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This is worth emphasizing. If you have a model with a parameter that represents the probability of something happening, and then you have uncertainty in that pa

This is worth emphasizing. If you have a model with a parameter that represents the probability of something happening, and then you have uncertainty in that parameter, your real probability needs to integrate over that uncertainty. But the final probability is still just a single number. But I suspect the GP's reasoning was getting interference from the valid point that poll numbers, which are not probabilities, are meaningless without confidence intervals or some other measure of uncertainty. That uncertainty will then feed, via some model, into a probability estimate of a candidate winning. And that's just a single number.

3pt14159 8y ago
Hmm. Doesn't it depend on whether re-rolls are allowed as to how confident we can be? For example, I can imagine a well engineered coin that has a 0.5 probability of heads with a 0.005 confidence (ie, we suspect that the true weighting between heads and tails is likely between 0.495 and 0.505 19 times out of 20) and I can contrast it with a hastily made coin that can still have a 0.5 expected probability with a 0.1 confidence (ie, we expect the true probability to be between 0.4 to 0.6, 19 times out of 20). Coin A and Coin B have dramatically different impacts on our decision making. For example, selling insurance against 5 identical flips in a row is a much more expensive proposition for Coin B than Coin A. I feel like I really should know this given my data science background, but sometimes the basics slip away.
- OscarCunningham 8y ago
  Right. Both coins have a probability of 0.5 on the next flip, but when you do multiple flips the hastily made coin has a higher chance of a result with lots of heads or lots of tails. We could do the same thing for the 2016 election, but we would have to specify exactly what we meant by a "repeat". Do we just let Hillary run for the 2020 election and see what happens? Or do we put back every atom to the exact position it had in 2014, so that the only divergences between the two elections are caused by quantum randomness? Or something in between, like looking at all elections where a demagogue outsider runs against an established insider? Really it doesn't matter what definition of "repeat" we choose. Since the repeat won't actually happen, we can't be called to bet on it, so knowing the probability in that case isn't too useful. Whereas a coin actually can be flipped multiple times.

3pt14159 8y ago

Hmm. Doesn't it depend on whether re-rolls are allowed as to how confident we can be? For example, I can imagine a well engineered coin that has a 0.5 probability of heads with a 0.005 confidence (ie, we suspect that the true weighting between heads and tails is likely between 0.495 and 0.505 19 times out of 20) and I can contrast it with a hastily made coin that can still have a 0.5 expected probability with a 0.1 confidence (ie, we expect the true probability to be between 0.4 to 0.6, 19 times out of 20). Coin A and Coin B have dramatically different impacts on our decision making. For example, selling insurance against 5 identical flips in a row is a much more expensive proposition for Coin B than Coin A. I feel like I really should know this given my data science background, but sometimes the basics slip away.

OscarCunningham 8y ago
Right. Both coins have a probability of 0.5 on the next flip, but when you do multiple flips the hastily made coin has a higher chance of a result with lots of heads or lots of tails. We could do the same thing for the 2016 election, but we would have to specify exactly what we meant by a "repeat". Do we just let Hillary run for the 2020 election and see what happens? Or do we put back every atom to the exact position it had in 2014, so that the only divergences between the two elections are caused by quantum randomness? Or something in between, like looking at all elections where a demagogue outsider runs against an established insider? Really it doesn't matter what definition of "repeat" we choose. Since the repeat won't actually happen, we can't be called to bet on it, so knowing the probability in that case isn't too useful. Whereas a coin actually can be flipped multiple times.