The Alabama Paradox

I'm still not talking about Coach Nick Saban and the Alabama Crimson Tide losing to Clemson in the National Championship College Football Game a few weeks ago.  Plain and simple, he was outcoached and the team was outplayed.  It still doesn't make it less painful.  So, for all of you Alabama haters, today's blog has absolutely nothing to do with football or the Crimson Tide!

The so-called Alabama Paradox was first described by C.W. Seaton, chief clerk of the United States Census Bureau shortly following the 1880 census (making it just slightly older than the University of Alabama football team, which first started playing in 1892).  Basically, the issues at hand involve the rules of apportionment, the process by which seats in a legislative body (in this case, the U.S. House of Representatives) are distributed among the different administrative divisions (in this case, the individual states).  Apparently this is not as easy as it sounds, as various methods of apportionment have been suggested and employed since the signing of the U.S. Constitution (in fact, President George Washington vetoed one of the original apportionment bills passed by Congress - just one of only two times when he actually vetoed a bill).  The method that was used after 1852 (which was the method for apportionment that Alexander Hamilton had originally suggested and that President Washington had vetoed) went something like this:

1.  The proportional share of seats that each state would receive (i.e., the fair share - remember that we can use fractions when it comes to actual individuals representing the states) if fractional values were allowed is determined.

2.  Each state receives as many seats as the whole number portion of its fair share determined above (i.e., if they were to receive a fair share of 8.56 seats, then they would receive 8 seats).

3.  Any state whose fair share is less than one receives one seat, regardless, as required by the Constitution.

4.  Any leftover seats are distributed, one at a time, to the states whose fair shares (fractional share) have the highest fractional parts (i.e., the numbers to the right of the decimal point).

So, for example, say there are 10 total seats to be distributed among three states, A, B, and C, with a fair share of 4.286, 4.286, and 1.429 seats each.  The apportionment method described above would give 4 seats to both A and B and 2 seats to C (the remaining fraction, after the whole number, for state C, 0.429 is higher than either the remaining fraction for state A and B, 0.286, so state C receives the additional remaining seat).

The problem was that Seaton noted that for all House sizes between 275 and 300 seats, the state of Alabama would get eight seats with a House size of 299 and only seven seats with a House size of 300!  Pretty strange, right?

As it turns out, there were similar paradoxical issues with just about every other apportionment method tried.  Even more interesting, in 1983, two mathematicians (Michael Balinski and Peyton Young) proved what is now known as the Balinski-Young theorem, which states that any method of apportionment will result in paradoxes whenever there are three or more administrative divisions (in our case, states). 

So other than being just really cool, what is my point?  What does the "Alabama Paradox" have to do with leadership?  I would say that the "Alabama Paradox" has two lessons for us, both of which are important for leadership in any organization. 

My first point is that nothing is simple.  There are just no easy ways to resolve certain issues, so we shouldn't really try to find an easy solution.  Complex problems (like apportionment in the U.S. House of Representatives) usually require complex solutions.  Most high reliability organizations have already learned this lesson, and "Reluctance to Simplify" is one of the five bedrock high reliability principles.

My second point is that life is not always fair.  Regardless of which apportionment method is used, some state will always lose out and have fewer seats than their so-called "fair share" (again, we can't divide seats into fractions).  Whatever solution we find, someone is not going to be satisfied.  You can't always make everyone happy, and some times you just have to find the solution that is the most acceptable to everyone.

All of this, from a paradox named after the 2018 college football national runner-ups!