Kolassa, Stephan
(2005)
*Two-Step Drawing From Urns.*
In:
Operations Research Proceedings 2004.
Operations Research Proceedings
.
Springer, pp. 313-318.
ISBN 9783540242741

## 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?