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I guess Austria is the AI because

it consistently capitalizes place names.

Regarding the question of how to force all the incentives into one box, what about the following strategy: choose box 1 with probability 1 - (400 - x) epsilon, where x is the payoff of box 1. Then it is obviously in each host's interest to predict box 1, since it has the largest probability of any box, but then it is also in each host's interest to minimize 400 - x i.e. maximize x. This is true even though the hosts' competition is zero-sum.

If the hosts are all predicting box 1, why does it matter with what probability the human picks box 1? (If the hosts' payoffs for all-predict-correctly and all-predict-incorrectly are different, then their game isn't zero-sum.)

The event is more likely to occur if the person is a conspirator, so you hearing the statement should indeed increase your credence for conspiracy (and symmetrically decrease your credence for not-conspiracy).

We called this "Lava Monster Tag" when I was a kid since "the ground is lava", though we only had one monster at a time (sometimes a fixed, larger number for a large playground).

If team pineapple presses their button, the other team is forced to put pineapple on the pizza they have, and if they press theirs, team pineapple has to pick off their pineapples and throw them away.

I would just call this an extra 'y' sound before the vowel. ([ˈkjuːt] vs. [ˈkuːt])

Why did this post from last month get reposted now?

Something like squaring the size of each voting bloc before doing a weighted random selection? This gives a 90% chance for a 75% majority to win.

wrote the book on how to do it right

Your link just points back to this post.

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