I don't understand what the probabilities for an election actually mean. I was reading this piece but I still don't get it. What could it possibly mean to say that candidate A has 70% chance of winning while candidate B has 30% chance of winning.
There is no randomness at any point of the election. Votes are not random, people don't usually show up to the voting places and flip a coin, they already know who they are voting for. The counting process is also not random.
The repeating events interpretation also makes no sense. It sort of implies that some people would vote different in each trial, which also makes no sense to me, unless we are talking of non-independent trials.
The only way I can interpret these probabilities is if we are talking about the probabilities of getting those poll results assuming one of the outcomes.
Gelman clearly thinks this view is wrong, so my guess is I must be wrong. What am I missing?