on a chain of inequalities, some of which may be rather loose in many cases. steady-state distribution can now be obtained by solving the Fredholm integral equation (19) in φ * (p); • at last, in Sec. 4.3 we consider the most challenging scenario where bounded confidence is in place.…”

“…Another relevant class of models is represented by the so-called bounded confidence, in which social interactions occur only between agents with similar beliefs [11], [13], [14], [15], [16], [17], [18], [19], [20]. In particular, [19], [20] show how bounded confidence models can be used to represent social interactions between Bayesian decision makers. Relevantly to our work, [15] models the social influence on the global opinion evolution in the case of homogeneous agent interactions.…”

“…On the one hand, bounded confidence models are particularly interesting because they permit to represent belief-dependent social behaviors, such as "homophily", which are often observed in real systems. On the other hand, their analysis poses several challenges because the equations driving the agents' interactions become non linear [11], [15], [16], [17], [18], [19], [20].…”

A tutorial on modeling and analysis of dynamic social networks. Part II

“…Bounded confidence models appear to be related with community detection algorithms in graphs [169], Bayesian algorithms for distributed decision making [170] and algorithms of data clustering [171]. Bounded confidence models have been proposed for dynamics of "uncertain" opinions (standing for intervals of possible values) [172] and "linguistic" opinions representing words of a formal language [54,173].…”

Effect of Stubborn Agents on Bounded Confidence Opinion Dynamic Systems: Unanimity in Presence of Stubborn Agents

“…This model is developed to simulate fragmentation and polarization of opinions and effect of various type of agents in such a system has been analyzed. Authors in [14] have illustrated the effect of charismatic and radical agents, while [15] derived optimal controller for a leader and [16] has analyzed Bayesian decision makers in bounded confidence opinion dynamics. Also, various modifications are published to extend H-K model for various goals [11,[17][18][19].…”