It seems a Bayesian interpretation of probability is more general. The frequency of events over an infinite number of trials is one way of interpreting probability for things that are able to be repeated. But this wouldn’t make sense to apply for an election that is only going to happen once and yet one still wants to be able to quantify uncertainty in these situations.
There are a few things intermingled in this election example.
1. The outcome of the election here is not a probability. It is the population value - the ratio of people voting for candidate X on the election date. It doesn't have to be repeated in the same way measurements of height for all people in United States would not have to be repeated, if instead of vote we were measuring heights.
2. Frequentist probability doesn't require to physically repeat things. It can reason about what would happen in the repeated sampling under certain conditions, and then draw inferences about those assumed conditions. With the election example: if you get a survey of 100 people with 70% voting for candidate "A" we don't need to repeat this survey in order to know the likelihood (frequency) of this result happening if the real proportion of people voting for candidate "A" across the US is 50%.
If you’re trying to quantify your uncertainty about who will win the election, a poll would only be part of it. You want to be able to combine disparate sources of information. Maybe there is preference falsification and you want to incorporate as some sort of prior. As things get further from simple sampling from a population the frequency interpretation makes less and less sense to me.
