The Impact of Liars on Reputation in Social Networks

We consider a closed social network with a certain proportion of liars who are trying to influence their peers reputation about some subject. Each persons reputation about this subject is based on both own direct experience and second hand information from their peers which cannot be verified. Given certain assumptions on when people believe or do not believe second hand information, we investigate the liars impact on their peers reputation about the subject. We present a mathematical model for this situation and show that there is a threshold proportion of liars below which they have no impact. Above it, liars do have an impact. We quantify this impact and give the threshold proportions. We compare our results in two fundamentally dierent scenarios: In the first one, reputation is passed on as second hand information. In the second one, direct experience only is passed on as second hand information. We find that in the latter scenario liars have less impact.