From Joe Vanderlans, a current constitutional problem:
Imagine that U.S. Supreme Court Nominees are only confirmed if the same party holds the presidency and the Senate. What is the expected number of vacancies on the bench in the long run?
You can assume the following:
- You start with an empty, nine-person bench
- There are two parties, and each has a 50 percent chance of winning the presidency and a 50 percent chance of winning the Senate in each election.
- The outcome of the Senate elections and presidential elections is independent.
- The length of time for which a justice serves is uniformly distributed between 0 and 40 years.
Additional assumptions I added:
- Presidents always serve for 4 years; Senators always serve for 6, but the probability of winning the senate is 50/50 for each party, regardless of the prior state. Therefore, the Senate control can turn over every 2 years, but the presidency can only turn over every 4.
- Empty seats are filled immediately.