Selection of nonextremal candidates from a random sequence

Problems of optimal choice generally invoke monotone preference functions; consequently, optimal strategies consider stopping the sequence only when extremal (best/worst) or nearly extremal candidates are presented. The objective of the present investigation is to select a candidate representative of the entire sequence. In particular, selection of the median object and selection of any object from a set of middle ranks are considered.Portions of this paper were presented at the Joint National Meeting of the Institute of Management Sciences and the Operations Research Society of America, Washington, DC, 1980.The author is grateful to Professor M. DeGroot, who suggested the median problem of Section 2 and who has been most encouraging.The proof of Theorem 2.1 is due to an anonymous referee and constitutes a significant improvement upon the original version.