Election predictions

[robve]

(11-08-2020 08:15 PM)Dave Britten Wrote:  As for the specifics of the statistical models they're using, I can only assume it's quite a bit more complicated than z-scores on a normal distribution. There's a dizzying amount of variables in play.

A more accurate way to determine the confidence in the outcome is to perform Monte Carlo simulations with the remaining votes, each vote is heads or tails with an individual bias/weight (we can ignore all other non-H-T outcomes for now, which does not invalidate the model.) This way we get a weighted sum of random Bernoulli trials. However, that can be very expensive to compute and we may not have sufficient information on the folks who cast the remaining votes to be able to determine the individual weights. If the weights are the same, then the Central Limit Theorem of Bernoulli trials tells us that the sum converges to the normal density function. Hence we can compute our p with a normal PD.

If we assume that all remaining votes are cast by mail, then sampling a portion of the mail-in ballots can tell us the mean and variance of the normal PD of the remaining votes, offering a means to achieve 99.5% confidence in the election prediction.

In (other) elections a multinomial distribution should be used that describes the probabilistic structure of a series of independent and identical Bernoulli trials with constant probabilities and multiple possible outcomes. However, in our case the votes are so close for the two candidates that a normal PD should suffice with only two possible outcomes.

But perhaps multiple distributions can be used to improve the confidence level? For example by splitting the remaining votes into classes of some sort, such as Election Day ballots, mail-in ballots, overseas ballots, etc?