Military draft and randomness

Summary: Military drafts must make use of probabilities to ensure the draft is equitable.

The U.S. military is made up of volunteers. However, if more people are needed than the number of people who volunteer, there needs to be a method for procuring enlistment. The method used is called a “military draft.” It is the law that all male citizens ages 18–25 are to register with the Selective Service. If a need arises, the U.S. Congress would have to pass legislation instituting a draft. The U.S. president would have to sign the bill into law.

When a draft occurs, there is a lottery of the registered men that is intended to be fair. Each registered man of the same age should be as likely as every other registered man to be selected. Once selections are made, some men are excused if they are not fit to serve. A military draft has not been used since 1973.

The Current Lottery

The current lottery method that would be employed if there were to be a draft is to place a capsule with dates for every possible day of the year (month and day) into a barrel. For example, December 1, January 27, and March 13 would be three such capsules. A second barrel will contain the numbers 1 through 365. These barrels are well mixed. In fact, one way to mix the barrels is to not place the capsules into the barrels in order. Rather, the capsules are placed into the barrels in a random manner. One capsule is drawn from each barrel, one at a time, and paired. For example, if November 4 is drawn from one barrel and 78 is drawn from the other barrel, then November 4 and 78 are paired. This continues until all 365 days have a number. The number becomes the day’s rank. This process forms 365 ranked groups. Each group consists of those registered men whose birthday is the corresponding date pulled from the barrel and who will turn 20 in the current year.

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For example, assume that each date is paired with the following number:

November 4 paired with 78,

December 28 paired with 1, and

January 12 paired with 25.

Then all men who turn 20 in the current year of the draft and have a birthday on November 4 will be the 78th group to be called to serve. Before they are drafted, groups 1–77 would be exhausted of possibilities (that is, all fit to serve in the previous 77 groups would be called to serve first). All registered men who turn 20 in the current year and have a birthday on December 28 are in the first group. All men who turn 20 in the current year and have a birthday on January 12 are in the 25th group. Again, these groups are made up of men who will turn 20 in the year of the draft. Once all 365 groups are used, then the rankings are followed again, calling all men turning 21, then 22, 23, 24, 25, 18, and 19.

What it Means to be Random

A selection process of this nature is random only if any person is as likely as any other person to be selected to serve. Thus, each of the 365 birthdays must be as likely as each other birthday to be ranked first. Each of the remaining birthdays must be as likely as any to be ranked second. A man’s birthday should not allow one to predict the likelihood of his being drafted.

Vietnam Draft

The 1969 lottery drawing for the Vietnam War was demonstrated not to be random. A barrel with 366 plastic capsules was used, where each capsule had a birth date on it (month and day); one capsule was for those who were born on leap day. One at a time, the capsules were drawn by hand. The first to be drawn was ranked first. The second to be drawn ranked second. Thus, if September 21 was drawn first, then all men aged 18–26 with a birthday on September 21 would be the first group called to service.

The procedure that was followed to order the men with the shared birthday depended on each man’s initials. A separate lottery was held in which the 26 letters of the alphabet were ranked. This followed the same process as the birthdays, in that 26 letters were placed in a barrel and one by one were drawn. Using the resulting ranking, each man within a shared birthday was ranked according to the permutation of the first letter of his last name, the first letter of his middle name, and the first letter of his first name. Overall, this should have been a fair method for selection, as it was based on randomized birthdays and letter permutations.

Why It Was Not Random

The above-mentioned method would be random if implemented properly. However, it turned out that men with birthdays later in the year (for example, December birthdays) were much more likely to be drafted than those with birthdays in the beginning of the year. What happened is quite simple. The capsules were placed in the barrel month-by-month beginning with January, and the barrel was not well mixed. The December capsules were on top and they had a higher probability of being pulled out first, resulting in lower draft numbers for those men.

Bibliography

Friedman, Lauri S. Military Draft (Writing the Critical Essay: An Opposing Viewpoints Guide). Farmington Hills, MI: Greenhaven Press, 2007.

Hay, Jack. Military Draft (History of Issues). Farmington Hills, MI: Greenhaven Press, 2007.