Statistics of Democide
Chapter 1: Summary and Conclusions [Why Democide?...]
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For all regimes at this general level, there is virtually no relationship to diversity, culture, religion, regional variation, economics, education, health, transportation, demography, and geography. Overall eighty-three measures
We now know the empirical patterns and the indicators that have some meaningful relationship to democide. We have partialled out unrelated patterns among diverse measures. We can say from Table 22.1 that the dominant pattern of democide, that centrally involving domestic democide, is exclusively related to patterns of total and political power on the one hand and the likelihood of rebellion against a regime. The aim now is to focus on democide within the social field and determine how much variation in this century's democide among the 214 state regimes we can predict. This is not a matter of what patterns are related, but rather of what of all our political, diversity, cultural, and other indicators best fits, explains, predicts the variation in a specific type of democide across the 214 regimes.
Table 22.2 presents the results of an interactive regression analysis
As to interpreting the t-tests, when used as descriptive and not probability measure, like a standardized score (which the t-test is for a regression coefficient) they give a good and intuitive way of interpreting the strength and direction (negative t-tests means an inverse relationship) of an independent variable's relative ability to account for the variation in the dependent variable. If used probabilistically, a t-test of 1.645 has a one-tailed probability p £.05, a t-test of 2.00 is p £ .025. When the t-test gets up into the 4 and above, p £ .0001. So the t-test for TotalPower squared of 7.9 (in the first column of results in Table 22.2) shows indeed a very significant relationship of Power (of which TotalPower is the indicator) to democide.
Now looking at the results of Table 22.2, overall democide (logged) is best accounted for by the power and violence indicators and their interaction terms, and secondarily by refugees and the family basis of the social structure (i.e., social modernization). Only six indicators account for almost three-quarters of the variation (R squared) in democide across all 214 regimes, truly in social science research a remarkable result. And among all independent variables, the indicator most significantly accounting for this dependency is TotalPower squared. Again, as for the results described in Chapter 17, it is not only that the greater Power the more democide, but the greater the Power the more its effect is multiplied (see again Figure 17.3). This effect also holds true for domestic democide alone (the second column of results shown in the table) and, less so, for genocide and the annual rate.
But for foreign democide, this indicator of Power has no significant relationship, as here measured. This is consistent with the findings of previous chapters and should be understood in this way. Totalitarian power and the other measures for regimes have been defined as central government characteristics. What I have not measured is the islands of near absolute Power that can exist at one time or another even within democratic regimes. This is most notable in time of war, when for democracies the military are given considerable if not near absolute power within a restricted domain, and absolute secrecy and even deception of elected representatives by military and political leaders is practiced. Although the regime would still be characterized as democratic, in the pursuit of victory in war totalitarian-military power can flourish. It is thus not inconsistent with our other findings that foreign democide, generally occurring for democratic and many authoritarian regimes in time of war, should have little relationship to whether a regime is, centrally, democratic or totalitarian.
Note the very close relationship of national power times war-dead to overall democide, almost the same as that for TotalPower. This is in part due to democide including the foreign component, to which this interaction term has a significant relationship; it has none to domestic democide. The higher the national power of a regime measured by its population (and which also reflects its size and energy consumption per capita--see Table 20.2) times the greater the characteristic severity of its wars, the greater its democide. The greater a regime's national power and characteristic war-dead, the more the democide is multiplied.
Summarizing the results overall, we find much the same indicators related to types of democide, as summarized in Table 22.1. The addition of the four interaction terms shown at the bottom of Table 22.2 improve our ability to account for different types of democide. We also find some differences from previous chapters. When focusing on specific types of democide as we do in the regression analysis, one indicator of diversity--percent of minorities at risk--does have a significant, but compared to the other indicators, relatively minor positive relationship to domestic democide. And so does an indicator of African culture, whether a culture and society is dominated by clans or not. Overall democide and the subset of foreign democide tend to be greater for non-African regimes. And for the political variables, political power has no meaningful effect (I also experimented with it squared), while genocide is accounted for to some extent by the degree of authoritarian power and the absence of traditional elite power (that is, more socially modernized regimes have a slight tendency to commit genocide).
Given the regressions, how well can we actually predict democide? The best results are for the overall democide, and I will concentrate on that. Table 22.3 shows the ability of the six indicators and interaction terms to predict the magnitude of a regime's democide. For the four deka-megamurders, it correctly estimated that three of them would kill over ten-million and the other between one and ten-million. For the ten who killed between one and ten-million, the estimate places four correctly, five between 100-thousand and one-million, and one less than 100-thousand. Of the seventy-three regimes with no democide and four with democide less than 1,000 killed, it correctly predicted 43 of them, and predicted all but one of the rest would be one magnitude higher.
A different way of looking at these predictions is by ranking the best and worst of them, as in Table 22.4. The table's right most column gives the prediction residuals (errors) standardized by the standard deviation of democide. This was done to ease the interpretation of the residuals. A residual of plus or minus 2.0 would have around a 95 percent chance of occurring by chance,
Of all, post-fascist Italy has the worst over prediction. While the literature suggests that the regime was responsible for the deaths of somewhere around 1,000 people, the regression predicted that this should be over 10,000. From my reading of the period and knowledge of this regime, I think that this is a clear misprediction, and most likely due to this being a war-time, pre-democratic regime. But then there are the democides of Somalia and Afghanistan, which in fact may have killed as many as the regression estimate, if not more. By 1987 over a million Afghans had died in the civil and international war carried out by the Soviet Union in Afghanistan and the Afghan communist government against the rebels, and after the Soviet's withdrawal from the country, tens of thousands more would die. And by the early 1990s, Somalia would become a cauldron of violence and democide.
Then there are those listed in Table 22.4 for which the regression predictions were too low (although not significantly so), as for the Portuguese, Mexican, and Ugandan regimes. The two underestimated Portuguese regimes did their killing in their colonies and there is nothing in the regressions to account for the extent and nature of a regime's exploitation of its colonies through forced labor. Mexico also had an authoritarian regime, but was almost unique in the extent of its deadly, domestic forced-labor system, and the barbarity of its bloody civil war. Then there was the authoritarian Ugandan regime of Idi Amin. Although not unique in the extent of his killing, that his murder of tens of thousands of Ugandans was non-ideological, usually non-genocidal, and often at his whim, for the fun of it, made him a very unusual authoritarian dictator.
The megamurderers are shown in Table 22.4 also. With the exception of the Mexican regime, the regression predicted that each should have killed at least 100,000 people and for eight of them at least 1,000,000. As also seen in Table 22.3, three of the four that killed at least 10,000,000 are so predicted, with the Soviet Union predicted to have killed over 100,000,000. This is actually where the high from my low-high democide range places it. Nazi Germany, which murdered almost 21,000,000 people, is estimated by the regression to have killed near 5,000,000.
Regardless of the extent of these over and under predictions of democide, in almost all cases the regression was able to isolate among the 214 regimes those that would murder a large number of their citizens. More-over, it was able to well discriminate even among these those that would kill in the hundreds of thousands and, indeed, millions. Finally, all its predictions were well within a 95 percent confidence interval. This overall ability to discriminate is pictured in Figure 22.1. Along the regression line (the line of predicted democide) the separate magnitudes of democide are distinguishable, with the truly monstrous megamurderers set off in the upper right.
A regression analysis takes the data on the dependent variable, such as domestic democide, as given and tries to estimate them as best possible. By contrast, the analyses of the previous chapters had tried to find relationships between patterns among different types of democide and those among theoretically possible causes and conditions. Both kinds of patterns were analyzed within the same social space and the results delineated intercorrelations common to democide, politics, diversity, etc. There is another way of looking at democide, however, and that is as a space unto itself--a democide space.
I have already dealt with the democide space in terms of its major dimensions--patterns of democide. But now I want to focus on the space of democide itself. The usefulness of doing this is in its generality. If we lock ourselves into specific democide types or patterns, we then ignore other ways in which democide could have been measured or patterned consistent with the data. That is, so far we have analyzed one way of measuring the democide data and patterns among an infinite number of other ways of doing so. For example, the patterns among democide types alone, or of democide and the various social indicators, were defined by a specific kind of orthogonal varimax rotation of the factors of a component analysis (with an eye towards oblique rotation--on such rotation, see "Understanding Factor Analysis"). There are, however, an infinite number of other rotations for the same data, many defining substantively different results. I relied on the one rotation because it best simplified the interrelationships in the data. But there may be other meaningful rotated solutions that provide even a better fit to the possible causes and conditions.
To deal with this fundamental substantive arbitrariness I will do this. I will find for the space of democide (as defined by the various types of democide and all their possible linear functions, including functions of functions), the best (rotated) fit to the space of all the political, social, etc., indicators used in previous chapters. This fit will be such that not only will we be able to say how dependent the democide space is on the indicators, but what patterns in each space best reflect this fit. This will be through canonical analysis, the results of which are shown in Table 22.5.
Each column in the table defines two patterns (variates), one for democide and the other for the social indicators. The first column gives the linear combination of the democide types that have highest (canonical R) correlation with a linear combination of the social indicators. The next column defines, independent of the first, the second best linear combinations with the highest canonical correlation, and so on for the third, fourth, etc. Each pair of canonical variates can be interpreted as resulting from a form of regression analysis, where instead of one dependent variable one has a set of them, and the result is regression coefficients on each side of the equality.
The canonical correlation (canonical R) for each pair of variates also is comparable to the multiple correlation coefficient. Squared it measure the proportion of variation in a linear combination of the dependent democide indicators accounted for the independent social indicators. Thus the first fit is .92, which means that the social indicators collectively account for about 85 percent of the variation in the first linear combination of democide types. The trace correlation for this canonical fit of the two spaces is .53 and the square of this measures how much of the democide space is explained, predicted, by the social indicators. That is, about 28 percent of all they might form (all the possible rotations)--is statistically dependent upon the social indicators. For the fit of two spaces with so many variables on both sides this is good (recognizing again the capitalization of error problem) and indicates that regardless of which linearly consistent way democide is measured, it has a common social basis. What this is can be determined from the coefficients in Table 22.5.
In the table I have simplified these to best show the relationships involved, first by using only the correlations between patterns and measures, rather than canonical coefficients (which like regression coefficients depend upon the units and variance in the original data and are thus difficult to compare), and then by outlining high correlations and eliminating from the table near zero correlations less than an absolute .20. The best fitting patterns and consistently best indicators are sharply outlined thereby.
As can readily seen, the best fit is between a general pattern of democide defined by the overall democide totals, and the various power, war-dead, and rebellion-dead indicators and interaction terms. The best of all is the square of war-dead followed by national power times war-dead and war-dead itself. Both TotalPower and TotalPower squared are included, but have less significance than for the regression of democide on the six indicators (Table 22.2).
As mentioned, the canonical correlation of this fit for democide is .92. This seems very high, but this is for fourteen dependent and twenty-three independent variables, a number that carries with it the danger that the canonical correlations capitalize on random error and chance in the data. By comparison, the regression of overall democide alone on only six independent variables as shown in Table 22.2, had a multiple R of .84, or a fit of about 71 percent to the variation in the democide. The difference in variance accounted for between the best regression and best fitting canonical variates is a matter of 14 percent. The simplicity and theoretical relevance of the regression seems more significant to me than the loss of 14 percent of the variance, a good deal of which may simply be due to chance.
Looking at the canonical variates as a whole, we find that the democide annual rate has virtually no relationship to any of these canonical patterns. Nor did its regression analysis result in even a moderate multiple R--its .41 in Table 22.2 means that only about 17 percent of its variation could be accounted for by the sixteen indicators, only national power among them having any significant relationship. To explain this apparent lack of relationship, let me first reconsider what this measure means.
The annual rate of democide is an intuitively useful measure of regime killing. It communicates the relative intensity of democide across regimes by holding constant both a regime's population and its life span. It measures the average risk of a citizen being murdered by their regime during a year. Thus we can say that the Khmer Rouge murdered one out of every 12 people per year while the Vietnamese killed one out of every 833 and the Chinese communists one out of every 952. If one had a choice, then, presumably one would prefer to live in communist China than Cambodia or Vietnam, even though the former killed something like 35,000,000 people, or over 17 times the number the Khmer Rouge slaughtered.
As intuitively useful as it is there is little among the social indicators, including that of Power, to account by itself for the differences in annual rate between the Khmer Rouge, for example, and the Vietnamese and Chinese communist regimes or other megamurderers. One reason for this is statistical. This annual rate is created by dividing by both a regime's duration and its population. This then partials out of the annual rate their potential effects and necessarily reduces the annual rate's potential correlation with them to near zero (how close to zero depends on the variances in the numerator and denominator). Part of the lack of relationship is therefore artifactual, and the lack of relationship with national power (i.e., regime population) should not be surprising. But there is nothing artifactual about the lack of correlation with Power or those dead from war or rebellion.
Another statistical point should be made. Consider that we have quantified power, war, and rebellion by absolute measures. These are defined by the amount (or amount squared) of TotalPower, or war or rebellion-dead. It is their absolute amount that is highly related with the absolute amount of democide. Is there a way we can transform these variables to rates comparable to the democide rate? I have experimented with this and found that TotalPower undivided remains more related to the annual rate than any way of norming or proportioning it, as by duration or population.
Lets look at another side of this, then. It may be that we must further boost the high Power end of TotalPower to account for the intensity of democide--that we have not given enough weight to the impact of Power on this intensity in the prior measurements or interaction terms. This is suggested by Figure 22.2, which plots the regression of the logged annual rate of democide upon the third order polynomial of TotalPower (that is, TotalPower, TotalPower squared, and TotalPower cubed). The plot is instructive. It shows that there are many regimes along the base line for low and high power, but as the rate moves much from zero, it does so at the higher power end. This is reflected in the polynomial regression curve moving increasingly upward.
This scatter of regimes is better seen in Figure 22.3, where for TotalPower now dichotomized the proper relationship between the annual rate and Power is clear. Then why does this not show up in the regression and canonical analyses? The answer lies in the spread of many regimes along the TotalPower axis at or near an annual democide rate of zero. That is both low and high Power regimes can have no domestic democide or very low relative intensities. In logical terms this means that Power is a necessary, not sufficient condition for intense democide. This is indeed what I've been arguing from the beginning: that non-democracy is necessary for other than relatively small amounts of domestic democide. Nondemocracy and especially high TotalPower does not automatically lead to democide, but it must be present for other than small levels of democide to occur. We see this best with the intensity of domestic democide.
Even then, when the copatterns of democide and social indicators were looked at in the same space, we found that the annual rate was part of the domestic democide pattern and this in turn was interrelated with TotalPower. The finding that the regression of domestic democide is linearly better accounted for by TotalPower or its interaction terms, or that the canonical variates show a better relationship of overall and domestic democide with TotalPower, simply reflects the fact that while there are still low domestic democide regimes at the high end of Power, most have high domestic democide. That is, although for the high magnitude of democide TotalPower is also necessary and not sufficient, the existence of high TotalPower is a positive force towards domestic democide that steps up in potency as absolute Power is approached. The difference for the democide rate is that the potency multiplies much more at the extremely high ends. This is seen in Figure 22.4, where by comparison to the third order polynomial plotted in Figure 22.2 the effect on the intensity of democide of TotalPower for the fifth order polynomial is much greater, and that even the seventh order polynomial shows an increasing effect. The upshot of all this is that the annual rate--the intensity of domestic democide--alone is also accounted for by Power, but mainly when the higher levels of Power are greatly multiplied. Increasingly high Power, not in an additive sense but multiplicatively, predicts to a regime killing more people per year per capita.
Recall that the regression analysis showed (Table 22.2) that six social indicators, including Power and rebellion-dead, well estimate the domestic democide of regimes, including the megamurderers. But the emphasis was on accounting for the variation in democide across 214 state regimes, and not classifying regimes in terms of their democide. If we now focus on so classifying regimes, how well can the indicators do this and which is the best for this purpose? This is the ultimate practical question.
I will use discriminant analysis to answer this. Discriminant analysis is a type of canonical analysis, where rather then calculating how dependent the space of democide is on the space of political, social, and other indicators, and the best linear combinations in both spaces to define this, we can determine instead how these social indicators account for the space of regime groups, each being a different magnitude of overall democide. For example, in a discriminant analysis of democide I can code one group of regimes such that all those committing democide within the range 10,000 to 99,999 killed are coded 1, all other regimes coded zero; another group can be coded 1 if their democide is 100,000 to 999,999, all others coded zero; and so on. A group can be created similarly for each magnitude of democide. The resulting groups (variables), each defining a magnitude of democide, then comprise a space. The question is now the same as for canonical analysis. What is the best linear combination of these groups that can be best accounted for by the political, social, and other indicators such that each regime is correctly, or as close to being correctly as possible, classified in its group?
Table 22.6 displays the discriminant results. There were only two patterns (factors or variates) among the indictors significantly accounting for the democide groupings. In the table I have given the correlations between the indicators and these factors to best bring out the relationships involved, as in canonical analysis Table 22.5. The results are similar to those for the canonical analysis, with the dominance of TotalPower, and war and rebellion-dead, and their interaction terms. The first factor has a canonical correlation of .92 to the democide groupings, meaning the it can account for about 85 percent of the regime variation in group membership.
The ability of these factors to predict group membership can be seen from Table 22.7. It gives the frequency of the predicted and actual groupings from the discriminant analysis. Sixty-four out of seventy-seven regimes that killed less than one-thousand citizens or foreigners are correctly predicted; three out of the four that killed 10,000,000 or more are also predicted, while the remaining one is predicted to still kill in the millions. Overall, the magnitudes of 132 regimes are correctly predicted, while an additional fifty-eight are off by only one magnitude. These successes or errors of prediction are summed at the bottom of the table.
I have also included in parenthesis the results of the regression shown in Table 22.3. Even though the regression was only of overall democide onto six indicators and does not do near as well in correctly classifying regimes, it does slightly better in keeping predictions within one-magnitude. Table 22.8 lists the worse and best predicted group classifications from the discriminant analysis.
Even though the discriminant analysis does a better job of predicting democide groups than the regression analysis, as can be seen both by the frequency tables (Table 22.3 and Table 22.7) and listing of worse predicted (Table 22.4 and Table 22.8), the actual spread of the regression predictions against actual democide is closer. Figure 22.5 displays the ability of the discriminant analysis to actually discriminate among the various groups. The tight clusters of regimes at the lower right is not well unpacked.
In sum, then, there are four indicators or their interaction terms that best account for democide and predict which regimes will commit how much democide and with what intensity. These are a regime's TotalPower, national power, and characteristic war-dead and rebellion dead. These well explain particular types of democide, linear combinations of types of democide, and the space of democide.
* From the pre-publisher edited manuscript of Chapter 22 in R.J. Rummel, Statistics of Democide, 1997. For full reference to Statistics of Democide, the list of its contents, figures, and tables, and the text of its preface, click book.
1. This includes nine measures of war and rebellion, where only the best indicators of the resulting two patterns have been presented here.
2. See endnote 6 of Chapter 17.
3. Were all twenty-four included in the final regression, with only the significant independent variables shown, the multiple R would capitalize on the small but non-zero covariance between the dependent variables and the many non-significant independent variables, thus making R misleadingly high. But also, this would distort the t-tests for those independent variables that have high correlations among themselves, such as TotalPower and TotalPower squared.
4. In this case, the residuals can be assumed independent and the distribution normal.
5. That these four megamurders range above the regression line suggests that at the very high end we might square or cube one or more of the independent variables. I did try this with no success. Nonetheless, since this deviation appears nonrandom, there is some condition that could be added to the regression to better account for these great megamurderers that was not included among all the indicators and interaction terms. These four aside, the distribution of the other 210 regimes around the regression lines, which is fairly even and shows no curvilinearity, testifies to the goodness of fit of the regression.
6. This chart cannot be compared to the regression plot in Figure 22.1. This is because the discrimination (variance) along the X-axis the figure is for the actual data-it is the discrimination only along the Y-axis that is predicted. In Figure 22.5, however, it is the discrimination along both the X and Y-axis that is predicted.
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