What if the US military starts pursuing an AI's objectives through persuasion/manipulation? At what point would this qualify as defeat?

@RemNi Let's say when it causes them to fail their mandate of defending the U.S. from threats.

Some manipulations that count:

-Tricking them into sending their units far from U.S. soil, which is then conquered.

-Manipulating the pentagon to fund more of something the AI needed, and that helped the AI reach some threshold where it then defeats everyone.

Some manipulations that don't count:

-Manipulating the pentagon to send money to something the AI values, but that AI never conquers nor displaces the U.S. military (nor broader American society)

-A manipulation that results in losing a battle, but not a whole war.

Let me know if that helps.

A majority of people on this platform only care about their mucks in one of the hypothetical outcomes, so they no longer have the incentive to bet in accordance with their beliefs.

Added another example of the military being "defeated", meant to be very broadly about defending America from hostile threats (including things like air-dropping poisons into the atmosphere, and the army fails to prevent societal collapse from this sabotage.)