Naïve Learning with Uninformed Agents

The DeGroot model has emerged as a credible alternative to the standard Bayesian model for studying learning on networks, offering a natural way to model naïve learning in a complex setting. One unattractive aspect of this model is the assumption that the process starts with every node in the network having a signal. We study a natural extension of the DeGroot model that can deal with sparse initial signals. We show that an agent’s social influence in this generalized DeGroot model is essentially proportional to the degree-weighted share of uninformed nodes who will hear about an event for the first time via this agent. This characterization result then allows us to relate network geometry to information aggregation. We show information aggregation preserves “wisdom” in the sense that initial signals are weighed approximately equally in a model of network formation that captures the sparsity, clustering, and small-world properties of real-world networks. We also identify an example of a network structure where essentially only the signal of a single agent is aggregated, which helps us pinpoint a condition on the network structure necessary for almost full aggregation. Simulating the modeled learning process on a set of real-world networks, we find that there is on average 22.4 percent information loss in these networks. We also explore how correlation in the location of seeds can exacerbate aggregation failure. Simulations with real-world network data show that with clustered seeding, information loss climbs to 34.4 percent. (JEL D83, D85, Z13)

Using a novel genetic algorithm to assess peer influence on willingness to use pre-exposure prophylaxis in networks of Black men who have sex with men

The DeGroot model for opinion diffusion over social networks dates back to the 1970s and models the mechanism by which information or disinformation spreads through a network, changing the opinions of the agents. Extensive research exists about the behavior of the DeGroot model and its variations over theoretical social networks; however, research on how to estimate parameters of this model using data collected from an observed network diffusion process is much more limited. Existing algorithms require large data sets that are often infeasible to obtain in public health or social science applications. In order to expand the use of opinion diffusion models to these and other applications, we developed a novel genetic algorithm capable of recovering the parameters of a DeGroot opinion diffusion process using small data sets, including those with missing data and more model parameters than observed time steps. We demonstrate the efficacy of the algorithm on simulated data and data from a social network intervention leveraging peer influence to increase willingness to take pre-exposure prophylaxis in an effort to decrease transmission of human immunodeficiency virus among Black men who have sex with men.

TRUST MODELING: A PROBABILITY APPROACH

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).

A Survey on Nonstrategic Models of Opinion Dynamics

The paper presents a survey on selected models of opinion dynamics. Both discrete (more precisely, binary) opinion models as well as continuous opinion models are discussed. We focus on frameworks that assume non-Bayesian updating of opinions. In the survey, a special attention is paid to modeling nonconformity (in particular, anticonformity) behavior. For the case of opinions represented by a binary variable, we recall the threshold model, the voter and q-voter models, the majority rule model, and the aggregation framework. For the case of continuous opinions, we present the DeGroot model and some of its variations, time-varying models, and bounded confidence models.

Notes on self-confidence in opinion dynamics

In some research involving opinion formation, there are some details that have not been studied deeply, just as the role of a person’s self-confidence in opinion dynamics. This small but important detail needs to be cleared up. Hence, in this paper, we want to discuss the self-confidence in opinion dynamics with regard to some common linear and nonlinear models: DeGroot, Friedkin–Johnsen, Deffuant–Weisbuch and Hegselmann–Krause (HK) model. We unfold that (1) A person’s self-confidence assumption has an important impact on the consensus condition in DeGroot model; (2) The relationship between the self-confidence on the initial opinion and the current opinion follows a Kuznets curve in Friedkin–Johnsen model; (3) A person’s self-confidence has a close relationship with the convergence parameter in Deffuant–Weisbuch model, which has little impact on the number of opinion clusters at the stable stage; and (4) A person’s self-confidence varies with time at first and then stays at a certain level finally in the HK model, while the person’s self-confidence does not change with time in above three models.

Experiments on Belief Formation in Networks

We study belief formation in social networks using a laboratory experiment. Participants in our experiment observe an imperfect private signal on the state of the world and then simultaneously and repeatedly guess the state, observing the guesses of their network neighbors in each period. Across treatments we vary the network structure and the amount of information participants have about the network. Our first result shows that information about the network structure matters and in particular affects the share of correct guesses in the network. This is inconsistent with the widely used naive (deGroot) model. The naive model is, however, consistent with a larger share of individual decisions than the competing Bayesian model, whereas both models correctly predict only about 25%–30% of consensus beliefs. We then estimate a larger class of models and find that participants do indeed take network structure into account when updating beliefs. In particular they discount information from neighbors if it is correlated, but in a more rudimentary way than a Bayesian learner would.