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?
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References
Kolassa S. (2004a) An Anomaly in Two-Step Shortlisting by Imperfect Experts. Submitted to Mathematics and Computers in Simulation
Kolassa S. (2004b) Multi-Step Shortlisting by Imperfect Experts. Submitted as dissertation at the Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, Germany.
Kolassa S., Schwarz S. (2003) Two-Step Shortlisting by Imperfect Experts. Technical Report 03-19. Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, Germany, http://www.minet.uni-jena.de/preprints/kolassa_03/two_agent_shortlisting.pdf
Schmidt R. (2004) Multiple-Choice-Optimierung am Beispiel des Urnenmodells. Unpublished manuscript. Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, Germany
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© 2005 Springer-Verlag Berlin Heidelberg
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Kolassa, S., Schwarz, S. (2005). Two-Step Drawing from Urns. In: Fleuren, H., den Hertog, D., Kort, P. (eds) Operations Research Proceedings 2004. Operations Research Proceedings, vol 2004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27679-3_39
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DOI: https://doi.org/10.1007/3-540-27679-3_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24274-1
Online ISBN: 978-3-540-27679-1
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