Increasing returns and the efficient acquisition of information

Increasing returns are inherent in information: the number of events that can be distinguished is an exponential function of the number of partitions applied to a state space. Just as factories should run at a large scale in the face of increasing returns, each partition should be coarse to allow the number of partitions to be large. This principle also holds for partitions, or equivalently questions, that are applied sequentially. When agents need to process all the answers to a question, 3-answer questions dominate the efficient arrays of questions. If however agents can deduce that when all but one of the answers to a question are rejected then the remaining answer must be accepted, binary questions are efficient. Counterintuitively, a decrease in the cost of processing answers reduces the efficient number of answers.