There are definitely tangible predictive differences in the case of, say, Russia vs USA. Things like "If you go to the capital with a bunch of friends carrying placards saying '$LEADER is corrupt and evil and should be replaced by $OPPOSITION' how many of you end up in a jail cell in the next day?".
If there is literally no tangible difference then it's just label games and metaphysics and doesn't matter.
> Your personal income has absolutely no predictive value on gdp.
It actually is correlated (admittedly in most day-to-day cases it's just a lagging indicator, but things like natural disasters hit both). It's not the strongest correlation but it would still be evidential. Definitely under 1.0 bits though... One would need a LOT of such observations and having them not screen each other off to start getting a convincing number of bits.
Probably not realistic to have humans manage these sorts of numerous tiny updates though...
/nitpicks
> Ah, but if either side distrusts the other about whether the observation made is truthfully reported, how do you solve that? It requires some amount of trust and right now there’s a very clear divide there.
Yeah, it gets much trickier like that. But I do think two reasonable people from the opposite political sides could agree on some sort of observable to the extent their disagreement is anything other than narrative.