It Was to Be Announced at the Party Meeting on Monday

The Soviet Union actually did have a doomsday device, and Russia hasn't dismantled it:

Yarynich is talking about Russia's doomsday machine. That's right, an actual doomsday device—a real, functioning version of the ultimate weapon, always presumed to exist only as a fantasy of apocalypse-obsessed science fiction writers and paranoid über-hawks. The thing that historian Lewis Mumford called "the central symbol of this scientifically organized nightmare of mass extermination." Turns out Yarynich, a 30-year veteran of the Soviet Strategic Rocket Forces and Soviet General Staff, helped build one.

The point of the system, he explains, was to guarantee an automatic Soviet response to an American nuclear strike. Even if the US crippled the USSR with a surprise attack, the Soviets could still hit back. It wouldn't matter if the US blew up the Kremlin, took out the defense ministry, severed the communications network, and killed everyone with stars on their shoulders. Ground-based sensors would detect that a devastating blow had been struck and a counterattack would be launched. ...

The system remains so shrouded that Yarynich worries his continued openness puts him in danger. He might have a point: One Soviet official who spoke with Americans about the system died in a mysterious fall down a staircase. But Yarynich takes the risk. He believes the world needs to know about Dead Hand. Because, after all, it is still in place.

As Dr. Strangelove notes in the video above, the whole point of a Doomsday device is lost if you don't tell anybody about it. So why did the Russians keep it a secret?

So why was the US not informed about Perimeter? Kremlinologists have long noted the Soviet military's extreme penchant for secrecy, but surely that couldn't fully explain what appears to be a self-defeating strategic error of extraordinary magnitude.

The silence can be attributed partly to fears that the US would figure out how to disable the system. But the principal reason is more complicated and surprising. According to both Yarynich and Zheleznyakov, Perimeter was never meant as a traditional doomsday machine. The Soviets had taken game theory one step further than Kubrick, Szilard, and everyone else: They built a system to deter themselves.

By guaranteeing that Moscow could hit back, Perimeter was actually designed to keep an overeager Soviet military or civilian leader from launching prematurely during a crisis. The point, Zheleznyakov says, was "to cool down all these hotheads and extremists. No matter what was going to happen, there still would be revenge. Those who attack us will be punished."

Via Cheap Talk, who questions the logic:

The logic is a tad fishy. But it is not obvious that you should reveal a doomsday device if you have one. It is impossible to prove that you have one so if it really had a deterrent effect you would announce you have one even if you don’t. So it can’t have a deterrent effect. And therefore you will always turn it off.

What you should worry about is announcing you have a doomsday device to an enemy who previously was not aware that there was such a thing. It still won’t have any deterrent effect but it will surely escalate the conflict.