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.
|50||District of Columbia||5.731036e-74117|
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.