People have always been influenced by the opinions of their acquaintances. Increasingly, through recommendations and ratings provided on all sorts of goods and services, people are also influenced by the opinions of people that are not even acquaintances. This ubiquity of the sharing of opinions has intensified the interest is the concept of herding (or informational cascades) introduced in 1992. While agents in most previous works have only individualistic goals, this talk focuses on social influence among agents in two collaborative settings.
We consider agents that perform Bayesian binary hypothesis testing and, in addition to their private signals, observe the decisions of earlier-acting agents. In the first setting, each decision has its own corresponding Bayes risk. Each agent affects the minimum possible Bayes risk for subsequent agents, so an agent may have a mixed objective including her own Bayes risk and the Bayes risks of subsequent agents; we demonstrate her tension between being informative to other agents and being right in her own decisions, and we show that she is more informative to others when she is open minded. In the second setting, opinions are aggregated by voting, and all agents aim to minimize the Bayes risk of the team's decision. We show that social learning is futile when the agents observe conditionally independent and identically distributed private signals (but not merely conditionally independent private signals) or when the agents require unanimity to make a decision. Our experiments with human subjects suggest that when opinions of people with equal qualities of information are aggregated by voting, the ballots should be secret. They have also raised questions about rationality and trust.
Vivek Goyal received the B.S. degree in mathematics and the B.S.E. degree in electrical engineering from the University of Iowa, where he received the John Briggs Memorial Award for the top undergraduate across all colleges. He received the M.S. and Ph.D. degrees in electrical engineering from the University of California, Berkeley, where he received the Eliahu Jury Award for outstanding achievement in systems, communications, control, or signal processing. He was a Member of Technical Staff in the Mathematics of Communications Research Department of Bell Laboratories, a Senior Research Engineer for Digital Fountain, and the Esther and Harold E. Edgerton Associate Professor of Electrical Engineering at MIT. He is now on leave from the Department of Electrical and Computer Engineering of Boston University. He was an adviser to 3dim Tech, Inc., and is now with Google.
Dr. Goyal is a Fellow of the IEEE. He was awarded the 2002 IEEE Signal Processing Society Magazine Award, an NSF CAREER Award, and the Best Paper Award at the 2014 IEEE International Conference on Image Processing. Work he supervised won student best paper awards at the IEEE Data Compression Conference in 2006 and 2011 and the IEEE Sensor Array and Multichannel Signal Processing Workshop in 2012 as well as four MIT thesis awards. He currently serves on the Editorial Board of Foundations and Trends and Signal Processing and the Scientific Advisory Board of the Banff International Research Station for Mathematical Innovation and Discovery. He is a Technical Program Committee Co-chair of Sampling Theory and Applications 2015 and a permanent Conference Co-chair of the SPIE Wavelets and Sparsity conference series. He is a co-author of Foundations of Signal Processing (Cambridge University Press, 2014).