4 ms·

How do we quantify the difference between coin tosses, which we are very certain is 50% likely to end up heads, from political elections, where we only have a f

• edbaskerville 8y ago
  In terms of predicting what's going to happen next, it really isn't that different if your model's any good. Looking backwards, if the 2016 election had been determined by two coin tosses both coming up heads, would we be surprised? And yet 538's polling model indicated that the probability was even better than two coins coming up heads. They probably should have just written that right there: "71%, better odds than two coins coming up heads." But: in order to understand if the model is any good, you need to try to build a good model, describe your model, and describe what you know about the underlying processes. With words, visuals, and math. Which is pretty much what 538 does better than most.
• OscarCunningham 8y ago
  Good question. The difference is how the probability changes in response to new information. Learning more about the coin won't change the probability of heads from 50%, but doing more exhaustive polls would have likely improved our prediction about the election. However I don't think there's as much of a difference as you think. If we learnt more about how the coin was going to be flipped then that would certainly improve our estimate of the outcome. If we found out the exact way it would be flipped we could calculate the outcome exactly. So we can't really compare the two situations quantitatively, since there's no way to match up like-for-like the information we could receive. But we can say, for each possible piece of information we could receive, how much we expect it to change our probability.