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Two-Step Drawing from Urns

In: Operations Research Proceedings 2004

Author

Listed:
  • Stephan Kolassa

    (Friedrich-Schiller-Universität Jena)

  • Stefan Schwarz

    (Friedrich-Schiller-Universität Jena)

Abstract

Consider the following situation of two-step shortlisting: two experts Alice and Bob are faced with a large number of alternatives which they can only observe imprecisely. They have to choose one of the alternatives, without knowing which one is best. Alice first compiles a shortlist of alternatives by choosing her k best observations. Bob then chooses his best observation among the shortlisted alternatives. Previous research showed that this procedure sometimes yielded worse results than if a single expert made the entire decision himself. Here, we consider an urn containing n — 1 homogeneous balls and one ball with larger weight. When drawing balls at random from the urn, the probability of drawing any one ball is proportional to its weight. Alice draws k balls and puts them in another urn, from which Bob then draws a single ball. Which value of k maximizes the probability that Bob draws the distinguished ball?

Suggested Citation

  • Stephan Kolassa & Stefan Schwarz, 2005. "Two-Step Drawing from Urns," Operations Research Proceedings, in: Hein Fleuren & Dick Hertog & Peter Kort (ed.), Operations Research Proceedings 2004, pages 313-318, Springer.
    • Handle: RePEc:spr:oprchp:978-3-540-27679-1_39
    DOI: 10.1007/3-540-27679-3_39
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