> So when the CIA tells me some foreign government is doing something bad, I should believe them?
Honestly, yes.
> Then when the CIA denies they lied about the foreign government was doing something bad
When have they done this? A few times probably, but not really a high percentage.
At any rate, P(CIA telling the truth about a foreign govt|foreign govt is doing something bad) is much higher than P(CIA lying about foreign govt|foreign govt is not doing something bad). The rational thing is to put higher weight on such statements than when the CIA is trying to cover their own ass.
There's a difference between them telling what they think is the truth, and them actually knowing something and telling it. The whole "Havana Syndrome" thing might actually be them telling what they think is the truth (Russian/Cuban conspiracy to use secret weapons to give headaches to people), even though it's complete nonsense.
Honestly, yes.
> Then when the CIA denies they lied about the foreign government was doing something bad
When have they done this? A few times probably, but not really a high percentage.
At any rate, P(CIA telling the truth about a foreign govt|foreign govt is doing something bad) is much higher than P(CIA lying about foreign govt|foreign govt is not doing something bad). The rational thing is to put higher weight on such statements than when the CIA is trying to cover their own ass.