# Number of possible electoral college ties

1. Nov 1, 2004

### 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?

2. Nov 1, 2004

### Gokul43201

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

3. Nov 1, 2004

### Loren Booda

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

4. Nov 1, 2004

### 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 [Broken]

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

Last edited by a moderator: May 1, 2017
5. Nov 1, 2004

### CRGreathouse

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

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.

6. Nov 1, 2004

### 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!

7. Nov 1, 2004

### CRGreathouse

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:

Last edited: Nov 1, 2004
8. Nov 1, 2004

### Loren Booda

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

9. Nov 1, 2004

### robert Ihnot

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.

Last edited: Nov 1, 2004
10. Nov 2, 2004

### Gokul43201

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

11. Nov 2, 2004

### CRGreathouse

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.)

12. Nov 2, 2004

### robert Ihnot

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