The enclosed lesson about the Dilemma of Superintendent Millhouse is an allegory about the military draft prior to 1969.  During the Vietnam era, all males age 18 were required to register with the Selective Service and were then eligible to be drafted until they reached the age of 26.  Deferments were given to all women, men attending college - and in some cases graduate school, men with physical or mental problems, men pursuing religious vocations, and conscientious objectors - those who as part of their religion and/or basic beliefs felt that war was wrong.

The draft became very unpopular as more and more young men were drafted in the prime of life and casualties increased.  The particular system that was used was felt to be very unfair because an inordinate number of lower socioeconomic men were being sent to Vietnam.  This happened for several reasons:  (1) The college deferment favored those who could afford to send their sons to college.  If a young man could not afford to go to college, he would be a prime candidate for being sent to Vietnam.  (2) Families of wealth found creative ways to avoid having their sons be drafted.  This was done in a variety of ways, not the least of which was lobbying friends with connections to the draft board, a local committee that determined who would be drafted.  An example of this activity was done by President Clinton, who lobbied successfully to further his education abroad, thereby avoiding the draft.
(3) Some connected families also found friendly doctors who would provide evidence of injuries to young men that would prevent them from serving.  These type of activities were not, in large part, practiced by lower socioeconomic families.  In most cases these particular men also ended up being the grunts in the field, rather than being in safer support positions in the rear.  Hence, this particular socioeconomic class had a very high casualty rate relative to others classes.

Another problem with the pre-1969 draft system was that young men were eligible for the draft through age 26, which left them wondering if they would be drafted for up to eight years.  This left men in a quandary about what to do with their lives and stunted their personal growth opportunities.

Students on college campuses became increasingly worried about being sent to Vietnam as their college days ended and they became eligible for the draft.  Protests increased and some young men burned their draft cards, while others fled to Canada and Europe.   Although the number of men who registered but avoided the draft is unknown, I believe it is fair to estimate that number easily exceeds the 250,000 estimated to have avoided even registering for the draft.
 
 

In 1969, President Richard Millhouse Nixon believed he could stop some of the problems on college campuses and in the streets, by changing the way the draft was held.  This also coincided with his plan to gradually remove the United States from engagement in Vietnam.  As the numbers of men being sent to Vietnam decreased, President Nixon realized he would not need to draft as many men.  By executive order, President Nixon instituted a birth date lottery system.  He also ended the college deferment and he limited the draft to 19-year old men.

This approach meant the 8-year worry was over and the socioeconomic playing field was leveled.  President Nixon also dramatically cut back on some of the other typical deferments, such as graduate school.  Still, some young men, such as eventual Vice President Dan Quayle, avoided Vietnam by joining the National Guard, while others lobbied their connections all the harder.

On December 1, 1969 birth dates enclosed in small plastic capsules were randomly pulled from a glass bowl.  Each date was pulled and was assigned a draft number based on the order it was pulled.  In 1969, the first date pulled was September 14.  This meant that any healthy 19 year old male with a birth date of September 14 had a lottery number of 1 and was certain to be drafted in 1970.  The military projected how many men they would need in that year and they were able to fairly accurately determine how many lottery numbers would be drafted.  It didn’t work out exactly like this, but roughly, men with lottery numbers in the first one-third of birthdays chosen knew they would be drafted and could plan accordingly, men with lottery numbers in the middle third of birthdays sat on the edge of their seats for a year, while  men in the lower third of lottery numbers celebrated.

Complaints about the system did not go away entirely, but there was a clear reduction      in protesting about this issue.  One of President Nixon’s major goals - to reduce campus protests - was met by developing a more fair way to hold the draft.

But was this system fair?  A famous lawsuit studied in statistics courses all over the country involves the 1970 lottery.  A group of men analyzed the lottery birth dates and their correlation to low draft numbers.  In a totally random pull of birth dates, the correlation between birth date and a low lottery number should be 0.  However, the correlation of the 1970 lottery showed a significant -.28.  The group of men felt this correlation showed that the way the lottery was held was improper and therefore unfair.  They sued to have the lottery and the draft ended.  Despite strong evidence that the method used for pulling numbers was not fully random, the judges ruled the lottery was valid and the draft remained intact.  Perhaps the judges based their decision on Xavier research professor, James Gaffney’s, mantra “Correlation does not indicate causation.”  The following year corrections and improvements were made to the method of pulling the numbers.

So what was wrong with the method used? What could not be random about pulling birth dates out of a glass bowl?  Well, there were many faults with it.  Remember, this was 1970, prior to the wonderful age of computers we enjoy today. The birth dates were put in small blue plastic capsules and set in a cylindrical glass bowl by date as they were filled, which was not a random placement of the numbers in the bowl.  The bowl was shaken, but not in a sufficient manner to allow the capsules to mix randomly.  When the officials of the lottery put their hands in the bowl, they had a tendency to pull from the same area, which increased the likelihood that, in this case, birth dates in the latter third of the year had a high correlation to low lottery numbers.  Further, although the birth dates were selected randomly, the corresponding draft numbers were not.

In the following year, the dates were placed in the bowl randomly and were properly mixed.  Additionally, as a birth date was chosen at random, a draft number was also selected at random.

Many students wonder how math applies to their lives.  In this case, the proper application of math was a matter of life and death

A final and somewhat controversial point about the previously mentioned college deferment that I hesitate to add but do so because I have read more than a few books about Vietnam and this point has been made more than once.  It is believed by some historians of the Vietnam War that another problem with the college deferment was that the lower intellectual level of the men led to poor leadership in the field.  As a result, many problems, including some atrocities occurred.  For instance, some believe the My Lai incident involving Lieutenant Calley would not have occurred had he and his leaders been better educated.  It’s difficult to say if that is true, but it is a strongly held belief by some writers.  The My Lai incident will be covered in another lesson.  Food for thought.

Pat Bowes

A few years ago, Superintendent Millhouse announced that our elementary school was overcrowded and that 40 students would need to be sent to a different building.  The building where these students were to be sent is about 20 miles away, is rundown, there is no free breakfast or lunch, the books are old with many pages torn out, there is no recess because there is no playground, there are no computers in the classrooms, and the teachers aren’t very nice.  And to make matters worse, many people in the community believe the other school is very unsafe.

Superintendent Millhouse had a difficult time determining who should be sent to the different building so he decided on the following criteria:

1) Girls would not be sent to the other school.
2) Boys with all A’s and B’s would not be sent.
3) Boys with physical or mental problems would not be sent.
4) Boys in kindergarten, first, second, and third grades would not be sent.
5) All other boys in grades 4, 5, and 6 would be eligible to go.

There were 100 boys who qualified to go, but only 40 needed to be sent to the other school.  Superintendent Millhouse asked for volunteers, but unfortunately only 10 boys volunteered.  This meant that Superintendent Millhouse had to choose 30 more boys to go to the different school.  He decided to form a committee to meet with the 90 eligible boys to determine who should go to the different building and who should stay in our school.  Eventually, 30 boys were chosen and were sent to the rundown school.

Unfortunately, there was no way to add space to our school, so 40 or more students needed to be sent each year for the next several years.  Sadly, no one knew exactly how long this was going to be necessary, and so each year 40 boys were sent to the awful school that just kept getting worse and worse as time wore on.

Over time, many people in the community bitterly complained about the system of choosing the students who needed to go to the other school.  In fact, some people were so mad that they protested outside of Superintendent Millhouse’s office, and a few people  even threw rocks at his windows.  The police had to be called in to break up arguments, and some students even started to fight with each other.
 
 

Superintendent Millhouse didn’t know what to do.  He had to come up with a fair way of choosing the 40 boys who would be sent to the other school.  Superintendent Millhouse decided to form a committee to help him decide what to do.  You are on Superintendent Millhouse’s committee.  You are to meet with the other members of your team to determine a fair way of choosing the 40 students who should be sent to the other school.  Discuss the problem with your teammates, determine a solution, and present your ideas to the class.

A word of warning for your team discussions:  Please note that your assignment is to develop a fair way of choosing the 40 students who need to be sent to the other school.  Spending time trying to determine ways to add more space to our school, increasing class size, or using our available space in a different manner does not solve this problem and does not address this assignment.  Use your time wisely by  staying focused on the specific assignment.
 

Mr. Bowes