Ditional attribute distribution P(xk) are known. The solid lines in
Ditional attribute distribution P(xk) are known. The strong lines in Figs two report these calculations for every single network. The conditional probability P(x k) P(x0 k0 ) necessary to calculate the strength with the “majority illusion” working with Eq (5) may be specified analytically only for networks with “BIBS 39 wellbehaved” degree distributions, like scale ree distributions of the type p(k)k with three or the Poisson distributions with the ErdsR yi random graphs in nearzero degree assortativity. For other networks, such as the real world networks having a more heterogeneous degree distribution, we use the empirically determined joint probability distribution P(x, k) to calculate both P(x k) and kx. For the Poissonlike degree distributions, the probability P(x0 k0 ) could be determined by approximating the joint distribution P(x0 , k0 ) as a multivariate normal distribution: hP 0 jk0 hP 0 rkx resulting in P 0 jk0 hxi rkx sx 0 hki sk sx 0 hki; skFig 5 reports the “majority illusion” inside the very same synthetic scale ree networks as Fig 2, but with theoretical lines (dashed lines) calculated making use of the Gaussian approximation for estimating P(x0 k0 ). The Gaussian approximation fits final results fairly effectively for the network with degree distribution exponent 3.. On the other hand, theoretical estimate deviates significantly from information in a network with a heavier ailed degree distribution with exponent 2.. The approximation also deviates from the actual values when the network is strongly assortative or disassortative by degree. Overall, our statistical model that utilizes empirically determined joint distribution P(x, k) does a great job explaining most observations. Nonetheless, the international degree assortativity rkk is definitely an significant contributor to the “majority illusion,” a a lot more detailed view on the structure employing joint degree distribution e(k, k0 ) is essential to accurately estimate the magnitude from the paradox. As demonstrated in S Fig, two networks with the very same p(k) and rkk (but degree correlation matrices e(k, k0 )) can show various amounts in the paradox.ConclusionLocal prevalence of some attribute amongst a node’s network neighbors is usually incredibly distinct from its global prevalence, making 
an illusion that the attribute is far more typical than it actually is. In a social network, this illusion might lead to people to reach wrong conclusions about how typical a behavior is, leading them to accept as a norm a behavior that is globally uncommon. In addition, it might also clarify how international outbreaks can be triggered by quite couple of initial adopters. This might also explain why the observations and inferences folks make of their peers are frequently incorrect. Psychologists have, actually, documented a number of systematic biases in social perceptions [43]. The “false consensus” effect arises when folks overestimate the prevalence of their very own features within the population [8], believing their form to bePLOS A single DOI:0.37journal.pone.04767 February 7,9 Majority IllusionFig five. Gaussian approximation. Symbols show the empirically determined fraction of nodes within the paradox regime (identical as in Figs 2 and 3), whilst dashed lines show theoretical estimates employing the Gaussian approximation. doi:0.37journal.pone.04767.gmore frequent. As a result, Democrats think that most of the people are also Democrats, though Republicans believe that the majority are Republican. “Pluralistic PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/22570366 ignorance” is another social perception bias. This effect arises in circumstances when men and women incorrectly think that a majority has.