Social Networks and Social Choice Lecture Date : September 7 , 2010 Lecture : Aggregation of General Biased Signals

First, let us consider the case when n people make a decision between k alternatives, denoted 1, . . . , k, where one of the k alternatives is correct. We can make various assumptions on the type of signals individuals receive. The most general assumption is the following: there is a signal space X (e.g. X = R), and distributions P1, . . . , Pk on X, and if the correct alternative is i, then each individual receives independently a signal distributed according to Pi. A nice non-general assumption that we analyze in more detail is this: each individual receives independently the correct alternative with probability p > 1/k, and each other alternative with probability (1− p) / (k − 1).