Team Guessing with Lacunary Information
Published Online:1 Feb 1983https://doi.org/10.1287/moor.8.1.110
Abstract
Let E be an event of probability q and let U1, …, Un be independent random variables. There are n observers, the ith observing the n-1 random variables other than Ui. Each observer must guess whether E occurred. Then if pi is the probability of error of observer i, one has
$$\prod_{i-1}^n (p_i + p) \geq P^{n-1}$$
where p = max(q, 1 − q), and this bound is sharp.One application is related to a coding theorem. The coding is used to reduce degradation when data transmission is split over n parallel channels, any one of which might have broken down.
The result also has a more symmetric corollary which can be stated as a probabilistic inequality of an unusual type.
