Ranking Experiments under Sequential Sampling

We rank experiments when a decision maker samples sequentially and chooses when to stop. We define two orders: large-budget dominance compares values in every decision problem once the expected-sample budget exceeds a common threshold; small-cost dominance compares values net of sampling costs when the cost per observation is sufficiently small in each problem. Generically, the orders coincide and are characterized by directed Kullback--Leibler (KL) dominance: larger KL divergence for every ordered pair of states. We also characterize the cost per copy of producing a specified experiment at scale by sampling a fixed source experiment. With a full-support prior, these cost functions are precisely sums of statewise maxima of positively weighted directed KL divergences. These costs are additive with two states but exhibit economies of scope with three or more states. Both results rest on an exact reproduction theorem: any experiment generated by sequentially sampling one source can be reproduced exactly by sampling another, with sharp first-order KL conversion rates and a square-root remainder whose coefficient depends only on the two sources.