Lest We Forget: U.S. Selective Service Lotteries, 1917–2019

Abstract

The United States held 13 draft lotteries between 1917 and 1975, and a contingency procedure is in place for a selective service lottery were there ever to be a return to the draft. In 11 of these instances, the selection procedures spread the risk/harm evenhandedly. In two, whose anniversaries approach, the lotteries were problematic. Fortunately, one (1940) employed a “doubly robust” selection scheme that preserved the overall randomness; the other (1969) did not, and was not even-handed. These 13 lotteries provide examples of sound and unsound statistical planning, statistical acuity, and lessons ignored/learned. Existing and newly assembled raw data are used to describe the randomizations and to statistically measure deviations from randomness. The key statistical principle used in the selection procedures in WW I and WW II, in 1970–1975, and in the current (2019) contingency plan, is that of “double”—or even “quadruple”—robustness. This principle was used in medieval lotteries, such as the (four-month) two-drum lottery of 1569. Its use in the speeded up 2019 version provides a valuable and transparent statistical backstop where “an image of absolute fairness” is the over-riding concern.

Keywords:

• Datasets
• History
• Multiple-robustness
• Randomness
• Teaching

Acknowledgments

The author thanks the editors and referees, several students, family numbers, Sahir Bhatnagar, and Tim Johnson for their help in improving this article. He also thanks Melissa Lindberg at the Library of Congress for her help in relation to photographs of the 1940 lottery, and Jacob Daniels and Lee Alexander of the Selective Service System for their help in connection with Figure 6.