Mathematical Oddities in Affirmative Action

A thought experiment illustrates this. Imagine a company, United Differences (UD), operating in a community that is 25 percent black and 75 percent white and 5 percent homosexual, 95 percent heterosexual. Unknown to UD and the community is the fact that only 2 percent of the blacks are homosexual, whereas 6 percent of the whites are. (The numbers are fictitious and chosen for illustration only.) Making a concerted attempt to assemble a work force of 1,000 that "fairly" reflects the community, the company hires 750 whites and 250 blacks.

However, just five of the blacks (or 2 percent) would be homosexual, whereas 45 of the whites (or 6 percent) would be (totaling 50, 5 percent of all workers). Despite these efforts, the company could still be accused by its black employees of being homophobic since only 2 percent of the black employees (five of 250) would be homosexual, not the community-wide 5 percent. The company's homosexual employees could likewise claim that the company was racist since only 10 percent of their members (five of 50) would be black, not the community-wide 25 percent. White heterosexuals would certainly make similar complaints.

To complete the descent into absurdity, factor in several other groups — Hispanics, women, Norwegians even. Their memberships will likely also overlap to various unknown degrees. People will identify with varying intensity with the groups to which they belong. The backgrounds and training across these various cross-sections is extremely unlikely to be uniform. Statistical disparities will necessarily result. Racism and all other forms of group hatreds are unfortunately real enough without making them our unthinking first inference when confronted with such disparities.

Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy, and the just released A Mathematician Plays the Stock Market. His Who’s Counting? column on appears the first weekend of every month.

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