Number of possible electoral college ties

[Loren Booda]

Considering all 50 states and their current distribution of electoral votes, how many possible ties (totaling 269 to 269) can theoretically be generated?

[Gokul43201]

This is something you'll have to write a little code for.

[Loren Booda]

Then crunch it with a Cray. Are there any approximate methods?

[robert Ihnot]

Strange you should ask, I just got this from MSNBC: There are no fewer than 33 mathematical formulas by which the Electoral College winds up in a 269-269 tie. See:http://www.msnbc.msn.com/id/6385561/ Is this any help? Or were you hoping to see the math? (They have only considered the battleground states.)

By gosh! I found the answer: 17,057,441,245,652 ways, and the method is to use a generating pollynominal and check the 269th coefficient. This also allows us to compute the probability, if every state is a toss up, which is about one election out of 66. See: http://www.izzycat.org/math/index.php?p=28

Historical note: In the election of 1800, Thomas Jefferson and Aaron Burr each got 73 electoral votes.

[CRGreathouse]

There's at least one (relevant) mistake in that site. The basic method seems sound, and the coeffecient is correctly calculated, but:

In any case, when we do that expansion, the coefficient of x269 in g(x) is 17057441245652, which is the number of ways we can choose some states out of the 50 to have
269 electoral votes. Dividing by 250 (the number of ways in total to pick states) gives 0.01515, or about 1 in 66.

One must divide by 2^51, since the DC casts electoral votes and is included in the equation. This gives a probability of 17057441245652 / 2 ^51 ~ 0.758% ~ 1/132.

[Loren Booda]

robert,

I did indeed get my idea from NBC, whose calculation included only those states they saw as relevant.

CR,

Are you sure that DC gets an electoral vote? They have no representation in the House of Representatives (or the Senate), which has been a sore spot for them as of late.


Thanks for the "results," guys!

[CRGreathouse]

CR,

Are you sure that DC gets an electoral vote? They have no representation in the House of Representatives (or the Senate), which has been a sore spot for them as of late.

The District of Columbia has no representation in Congress, but casts 3 electoral votes (almost always for the Democratic candidate) per the 23rd Amendment, ratified in 1961:

Amendment XXIII.

Section 1.
The District constituting the seat of Government of the United States shall appoint in such manner as the Congress may direct:


A number of electors of President and Vice President equal to the whole number of Senators and Representatives in Congress to which the District would be entitled if it were a State, but in no event more than the least populous State; they shall be in addition to those appointed by the States, but they shall be considered, for the purposes of the election of President and Vice President, to be electors appointed by a State; and they shall meet in the District and perform such duties as provided by the twelfth article of amendment.

Section 2.
The Congress shall have power to enforce this article by appropriate legislation.

[Loren Booda]

It would appear that NBC got it wrong (see robert's link).

[robert Ihnot]

It would appear that NBC got it wrong (see robert's link).

The nine toss-up "states" would not include DC, which is heavily Democratic, but it should have been considered for the probability problem as CR Greathouse notes.

[Gokul43201]

The nine toss-up "states" would not include DC

Most certainly not. DC, currently polling at about 76% for Kerrry, is the most liberal 'state'.

[CRGreathouse]

Most certainly not. DC, currently polling at about 76% for Kerrry, is the most liberal 'state'.

That is certainly true -- the DC has never cast an electoral vote for a Republican. (They did abstain from one of their electoral votes in 2000, so they haven't always voted Democratic.)

[robert Ihnot]

Most certainly not. DC, currently polling at about 76% for Kerrry, is the most liberal 'state'.

Are you sure the figure isn't 90% for Kerry? That's how it looks election night.