On the Evidence Needed to Reach Agreed Action between Adversaries, with Application to Acceptance Sampling

Two decision makers disagree about a quantity of interest to them both. One of them, the “consumer,” has a choice of two decisions that are affected by the quantity. The other, the “manufacturer,” offers to perform an agreed type of experiment that it is hoped will change the consumer's view of the quantity and hence the decision. This article is devoted to the evaluation of how much experimentation should be done. Binomial, Poisson, and normal likelihoods, together with their conjugate utilities and probabilities, are considered and illustrated by numerical cases. The scenario considered here arises in applications to quality control, bidding, drug testing, marketing, and sales.