PACM Colloquium: An Axiomatic Foundation for Non-Bayesian Learning in Networks

Speaker: 
Ali Jadbabaie - Massachusetts Institute of Technology (MIT)
Date: 
Nov 9 2015 - 3:15pm
Event type: 
PACM Colloquium
Room: 
214 Fine Hall
Abstract: 

Rational learning postulates that individuals incorporate new information into their beliefs in a Bayesian fashion. Despite its theoretical appeal, this Bayesian learning framework has been criticized on the basis of placing unrealistic computational demands on the agents. Furthermore, experiments have  shown that the way agents update their beliefs in networked settings is often inconsistent with predictions of  Bayesian learning models.  Motivated by these issues, A large body of literature has emerged that  proposes a series of non-Bayesian updates that are often inspired by the linear (consensus) learning model of DeGroot. However, a systematic framework that captures behavioral deviations of such updates from Bayesian learning has been lacking. In this talk, I will present a theoretical foundations for non-Bayesian aggregation of beliefs by taking an axiomatic approach that introduces a set of axioms about  the agents’ behaviors. Rather than proposing functional form for the belief updates, I will present behavioral axioms from which updates are derived. The first behavioral assumption is a notion of imperfect recall, according to which agents take the current belief of their neighbors as sufficient statistics, ignoring how and why their current opinions were formed. Next, I will impose a set of behavioral axioms that are all satisfied by Bayesian agents. I will  show that a combination of these behavioral assumptions leads to an update that combines log-likelihood  ratios of the neighboring beliefs in a linear fashion.  Using the notion of group polarization from social psychology literature, I will provide conditions on these weights that lead to learning and mis-learning. I will  then discuss implications of relaxing some of the axioms not he functional form of the updates. If time permits, I will  also characterize the rate of convergence for this family of updates and describe how the rate depends on the network structure and information endowment of agents.

Joint work with Pooya Molavi (MIT Economics), Alireza Tahbaz Salehi (Columbia Graduate School of Business) , Shahin Shahrampour (Harvard), and   Amin Rahimian (Penn ESE)