Quantifying a Statistical Aspect of Segmented Selection/Quota Systems

Abstract

We consider the problem of filling n positions from a pool of N applicants. We assume that there exists an objective measure of each applicant's ability—the applicant's “score.” Letting Q be the mean score of the n accepted applicants, we study the difference in Q as the N applicants are stratified into K subsets, a certain number of the n accepted applicants necessarily coming from each subset. Clearly, any accepted group other than the top n out of N will result in a lower Q. We consider how the decrease in average score, Q, varies with various parameters and proportion allocations. There is no question that the issue of segmented selection (essentially, quota systems) can be controversial. Many argue for and many argue against using segmented selection, under such names as veteran's preference, affirmative action, and others. We take no “stand” on this controversy. We consider solely this one statistical/quantitative aspect of the segmented selection/quota system question. We believe that the results contained herein provide a useful backdrop under which the controversial aspects of the issue can be discussed.

Key Words:

• Normal distribution
• Order statistics
• Quota systems