Continuous-Time Distributed Learning for Collective Wisdom Maximization

Motivated by the well established idea that collective wisdom is greater than that of an individual, we propose a novel learning dynamics as a sort of companion to the Abelson model of opinion dynamics. Agents are assumed to make independent guesses about the true state of the world after which they engage in opinion exchange leading to consensus. We investigate the problem of finding the optimal parameters for this exchange, e.g. those that minimize the variance of the consensus value. Specifically, the parameter we examine is susceptibility to opinion change. We propose a dynamics for distributed learning of the optimal parameters and analytically show that it converges for all relevant initial conditions by linking to well established results from consensus theory. Lastly, a numerical example provides intuition on both system behavior and our proof methods.