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Abstract: Suppose there are n items, with each item having an unknown value. At any time, we can can either stop and declare which item has the largest value or else choose a subset of items to compare.
If subset S is chosen, then a given item in S will be preferred with a probability equal to the value of that item divided by the sum of the values of all items in S.
Assuming a Bayesian prior on the values, and subject to the proviso that the policy employed will make the correct choice with probability at least some specified value, we are looking for a policy that needs a relatively small mean number of comparisons before making a decision. Some heuristic policies are presented and analyzed.