20 research outputs found
Making Consensus Tractable
We study a model of consensus decision making, in which a finite group of
Bayesian agents has to choose between one of two courses of action. Each member
of the group has a private and independent signal at his or her disposal,
giving some indication as to which action is optimal. To come to a common
decision, the participants perform repeated rounds of voting. In each round,
each agent casts a vote in favor of one of the two courses of action,
reflecting his or her current belief, and observes the votes of the rest.
We provide an efficient algorithm for the calculation the agents have to
perform, and show that consensus is always reached and that the probability of
reaching a wrong decision decays exponentially with the number of agents.Comment: 18 pages. To appear in Transactions on Economics and Computatio
Complexity of Bayesian Belief Exchange over a Network
Many important real-world decision making prob- lems involve group interactions among individuals with purely informational externalities, such situations arise for example in jury deliberations, expert committees, medical diagnosis, etc. In this paper, we will use the framework of iterated eliminations to model the decision problem as well as the thinking process of a Bayesian agent in a group decision/discussion scenario. We model the purely informational interactions of rational agents in a group, where they receive private information and act based upon that information while also observing other people’s beliefs. As the Bayesian agent attempts to infer the true state of the world from her sequence of observations which include her neighbors’ beliefs as well as her own private signal, she recursively refines her belief about the signals that other players could have observed and beliefs that they would have hold given the assumption that other players are also rational. We further analyze the computational complexity of the Bayesian belief formation in groups and show that it is NP -hard. We also investigate the factors underlying this computational complexity and show how belief calculations simplify in special network structures or cases with strong inherent symmetries. We finally give insights about the statistical efficiency (optimality) of the beliefs and its relations to computational efficiency.United States. Army Research Office (grant MURI W911NF-12- 1-0509)National Science Foundation (U.S.). Computing and Communication Foundation (grant CCF 1665252)United States. Department of Defense (ONR grant N00014-17-1-2598)National Science Foundation (U.S.) (grant DMS-1737944
Asynchronous Majority Dynamics in Preferential Attachment Trees
We study information aggregation in networks where agents make binary
decisions (labeled incorrect or correct). Agents initially form independent
private beliefs about the better decision, which is correct with probability
. The dynamics we consider are asynchronous (each round, a single
agent updates their announced decision) and non-Bayesian (agents simply copy
the majority announcements among their neighbors, tie-breaking in favor of
their private signal).
Our main result proves that when the network is a tree formed according to
the preferential attachment model \cite{BarabasiA99}, with high probability,
the process stabilizes in a correct majority within
rounds. We extend our results to other tree structures, including balanced
-ary trees for any .Comment: ICALP 202
Dynamics of Social Networks: Multi-agent Information Fusion, Anticipatory Decision Making and Polling
This paper surveys mathematical models, structural results and algorithms in
controlled sensing with social learning in social networks.
Part 1, namely Bayesian Social Learning with Controlled Sensing addresses the
following questions: How does risk averse behavior in social learning affect
quickest change detection? How can information fusion be priced? How is the
convergence rate of state estimation affected by social learning? The aim is to
develop and extend structural results in stochastic control and Bayesian
estimation to answer these questions. Such structural results yield fundamental
bounds on the optimal performance, give insight into what parameters affect the
optimal policies, and yield computationally efficient algorithms.
Part 2, namely, Multi-agent Information Fusion with Behavioral Economics
Constraints generalizes Part 1. The agents exhibit sophisticated decision
making in a behavioral economics sense; namely the agents make anticipatory
decisions (thus the decision strategies are time inconsistent and interpreted
as subgame Bayesian Nash equilibria).
Part 3, namely {\em Interactive Sensing in Large Networks}, addresses the
following questions: How to track the degree distribution of an infinite random
graph with dynamics (via a stochastic approximation on a Hilbert space)? How
can the infected degree distribution of a Markov modulated power law network
and its mean field dynamics be tracked via Bayesian filtering given incomplete
information obtained by sampling the network? We also briefly discuss how the
glass ceiling effect emerges in social networks.
Part 4, namely \emph{Efficient Network Polling} deals with polling in large
scale social networks. In such networks, only a fraction of nodes can be polled
to determine their decisions. Which nodes should be polled to achieve a
statistically accurate estimates
Asynchronous Majority Dynamics on Binomial Random Graphs
We study information aggregation in networks when agents interact to learn a
binary state of the world. Initially each agent privately observes an
independent signal which is "correct" with probability for
some . At each round, a node is selected uniformly at random to
update their public opinion to match the majority of their neighbours (breaking
ties in favour of their initial private signal). Our main result shows that for
sparse and connected binomial random graphs the process
stabilizes in a "correct" consensus in steps
with high probability. In fact, when the process
terminates at time , where is the first time
when all nodes have been selected at least once. However, in dense binomial
random graphs with , there is an information cascade where the
process terminates in the "incorrect" consensus with probability bounded away
from zero