In all these cases, your paying/not paying imply the same futures, but it’s different because of the disagreement point.
I’m not sure about the others, but in the taxes/police example, the implied futures in the pay/not pay are not the same:
“pay your taxes, and the police will protect you from criminals” means if you don’t pay, P(shop smashed) = X, if you pay P(shop smashed) << X.
“pay your taxes, and the police won’t smash up your shop” means if you don’t pay, P(shop smashed) = X, if you pay P(shop smashed) >> X.
(Note that X is the same for both scenarios. That is, P(shop smashed|taxes not payed) does not depend on which scenario the police chooses.)
I’m not sure about the others, but in the taxes/police example, the implied futures in the pay/not pay are not the same:
“pay your taxes, and the police will protect you from criminals” means if you don’t pay, P(shop smashed) = X, if you pay P(shop smashed) << X.
“pay your taxes, and the police won’t smash up your shop” means if you don’t pay, P(shop smashed) = X, if you pay P(shop smashed) >> X.
(Note that X is the same for both scenarios. That is, P(shop smashed|taxes not payed) does not depend on which scenario the police chooses.)