2000 Presidential Election

Upon waking up Tuesday, November 7, 2000, little did each Florida voter know that he or she had a 0.000321 probability (0.03% chance) of casting the vote deciding the fate of the nation.

The probabilities of a single vote affecting the election are listed below by state.

RankStateProbability
1Florida0.000321
2Iowa5.958044e-16
3Wisconsin3.798302e-16
4Oregon2.878596e-16
5New Hampshire2.508000e-25
6New Mexico2.569015e-66
7Nevada1.356215e-181
8Minnesota1.493920e-331
9Maine3.050959e-387
10West Virginia8.029225e-583
11Missouri1.497412e-589
12Arkansas2.684043e-630
13Tennessee8.961736e-678
14Arizona4.489455e-694
15Vermont5.768208e-713
16Washington3.978235e-1034
17Delaware1.124796e-1348
18Ohio3.705362e-1480
19Pennsylvania2.202781e-1857
20Michigan1.033911e-2308
21Louisiana9.976479e-2337
22Colorado6.611621e-2895
23Hawaii6.548019e-3021
24Virginia9.697869e-3656
25South Dakota8.432212e-3826
26North Dakota2.419379e-5559
27Alaska1.874247e-6454
28Montana2.431342e-6692
29Mississippi8.353455e-6863
30Kentucky6.585567e-7967
31Alabama3.343797e-8068
32Georgia4.108782e-8078
33South Carolina2.529572e-8462
34Connecticut2.048592e-8497
35Rhode Island9.567400e-9127
36Wyoming1.499068e-9642
37North Carolina1.183025e-10418
38Kansas1.079145e-11341
39Indiana8.747481e-12231
40Maryland2.380179e-12495
41Oklahoma2.609160e-13665
42Nebraska1.664898e-14314
43Illinois2.057338e-14797
44New Jersey6.222645e-17374
45Idaho2.549807e-21707
46California2.191772e-34122
47Utah7.575737e-36151
48Massachusetts6.083853e-51569
49Texas1.819397e-68580
50District of Columbia5.731036e-74117
51New York5.401598e-90459

Details

The program I wrote to calculate these figures is in election-result.cc.

The ranking reflects how close the election was in each state, and the size of the state. (A single voter generally has more power in a smaller state.)

I've eliminated votes for candidates other than Bush or Gore for the calculation. The given probability is the product of

I assume that every voter is a "stochastic voter", i.e., they will randomly vote according to the distribution defined by their state. For example, California is populated by 9,310,650 "monkeys," each of whom votes for Gore 56.4% of the time and Bush 43.6% of the time. (These are the respective percentages of votes for each candidate.)

The probabilities are so astronomical because the probabiliy that, for example, California would have split 50:50 by the stochastic voters defined above is vanishingly small.

I make the normal approximation to the binomial distribution. The computations are done with log-probabilities instead of the probabilities themselves because their values are so small. The program does a neat trick with memoization to calculate all the different combinations that the electoral college votes can sum up to any given value.

All data was taken from http://dailynews.yahoo.com/fc/US/Presidential_Results/, except for Florida, for which I got the latest recount numbers from cnn.com.


Ken T Takusagawa
Last modified: Fri Nov 10 17:14:34 EST 2000