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CarlShulman comments on Probability and Politics - Less Wrong
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I don't like the coin model because it ignores replacement.
Assume there's ten other people in a room. Six like red and four like blue. Four of them will go to the polls, and you're trying to decide if you should, too. What's the probability your vote will be the deciding factor?
It's tempting to use the binomial distribution. p=0.5, n=4. Your vote matters if x=2.
So it'll be tied without you about 35% of the time.
But this is incorrect. If the first person who votes casts a red ballot, then the probability the next vote is red falls to 5/9, and the probability the next vote is blue increases to 4/9. The correct model is the Hypergeometric model because it doesn't assume replacement.
It computes a higher 43%.
As n increases from 10 to 300000000, I imagine the effect is more dramatic.
Either way, with large electorates, the sampling error will be swamped (by orders of magnitude) by correlated changes across voters. For instance, the swings in voting behavior from economic conditions regularly move results by a number of percentage points.
Move relative to what? Last year's results?
I was imagining getting the probabilities a single voter would vote for candidate X from Gallop.
I meant that that local stochastic things affecting individual voters are not important in the year-to-year variation in election outcomes, compared to systematic effects like the economy.
If you had an exact fraction of voters who would break for which candidate (which polling isn't accurate enough to give), you still would face uncertainty about turnout.
The standard error of polling is usually pretty small.