Third, I’m still uneasy about your choice to use annual proportion of population killed rather than number of deaths per war. This is just very rare in the IR world.
Looking into annual war deaths as a fraction of the global population is relevant to estimate extinction risk, but the international relations world is not focussing on this. For reference, here is what I said about this matter in the post:
Stephen commented I had better follow the typical approach of modelling war deaths, instead of annual war deaths as a fraction of the global population, and then getting the probability of human extinction from the chance of war deaths being at least as large as the global population. I think my approach is more appropriate, especially to estimate tail risk. There is human extinction if and only if annual war deaths as a fraction of the global population are at least 1. In contrast, war deaths as a fraction of the global population in the year the war started being at least 1 does not imply human extinction. Consider a war lasting for the next 100 years totalling 8 billion deaths. The war deaths as a fraction of the global population in the year the war started would be 100 %, which means such a war would imply human extinction under the typical approach. Nevertheless, this would only be the case if no humans were born in the next 100 years, and new births are not negligible. In fact, the global population increased thanks to these during the years with the most annual war deaths of combatants in the data I used:
From 1914 to 1918 (years of World War 1), they were 9.28 M, 0.510 % (= 9.28/(1.82*10^3)) of the global population in 1914, but the global population increased 2.20 % (= 1.86/1.82 − 1) during this period.
From 1939 to 1945 (years of World War 2), they were 17.8 M, 0.784 % (= 17.8/(2.27*10^3)) of the global population in 1939, but the global population increased 4.85 % (= 2.38/2.27 − 1) during this period.
Do you have any thoughts on the above?
I don’t know enough about how the COW data is created to assess it properly. Maybe one problem here is that it just clearly breaks the IID assumption. If we’re modelling each year as a draw, then since major wars last more than a year the probabilities of subsequent draws are clearly dependent on previous draws. Whereas if we just model each war as a whole as a draw (either in terms of gross deaths or in terms of deaths as a proportion of world population), then we’re at least closer to an IID world. Not sure about this, but it feels like it also biases your estimate down.
It is unclear to me whether this is a major issue, because both methodolies lead to essentially the same annual war extinction risk for a power law:
Like I anticipated, the best fit Pareto (power law) resulted in a higher risk, 0.0122 % (R^2 of 99.7 %), i.e. 98.4 % (= 1.22*10^-4/(1.24*10^-4)) of Stephen’s 0.0124 %. Such remarkable agreement means the extinction risk for the best fit Pareto is essentially the same regardless of whether it is fitted to the top 10 % logarithm of the annual war deaths of combatants as a fraction of the global population (as I did), or to the war deaths of combatants per war (as implied by Stephen using Bear’s estimates). I guess this qualitatively generalises to other types of distributions. In any case, I would rather follow my approach.
Looking into annual war deaths as a fraction of the global population is relevant to estimate extinction risk, but the international relations world is not focussing on this. For reference, here is what I said about this matter in the post:
Do you have any thoughts on the above?
It is unclear to me whether this is a major issue, because both methodolies lead to essentially the same annual war extinction risk for a power law: