[dontbeevil1992]

Another issue with this logic is that the probabilities are not independent.

Saying that you have probability x of nuclear war every year and so probability (1-x)^n of no nuclear war in n years assumes independence. In fact, if you don't have nuclear war on year 1, I would assume that the reasons for that lead to inferences and correlations that would affect the probability of nuclear war on year 2, possibly making it lower.

[LeonB]

No, that’s not quite right. Measuring “did we have a nuclear war?” is not the input you’d ever want to use there, it’s only one binary digit of information.

Instead take info like “did we have events/incidents with a high potential of nuclear war?”

If three “Cuban missile crisis” level events happened in year X, then the probability of nuclear war in year x+1 is higher than it was in other years — even though nuclear war didn’t occur in either year. If national leaders make no statements threatening war in year A, then it’s probably safer than year B where there were 100 such threats.

[dontbeevil1992]

I might not have said this clearly enough - I'm not saying that conditioning on "did we have a nuclear war" will change the probability to be less. I'm saying that the event "did we have a nuclear war in year n" is not independent from "did we have a nuclear war in year n+1" "n+2", ... because there are shared factors influencing them. Therefore the model of independent probabilities multiplying year over year and seeming to imply that nuclear war is inevitable because (1-p)^n goes to 0 as n grows doesn't make sense mathematically speaking.

[LeonB]

Ok. I think the question that we want to ask from the model is more like:

“What is (one minus (What is the chance we have had 0 nuclear wars by year “now plus 70”?)”

So if there is a nuclear war in year n+3 (for example) it’s effect on year n+4 is irrelevant as the answer to the question is already “0% chance of no nuclear wars by year 70”.

So the angle you’re initially coming from is not quite relevant.

We can then turn that a bit though and continue your point — we can rephrase your claim to be like this, for example:

“if we have had 0 nuclear wars in the next 69 years, then surely that would lower the probability of a war in year 70.”

And to that I’m saying — actually no. Or rather: not necessarily. Or more accurately: not much!

The info of “we’ve had no nuclear wars in 69 years” is not what the model would care about. More likely it would care about, running the model a bunch of times, in the cases where there no wars in the first 69 years, how many times is there a war in the 70th year? And “brink of war” or “HPI” scenarios would be a much better indicator than the simple absense of nuclear war in those first 69 years. Maybe better to said “there is a lot more information in the question of ‘how many times have we been on the brink of war’ than there is in the answer ‘did we have a nuclear war yet? No’. It’s more about that “how much info is there here?”

[dontbeevil1992]

I'll say it again: I'm not saying that we can use past lack of nuclear war to predict future lack of nuclear war. All I'm saying is that each year's probability is not independent, meaning the model of a probability of no nuclear war which geometrically goes to 0 is not accurate.