How Robust Is the Wisdom of the Crowds?

Noga Alon, Michal Feldman, Omer Lev, Moshe Tennenholtz

Abstract: We introduce the study of adversarial effects on wisdom of the crowd phenomena. In particular, we examine the ability of an adversary to influence a social network so that the majority of nodes are convinced by a falsehood, using its power to influence a certain fraction, µ 0:5. When we examine expander graphs as well as random graphs we prove such bounds even for stronger adversaries, who are able to pick and choose not only who the experts are, but also which ones of them would communicate the wrong values, as long as their proportion is 1 - p. Furthermore, we study different propagation models and their effects on the feasibility of obtaining the true value for different adversary types.