(Failure of the) Wisdom of the crowds in an endogenous opinion dynamics model with multiply biased agents

We study an endogenous opinion (or, belief) dynamics model where we endogenize the social network that models the link (‘trust’) weights between agents. Our network adjustment mechanism is simple: an agent increases her weight for another agent if that agent has been close to truth (whence, our adjustment criterion is ‘past performance’). Moreover, we consider multiply biased agents that do not learn in a fully rational manner but are subject to persuasion bias — they learn in a DeGroot manner, via a simple ‘rule of thumb’ — and that have biased initial beliefs. In addition, we also study this setup under conformity, opposition, and homophily — which are recently suggested variants of DeGroot learning in social networks — thereby taking into account further biases agents are susceptible to. Our main focus is on crowd wisdom, that is, on the question whether the so biased agents can adequately aggregate dispersed information and, consequently, learn the true states of the topics they communicate about. In particular, we present several conditions under which wisdom fails.