Abstract
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.
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Communicated by S. E. Dreyfus
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.
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Rose, J.S. Selection of nonextremal candidates from a random sequence. J Optim Theory Appl 38, 207–219 (1982). https://doi.org/10.1007/BF00934083
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DOI: https://doi.org/10.1007/BF00934083