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.

Rank | State | Probability |

1 | Florida | 0.000321 |

2 | Iowa | 5.958044e-16 |

3 | Wisconsin | 3.798302e-16 |

4 | Oregon | 2.878596e-16 |

5 | New Hampshire | 2.508000e-25 |

6 | New Mexico | 2.569015e-66 |

7 | Nevada | 1.356215e-181 |

8 | Minnesota | 1.493920e-331 |

9 | Maine | 3.050959e-387 |

10 | West Virginia | 8.029225e-583 |

11 | Missouri | 1.497412e-589 |

12 | Arkansas | 2.684043e-630 |

13 | Tennessee | 8.961736e-678 |

14 | Arizona | 4.489455e-694 |

15 | Vermont | 5.768208e-713 |

16 | Washington | 3.978235e-1034 |

17 | Delaware | 1.124796e-1348 |

18 | Ohio | 3.705362e-1480 |

19 | Pennsylvania | 2.202781e-1857 |

20 | Michigan | 1.033911e-2308 |

21 | Louisiana | 9.976479e-2337 |

22 | Colorado | 6.611621e-2895 |

23 | Hawaii | 6.548019e-3021 |

24 | Virginia | 9.697869e-3656 |

25 | South Dakota | 8.432212e-3826 |

26 | North Dakota | 2.419379e-5559 |

27 | Alaska | 1.874247e-6454 |

28 | Montana | 2.431342e-6692 |

29 | Mississippi | 8.353455e-6863 |

30 | Kentucky | 6.585567e-7967 |

31 | Alabama | 3.343797e-8068 |

32 | Georgia | 4.108782e-8078 |

33 | South Carolina | 2.529572e-8462 |

34 | Connecticut | 2.048592e-8497 |

35 | Rhode Island | 9.567400e-9127 |

36 | Wyoming | 1.499068e-9642 |

37 | North Carolina | 1.183025e-10418 |

38 | Kansas | 1.079145e-11341 |

39 | Indiana | 8.747481e-12231 |

40 | Maryland | 2.380179e-12495 |

41 | Oklahoma | 2.609160e-13665 |

42 | Nebraska | 1.664898e-14314 |

43 | Illinois | 2.057338e-14797 |

44 | New Jersey | 6.222645e-17374 |

45 | Idaho | 2.549807e-21707 |

46 | California | 2.191772e-34122 |

47 | Utah | 7.575737e-36151 |

48 | Massachusetts | 6.083853e-51569 |

49 | Texas | 1.819397e-68580 |

50 | District of Columbia | 5.731036e-74117 |

51 | New York | 5.401598e-90459 |

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

- The probability that all other states will split so that the election depends on your state,
- The probability that your state will split exactly 50:50, leaving you to cast the deciding vote

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