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

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.