[ikeboy]

No two people ever have the same set of information. And very few cases are even as clean as the coin case.

A more typical example is using polls to predict elections. 538's model ended with Biden around 90% to win. Andrew Gelman's model at the Economist ended with Biden around 95%. Do either of those represent objective probabilities?

Or take weather predictions. Per https://www.metaculus.com/questions/4617/will-2020-be-the-wa..., Berkeley Earth gives a 16% chance to something that NOAA gives 29.2% to. Is either of those an objective probability?

I would say no, and I think that just because two people happen to agree on a number in a particular case doesn't make it objective. If you want to use the word objective, I don't have any particular objection. I'm not here to fight over words, and none of these words are really well defined enough to be worth fighting over. I don't think it's useful to think of probabilities as "real" in any sense.