...the general concept you're talking about has been discussed much in serious probability theory. See Pascal's Wager.
Pascal's Wager doesn't quite fit with what I feel when I read such things. More along the line of unintended consequences. The consequences may be a possibility but will not stop someone from pushing the button no matter how grave they may be. If my bookie is coming tomorrow to collect a bundle or kill me and I only have 1/2 a bundle then Pascal would tell me to make a 2 to 1 bet with what I have tonight.
Source: July 16, 1945: Trinity Blast Opens Atomic Age @ Wired
"The Trinity test, as it was known, was the culmination of the American effort to win the race against Germany (and, ultimately, the Soviet Union) in building an atomic bomb. A mere three weeks after the test, the United States used atomic bombs to destroy the Japanese cities of Hiroshima and Nagasaki.
But prior to the 16th, none of those involved in the project knew if they had built a devastating new weapon or a spectacular dud.
With gallows humor, the Los Alamos physicists got up a betting pool on the possible yield of the bomb. Estimates ranged from zero to as high as 45,000 tons of TNT. Enrico Fermi, who won the Nobel Prize for Physics in 1938 for his work on nuclear fission, offered side odds on the bomb destroying all life on the planet."
"Ninety percent of baseball is half mental." -- Yogi Berra