Title: Sequential Decision Aggregation

Speaker: Francesco Bullo
	 http://motion.me.ucsb.edu

Joint work with: Sandra H. Dandach and Ruggero Carli


Abstract: 

This paper studies prototypical strategies to sequentially aggregate
independent decisions.  We consider a collection of agents, each performing
binary hypothesis testing and each obtaining a decision over time.  We
assume the agents are identical and receive independent information.
Individual decisions are sequentially aggregated via a threshold-based
rule. In other words, a collective decision is taken as soon as a specified
number of agents report a concordant decision (simultaneous discordant
decisions and no-decision outcomes are also handled).

We obtain the following results.  First, we characterize the probabilities
of correct and wrong decisions as a function of time, group size and
decision threshold. The computational requirements of our approach are
linear in the group size.  Second, we consider the so-called fastest and
majority rules, corresponding to specific decision thresholds. For these
rules, we provide a comprehensive scalability analysis of both accuracy and
decision time.  In the limit of large group sizes, we show that the
decision time for the fastest rule converges to the earliest possible
individual time, and that the decision accuracy for the majority rule shows
an exponential improvement over the individual accuracy.  Additionally, via
a theoretical and numerical analysis, we characterize various
speed/accuracy tradeoffs. Finally, we relate our results to some recent
observations reported in the cognitive information processing literature.