Two-Step Drawing from Urns

Stephan Kolassa () and Stefan Schwarz ()
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Stephan Kolassa: Friedrich-Schiller-Universität Jena
Stefan Schwarz: Friedrich-Schiller-Universität Jena

A chapter in Operations Research Proceedings 2004, 2005, pp 313-318 from Springer

Abstract: 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?

Date: 2005
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DOI: 10.1007/3-540-27679-3_39

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