The ambigous role of social influence on the wisdom of crowds: An analytic approach

“Wisdom of crowds” refers to the phenomenon that average opinion a group individuals on given question can be very close true answer. It requires large diversity opinions, but collective error, difference between and value, has small. We consider stochastic dynamics where change their based opinions others (social influence α), some degree also stick initial (individual conviction β). then derive analytic expressions for error diversity. analyze long-term behavior determine impact two parameters (α,β) distribution wisdom crowds. This allows us quantify ambiguous role social influence: only if is large, it helps improve crowds, in most cases deteriorates outcome. In these cases, individual still improves crowds because mitigates influence.