The expected value of potential lives lost during atomic testing

Rob Reid wrote a great explanation of the horrible risk taken during the Manhattan Project, when American nuclear scientists took a chance estimated at one-in-three million that the first atomic test would create a chain reaction that would ignite the atmosphere of the entire planet in a massive explosion and incinerate every living thing near the earth’s surface. 

 This prospect was first raised by Edward Teller, who later became the father of the hydrogen bomb. Robert Oppenheimer, who would soon lead the Los Alamos lab, called it a “terrible possibility”…

It’s also worth noting that Enrico Fermi took bets on the burnt-sky scenario on the big day…

The one-in-three-million estimate came from Arthur Compton, who oversaw the project’s plutonium production. And I’d say he was as smart as anyone there (Compton won the Nobel Prize for specifying light’s quantization from assumptions about the subatomic interactions of X-ray photons and their scattering angles — a sentence I don’t even understand)…

If we assume Arthur Compton’s reasoning was sound, we can derive the atomic test’s EV from the 2.5 billion people alive at the time. There’s a one-in-three-million chance that everyone dies, and 2.5 billion divided by three million is 833. Plus there are huge odds that no one dies — and any probability times zero deaths equals zero. Adding the two products, the net expected death toll using Compton’s odds is 833 (though, of course, that doesn’t account for the resultant loss of future generations). Does this mean the New Mexico test was morally equivalent to condemning 833 random people to certain death?…

 Even with the certitude of hindsight, he later declared, “Better to accept the slavery of the Nazis than to run the chance of drawing the curtain on mankind!”…
In his ingenious 2003 book, Britain’s Astronomer Royal, Martin Rees, applies a similar, and immensely provocative analysis to a certain experiment conducted at the CERN and Brookhaven supercolliders. It incurred a non-zero chance of destroying the Earth, and perhaps the entire universe. And for those who are skimming this article, I repeat:

Destroying. The motherfucking. Universe.

Yes, really. The experiment created conditions that had no precedent in cosmic history. As for the dangers, Rees characterizes “the best theoretical guesses” as being “reassuring.” However, they hinged on “probabilities, not certainties” and prevailing estimates put the odds of disaster at one in fifty million.

From the dawn of time until the start of the Cold War, no one was in a position to risk things on this scale…

Given the global population at the time, that EV was 120 deaths… 
Imagine how the world would treat the probabilistic equivalent of this. I.e. a purely scientific experiment that’s certain to kill 120 random innocents. It would never be allowed. No — not even if it was really, really, really clever.

These tests would have also in a way killed all future generations who would never be born, and a shortcoming of the above analysis is that it implicitly considers their lives to be worthless.  It also ignores other costs.  For example, the New Mexico testing also resulted in numerous people dying of radiation exposure including some of the scientists themselves who tended to die of cancer at an higher rate than others.