As Coleman prepares for his equal-protection appeals to any court of
proper jurisdiction that might conceivably hold up the seating of
Franken in the US Senate, we can ask why Coleman is seemingly hell
bent on castigating the current Election Contest proceedings (see,
e.g, the excellent summaries by FishFry and Winerev) rather than trying to
win the election outright.
In terms of Coleman actually winning the election contest, there are
two fundamental parameters: 1) How many ballots will the court allow
to be opened and counted, and 2) Given a random ballot from (1), what
is the probability that it will in fact be a vote for Coleman (i.e.,
statistically speaking, would we expect the ballots to favor Coleman,
and by how much?)
We need to recall that of the 933 absentee ballots already opened and
counted, a large majority favored Franken. And we need to understand
that while Coleman is cherry-picking the additional ballots he is
arguing should be opened, the Franken campaign will get a chance to do
the exact same thing when it presents its case.
Therefore while there is a lot of uncertainty around the statistical
properties of the (as yet theoretical) pile of unopened ballots the
court will eventually order counted, it is hard to make a strong case
that they, in aggregate, will favor Coleman. But let's assume that,
for whatever reason, they do -- how strongly will they have to favor
Coleman for him to have any kind of chance of winning?
The first graph below, computed using a mathematical technique known as
a binomial distribution, show us why Coleman is (and should be)
desperate to try anything other than actually have ballots opened and
counted.
It shows that even if 3300 ballots are ordered opened (which is
extremely unlikely at this point, but still theoretically possible),
and all of them were Coleman or Franken (no Barkley or Lizard people)
votes, they would have to favor Coleman by about 52.5% - 47.5% for
Coleman to have a 10% chance of coming out ahead, assuming that
Franken's 249 current vote lead remains intact otherwise.
If only 1000 ballots are ordered opened (the line is in fact invisible,
because it never rises above the X-axis), Coleman's chance of victory
is 0 -- nada, zip.
Marc Elias, one of Franken's lawyers, estimated that perhaps as many
as 1500 ballots might eventually be opened. In this case, they would
have to favor Coleman by 56.5% - 43.5% before Coleman's chances of
victory would approach 10%.
The second graph illustrates, by way of comparison, just how big
Franken's lead of 249 votes is. By presenting the same information
assuming Franken's lead was only 100 votes, we see that Coleman would
start to have some chance of winning even if the ballots only favor
him by 51% - 49%. But even in this case, if the ballots favor Franken
or are probabilistically 50%-50%, Coleman has no realistic shot.