Fuzzy inference based Hegselmann–Krause opinion dynamics for group decision-making under ambiguity

A Hybrid Opinion Formation and Polarization Model

The last decade has witnessed a great number of opinion formation models that depict the evolution of opinions within a social group and make predictions about the evolution process. In the traditional formulation of opinion evolution such as the DeGroot model, an agent's opinion is represented as a real number and updated by taking a weighted average of its neighbour's opinions. In this paper, we adopt a hybrid representation of opinions that integrate both the discrete and continuous nature of an opinion. Basically, an agent has a 'Yes', 'Neutral' or 'No' opinion on some issues of interest and associates with its Yes opinion a support degree which captures how strongly it supports the opinion. With such a rich representation, not only can we study the evolution of opinion but also that of support degree. After all, an agent's opinion can stay the same but become more or less supportive of it. Changes in the support degree are progressive in nature and only a sufficient accumulation of such a progressive change will result in a change of opinion say from Yes to No. Hence, in our formulation, after an agent interacts with another, its support degree is either strengthened or weakened by a predefined amount and a change of opinion may occur as a consequence of such progressive changes. We carry out simulations to evaluate the impacts of key model parameters including (1) the number of agents, (2) the distribution of initial support degrees and (3) the amount of change of support degree changes in a single interaction. Last but not least, we present several extensions to the hybrid and progressive model which lead to opinion polarization.

Mathematical measures of societal polarisation

In opinion dynamics, as in general usage, polarisation is subjective. To understand polarisation, we need to develop more precise methods to measure the agreement in society. This paper presents four mathematical measures of polarisation derived from graph and network representations of societies and information-theoretic divergences or distance metrics. Two of the methods, min-max flow and spectral radius, rely on graph theory and define polarisation in terms of the structural characteristics of networks. The other two methods represent opinions as probability density functions and use the Kullback-Leibler divergence and the Hellinger distance as polarisation measures. We present a series of opinion dynamics simulations from two common models to test the effectiveness of the methods. Results show that the four measures provide insight into the different aspects of polarisation and allow real-time monitoring of social networks for indicators of polarisation. The three measures, the spectral radius, Kullback-Leibler divergence and Hellinger distance, smoothly delineated between different amounts of polarisation, i.e. how many cluster there were in the simulation, while also measuring with more granularity how close simulations were to consensus. Min-max flow failed to accomplish such nuance.

Opinion Dynamics with Higher-Order Bounded Confidence

The higher-order interactions in complex systems are gaining attention. Extending the classic bounded confidence model where an agent's opinion update is the average opinion of its peers, this paper proposes a higher-order version of the bounded confidence model. Each agent organizes a group opinion discussion among its peers. Then, the discussion's result influences all participants' opinions. Since an agent is also the peer of its peers, the agent actually participates in multiple group discussions. We assume the agent's opinion update is the average over multiple group discussions. The opinion dynamics rules can be arbitrary in each discussion. In this work, we experiment with two discussion rules: centralized and decentralized. We show that the centralized rule is equivalent to the classic bounded confidence model. The decentralized rule, however, can promote opinion consensus. In need of modeling specific real-life scenarios, the higher-order bounded confidence is more convenient to combine with other higher-order interactions, from the contagion process to evolutionary dynamics.

Opinion Dynamics Model with Bounded Confidence and the Sleeper Effect

The evolution of opinions is a complex mechanism. The evolution of individual opinions is not only influenced by own and others but also by psychological effects. Therefore, based on the classical bounded confidence model and the sleeper effect, a new opinion evolution model is proposed in this paper. In this new opinion evolution model, we increase the opinions on every step and take into account the “discount opinions.” Since mental states for human are not easy to measure, we assumed three different initial networks and carried out simulation experiments. To verify the rationality on our model, we compared the effects with and without the sleeper effect, different thresholds, and discounting opinion ratio on opinion aggregation and convergence. Finally, we found the sleeper effect can differently affect the convergence of opinions in different opinion environments.