Can anyone explain to me how the "1 in 10 million chance" makes sense? I always thought the probability of a tie vote has to be based on the binomial distribution. If we take New Mexico voter population of 1,254,567, assume that the "actual" preference rate is something near even like 51%, then the probability of a tie is 7.11e-113. In general it will be astronomically low, because the binomial distribution is very narrow for large population sizes, like a whole state. Anywhere outside of the expected value, its density will be insignificant. One would need a background preference rate of nearly even, like 50.17% to get to the 1 in 10 million chance of a tie vote territory.
The linked paper said they looked at the marginal vote differences among 10,000 simulations, took the mean and standard deviation, and calculated the probability of marginal vote=0 using Student-t distribution. Didn't they use the poll results to drive the simulations? Does that mean that New Mexico's poll was exactly 50%? If voter preferences, presumably based on every individual's analysis of which choice is best for the nation as a whole, are really so break-even, then how can we as a nation then claim that any one candidate is preferrable to any other at all?
Can anyone explain to me how the "1 in 10 million chance" makes sense? I always thought the probability of a tie vote has to be based on the binomial distribution. If we take New Mexico voter population of 1,254,567, assume that the "actual" preference rate is something near even like 51%, then the probability of a tie is 7.11e-113. In general it will be astronomically low, because the binomial distribution is very narrow for large population sizes, like a whole state. Anywhere outside of the expected value, its density will be insignificant. One would need a background preference rate of nearly even, like 50.17% to get to the 1 in 10 million chance of a tie vote territory.
The linked paper said they looked at the marginal vote differences among 10,000 simulations, took the mean and standard deviation, and calculated the probability of marginal vote=0 using Student-t distribution. Didn't they use the poll results to drive the simulations? Does that mean that New Mexico's poll was exactly 50%? If voter preferences, presumably based on every individual's analysis of which choice is best for the nation as a whole, are really so break-even, then how can we as a nation then claim that any one candidate is preferrable to any other at all?