It's not rational, just like it's not rational to kill a hostage when your demands aren't met, but you need to actually carry the threat out, in order for your threats to be credible.
Isn't both sides alwats full of informants? I don't think you could confidently design a non functioning system and be sure the other side doesn't know it doesn't work
> I don't think you could confidently design a non functioning system and be sure the other side doesn't know it doesn't work
Well. The UK's "Letters of Last Resort" are kind of that. It intentionally keeps it ambiguous what will be the reaction of the British ballistic missile submarines in case of an unexpected decapitation attack.
The idea is that an incoming Prime Minister writes four identical, hand written letters to the commanders of the subs. They place these letters in safes on the submarines. Only the Prime Minister knows what the letters say.
In case the UK command structure is destroyed in a sudden decapitation strike, the submarine will detect this. For example by the fact that all naval broadcast cease to transmit. But nobody wants a single point of failure accidentally triggering a war, so they also check if the BBC 4 is still broadcasting, and they probably check other things too but the specifics are kept secret.
After the commander of the submarine, in agreement with a few other officers come to the conclusion that the UK is no more they open and read the letter. The letter gives them an instruction. It can tell them to retaliate with all they got. It can tell them to not retaliate, find a safe port and live the rest of their lives to the fullest. It can tell them to use their best judgement based on what they know. It can tell them to join the navy of a friendly country.
> Isn't both sides always full of informants?
The system assumes so yes. It is very hard to keep something secret once multiple people knows it. The idea here is that the secret is only known to one person, it is only distributed to a very limited set of very secure locations and everything is kept very low-tech to make it easier to manage the risk. Probably there are other undisclosed security arrangements too. (For example I wouldn't be surprised if the letter is carried by multiple trusted people, checking each other to prevent an enemy snooping or doing a switcheroo.)
If you decide now that you wouldn't counteract then, and your enemy knows this, your MAD deterrence plan has already failed.