Zachary Kilpatrick, Department of Applied Mathematics, University of Colorado Boulder
Heterogeneity improves speed and accuracy in social networks
How does temporally structured private and social information shape collective decisions? To address this question we consider a clique of rational agents who independently accumulate private evidence that triggers a decision upon reaching a threshold. Agents’ individual beliefs are given by drift-diffusion equations that receive pulsatile inputs from other deciding agents, according to a normative model derived using Bayesian sequential updating. When seen by the whole network, the first agent’s choice initiates a wave of new decisions; later decisions have less impact. The time and accuracy of the group decision is determined by the extremal statistics of a first passage time problem. In heterogeneous networks, first decisions are made quickly by impulsive individuals who need little evidence to make a choice, but, even when wrong, can reveal the correct options to nearly everyone else. We conclude that groups comprised of diverse individuals can make more efficient decisions than homogenous ones. This is joint work with Bhargav Karamched (Florida State), Krešimir Josić (U Houston), Megan Stickler (U Houston), Benjamin Lindner (Humboldt U Berlin), and Will Ott (U Houston).