  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.
