Impact of perception models on friendship paradox and opinion formation

TL;DR

This paper investigates how different perception models influence the friendship paradox and opinion formation in social networks, revealing that perception models significantly affect peer pressure and consensus dynamics.

Contribution

It compares three perception models' effects on the friendship paradox and demonstrates their impact on opinion formation and consensus times in social networks.

Findings

Mean-based perception model shows nontrivial behavior with assortativity.

Median-based perception model leads to the longest consensus time.

Proper perception modeling is crucial for understanding social dynamics.

Abstract

Topological heterogeneities of social networks have a strong impact on the individuals embedded in those networks. One of the interesting phenomena driven by such heterogeneities is the friendship paradox (FP), stating that the mean degree of one's neighbors is larger than the degree of oneself. Alternatively, one can use the median degree of neighbors as well as the fraction of neighbors having a higher degree than oneself. Each of these reflects on how people perceive their neighborhoods, i.e., their perception models, hence how they feel peer pressure. In our paper, we study the impact of perception models on the FP by comparing three versions of the perception model in networks generated with a given degree distribution and a tunable degree-degree correlation or assortativity. The increasing assortativity is expected to decrease network-level peer pressure, while we find a nontrivial behavior only for the mean-based perception model. By simulating opinion formation, in which the opinion adoption probability of an individual is given as a function of individual peer pressure, we find that it takes the longest time to reach consensus when individuals adopt the median-based perception model, compared to other versions. Our findings suggest that one needs to consider the proper perception model for better modeling human behaviors and social dynamics.