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So their estimate is just pieced together from other people's estimates? I'm be interested in seeing the actual sources used to make the estimates in the first place. Did somebody get a hold of State Documents? Has there been a study of mass graves or something? Are there credible contemporary reports from the region that can be used to approximate the number, or the conditions at least?
Ah, I see you're new to the question of demographic calculations. Do you think there would be so much variance/controversy if hard figures were available? ;)
To answer your question there are a multitude of sources. The Soviet effort in collecting statistics was far ahead of its time and the most relevant sources are the official Soviet censuses of 1926, 1937, and 1929. These figures are questionable however as from the early 30s TsUNKhU (essentially the central statistics office) and its practices came under sustained assault from Stalin. Distortions are certainly present in the initially published results of the '37 and '39 censuses* but there is enough information present to a) reconstruct the original findings, and b) extrapolate data to estimate population changes in the intervening years
Crucially the census, and other registration data, gives vital background information such as the birth/death rates, with which its possible to arrive at some reasonably accurate estimates, albeit with significant margin of error. For example, the detailed results of the 1937 census, ie beyond headline figures, were not published until 1990 but Lorimer (working in 1946) was able to predict the population level to a good degree of accuracy (he was only out by a million). Of course this also leads to controversy - Andreev, Darskii, & Khar'kova (ADK) assume a much higher rate of birth than Lorimer and thus arrive at a significantly higher number of excess deaths
Nonetheless, much data has been released since 1990 but there remains the stubborn difficulties of collecting data in an overwhelming peasant society and one marked by the massive internal migrations of urbanisation, dekulakisation, and the legacy of civil war. Confident estimates as to the numbers in NKVD camps (or executions) can be gleaned from official records but there will never be the same degree of confidence for the general population - the data simply isn't there. The best that can be done is assemble ranges of estimates and consensus seems to have settled on 5.5-10m excess deaths (note: different from population deficit) during the 1926-39 period
*For example, the aborted census of 1937 includes a completely arbitary increase of 1m people to account for "undercounting". There's no real basis for this, and it was not enough to prevent Kurman's arrest, and the 1939 census includes a similarly crude adjustment of another 1m upwards
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I'm not tring to be anatagonistic here, but it's well known that the most impeccable, prestigious, 'unbiased', objective research coming out of bourgeois scholarship, has no problem with just pulling numbers out of thin air when it comes to Socialism.
Which is in turn just as biased a generalisation. Remember that any Marxist writing during the decades 1917-53 (at the earliest) would have far more likely to swallow official distortions and handwave away the millions of deaths. Indeed until the sixties, and in many cases the nineties, it was common amongst communists to simply dismiss the whole affair as simple bourgeois propaganda
Its also worth noting that, by and large, the range of estimates has increasingly narrowed over the decades and have largely been revised downwards. For example, you will be hard pressed to find a credible demographer, or historian, today who takes the numbers given in the 'Great Terror', never mind the 'Black Book' or Rummel's works, any way seriously. Increased study in the past decade has significantly punctured the bourgeois myths that were common during the Cold War (when total of over 20m deaths for the same period was taken as the benchmark number!)
Edit: Mao Chi X correctly identities the infamous "Kurman gap" of eight million unregistered deaths - the difference between what the Soviet statisticians were expecting (based on their own population trend analyses) and the initial results of the 1937 census. Kurman himself, fearing for his job and life, attempted to handwave away this difference by claiming that at least half was due to emigration, undercounting in 1937, and overcounting in 1927. There's no basis for these assumptions. This leaves roughly 5.1m unregistered deaths which can be divided between the famine and unregistered deaths in the prison system. Whatever way that division goes, in addition to the 3.4m registered deaths during the same period it produces a total of 8.5m deaths
As I noted above, changing the birth rate (as ADK does) produces different totals. However if it didn't occur to Kurman, the head statistician, to account for either a different birth rate or detaching 2 million citizens (both very obvious possibilities) then I wouldn't really credit this as an explanation