If we can't make a reasonable estimate, what estimate do we make?

What's the status of error bars in doing this sort of reasoning? It seems to me that a probability of .5 +/- epsilon (a coin you have very good reason to think is honest) is a very different thing from .5 +/- .3 (outcome of an election in a country about which you only know that they have elections and the names of the candidates).

I'm not sure +/- .3 is reasonable-- I think I'm using it to represent that people familiar with that country might have a good idea who'd win.