Something similar certainly is useful in the case of flipping a coin. Suppose we have two coins, one of which we know is fair and one of which we know is biased

Something similar certainly is useful in the case of flipping a coin. Suppose we have two coins, one of which we know is fair and one of which we know is biased but we don't know which way. Then our knowledge about the bias of the first coin would be described by a distribution with a sharp peak around 0.5, but the distribution for the second coin would have two lumps either side of 0.5. Then the probability of heads on the next flip would be 0.5 for either coin. But if someone asked us to bet on the probability of heads on the next two flips, then the second coin would have a higher probability than the first. The different distributions for the two coins don't make a difference for one flip, but do for multiple flips. But there's no meaningful way to repeat an election, so I don't think similar distributions or confidence intervals are useful in that case. EDIT: We can imagine rerolling an election, but since we can't actually do it we don't have to bet on it so the information wouldn't be very useful to us.