Elementary indices of mass killing events
This protocol is extracted from research article:
Quantifying the Holocaust: Hyperintense kill rates during the Nazi genocide
Sci Adv, Jan 2, 2019; DOI: 10.1126/sciadv.aau7292

Some further remarks and warnings are necessary concerning simple procedures for comparing genocides, as routinely applied in the literature. Usually, this entails making use of one or more standard quantitative indices, often none of which are more correct or more valid than any other. An obvious index isEmbedded ImageClearly, the Holocaust has an extreme number of victims [K#(Holocaust) = 5.4 million to 5.8 million dead], even compared to most other genocides [e.g., K#(Rwanda) ≈ 800,000 dead]. So huge is the number that it falls outside the range of victims in Krain’s (18) listing of 35 genocides and politicides between 1948 and 1982 and in Harff’s (35) listing of 41 genocides and politicides between 1955 and 2005.

Another common index isEmbedded ImageOne of the most horrific attributes of Operation Reinhard is that, of the 1.7 million victims in the GG area, there were only very few survivors (2, 6). The genocide was characterized by almost complete extermination in this geographically large area with some tens of thousands of survivors only (6), so that Kp = 94 to 97% in the GG and Kp > 99.9% in the death camps.

A third mass killing index is Embedded ImageThis is a useful quantitative index as long as the time frame or window is chosen in an appropriate manner. For the genocides examined here, τ = 1 day would be far too small and possibly lead to large fluctuations in kill rates that might not be informative. Conversely, too large a value for τ (e.g., τ = 10 years) would not be representative. For the Operation Reinhard period, with a window of τ = 100 daysEmbedded ImageHere, the 100-day window is chosen to maximize Kr.

For Rwanda, for the same time window, τ = 100 days andEmbedded ImageClearly, two different indices may fail to rank the same dataset in the same way, and contradictory conclusions can easily arise for the same dataset. This opens the door for researchers to choose the index that suits their particular agenda best, and therefore, reasonable caution is needed when interpreting any analysis.

For the Holocaust, all of the above three indices Kr, Kp, and K# are unusually large, which would indicate that it is an extreme event, even in comparison to other recent genocides. Yet, there have been debates in the literature over whether the Holocaust is an extreme event (36).

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