The Supreme Court

Specifically, killing them.

Hang on there, Secret Service.  We're doing it statistically, so it's just an math problem.  No one is actually getting hurt, and I mostly did it to see how soon it's likely that there will be a vacancy due to death.  Someone could resign at any time, and that would make a vacancy, but that's not something that can really be predicted.  Death is a bit tricky, too, but due to the fact that despite the best attempts of some people, we still have a government that collects piles of data, so we can use the cohort life expectancy data from the Social Security Administration.

From that data, we're going to use the "High-cost" columns, and use the "at age 65" data.  The logic behind this is based on two facts.  First, the majority of the difference between the "at birth" and "at age 65" expectancies is due to infant mortality and things like that.  If you survive to 65, you didn't die as a baby.  The supreme court is universally comprised of people who did not die as a baby.  The choice of the "High-cost" is that being a supreme court justice is a pretty good job, so they're likely to have good health care.  The final assumption I have to make is that people born before 1940 have life expectancies similar to those born in 1940.  The table only goes back so far, and I don't really want to extrapolate it.

The next assumption is that the probability of surviving a year is based on the logistic function, largely due to a lack of better options.  The form I chose was P(age) = 1 / (1 + exp(-(expectancy - age))).  This sets the 50% probability at the expectancy age.  I could scale it, but I don't have any good idea of how to do that, so I'm just letting that be 1.0.

Using this table of birth dates and ages, we can make the following plot:

This shows the probability that that justice is alive.  I'm sorry that this claims Ruth Bader Ginsburg is 52% dead.

Ok, using these probabilities, we can plot up the number of justices statistically alive by simply summing these curves:

This suggests that (barring the Senate being jerks), Obama is likely to appoint two justices.  His successor falls into a generational gap between the Breyer and Thomas, and isn't likely to appoint anyone, even in an eight year term.  It's fairly linear over the next five terms, with about one each term.  This assumes that all newly appointed justices are younger than the current youngest, and that we're only concerned with the current set.

So again, barring the Senate terrible, we should have a significantly more liberal court within the next four years.

Batman and Robin are happy about that fact, too.