Macroscopes: Models for Collective Decision Making
We introduce a new model of collective decision mak- ing, when a global decision needs to be made but the parties only possess partial information, and are unwill- ing (or unable) to rst create a global composite of their local views. Our macroscope model captures two key fea- tures of many real-world problems: allotment structure (how access to local information is apportioned between parties, including overlaps between the parties) and the possible presence of meta-information (what each party knows about the allotment structure of the overall prob- lem). Using the framework of communication complex- ity, we formalize the ecient solution of a macroscope. We present general results about the macroscope model, and also results that abstract the essential computa- tional operations underpinning practical applications, including in nancial markets and decentralized sensor networks. We illustrate the computational problem in- herent in real-world collective decision making processes using results for specic functions, involving detecting a change in state (constant and step functions), and com- puting statistical properties (the mean).