[ExI] chances of a tie in the electoral college

[spike]

This isn't a political post, but rather about election game theory.

In the US presidential elections, each state is given a number of electors
equal to the number of congresshumans from that state.  Each state has two
senators, and from 1 to 53 reps depending on the state's population.  Fifty
states and the capital (which gets 3 electors) make for a total of 538, so
half of that is 269.  So if any candidate gets 270, that takes the election,
but since 538 is an even number, a tie is theoretically possible, in which
case each state gets one vote, and with the capital in there, the number of
votes is an odd 51, so a tie is not possible.  The constitution works out
all the rules on this.

Clearly a tie is unlikely, but how unlikely?  I wrote a program this evening
that estimates it at 2 percent, but I would like if someone were to verify.
Reason: the two major political parties are nearly equally popular.  Twice
recently we have seen it come down to a single state, in 2000 it was Florida
and in 2004 it was Ohio.

I took interest because a survey of polls this morning showed that depending
on how one interprets a statistically indeterminate Virginia, the two major
candidates are tied at 269 currently, with one candidate leading in 23
states: VT, NH, MA, RI, CT, NJ, DE, MD, DC, ME, NY, PA, MI, IL, WI, MN, IA,
WA, OR, CA, NV, HI, and NM.  The other candidate leads in MT, ID, UT, AZ,
AK, ND, SD, WY, NE, CO, KS, OK, TX, MO, AR, LA, MS, AL, GA, FL, SC, TN, NC,
KY, WV, OH, IN, and a small or statistically indeterminate lead in VA, for a
total of 28.

Of course it is early in the game and much can happen, but given the two
major parties are nearly equally popular, how would one estimate the chances
of a tie?  I ran 100,000 cases and found 2083 different combinations that
come up tied at 269.  Given that there are 2^51, over 2 quadrillion possible
combinations, which would be beyond an exhaustive simulation.  So how can
one determine the probability of a tie?

For now let us not get into personalities or parties, but rather for this
thread, all I am asking is how does one estimate the possibility of a tie?
I fear it might be higher than 2% because of the clustering effect, but I
don't know.  I will share my Microsloth excel macro with anyone who wants
it, if you agree to not ridicule my paleolithic coding technique.  Ideas?

spike




Here is a table of the states and their number of votes:

California		55
Texas			34
New York		31
Florida		27
Illinois		21
Pennsylvania	21
Ohio			20
Michigan		17
Georgia		15
New Jersey		15
North Carolina	15
Virginia		13
Massachusetts	12
Indiana		11
Missouri		11
Tennessee		11
Washington		11
Arizona		10
Maryland		10
Minnesota		10
Wisconsin		10
Alabama		9
Colorado		9
Louisiana		9
Kentucky		8
South Carolina	8
Connecticut		7
Iowa			7
Oklahoma		7
Oregon		7
Arkansas		6
Kansas		6
Mississippi		6
Nebraska		5
Nevada		5
New Mexico		5
Utah			5
West Virginia	5
Hawaii		4
Idaho			4
Maine			4
New Hampshire	4
Rhode Island	4
Alaska		3
Delaware		3
D.C.			3
Montana		3
North Dakota	3
South Dakota	3
Vermont		3
Wyoming		3