My purpose here is to test this conclusion directly against the occurrence of conflict and violence for all states for the five years, from 1976 to 1980, and for all interstate wars since 1816.

At a more basic theoretical level, libertarian states comprise social fields in which the actions of groups and individuals respond to many divergent and opposing social and psychological forces. These forces spontaneously resolve into interlocking and nested balances of powers and associated structures of expectations. These define the social order. Such systems (like the free market) tend to be self-regulating and to isolate and inhibit conflicts and violence when they occur. They tend to encourage exchange, rather than coercive and violent solutions, in conflict between groups and individuals.

Libertarian states are by theory not only less violence prone, but when foreign relations includes the perception of other libertarian states, this inhibition becomes a mutual barrier to violence. Their mutual domestic diversity and pluralism, their free and competitive press, their people-to-people and elite-to-elite bonds and relationships, and their mutual identification and sympathy will foreclose on any expectation or occurrence of war between them; violence may occur only in the most extraordinary and unusual circumstances, or at the margins of what it means to be libertarian.

In sum, there are two propositions implied, one relating to interstate violence, the other to the overall violence of a state (operational statement in parentheses):

• Joint Freedom Proposition: Libertarian systems mutually preclude violence (violence will occur between states only if at least one is nonlibertarian (Rummel, 1979: Joint Freedom).

• Freedom Proposition: Freedom inhibits violence (the more libertarian a state, the less it tends to be involved in violence (Rummel, 1979: Freedom).

As to systematic evidence for the first Proposition, a survey of the literature uncovered fourteen relevant empirical studies. Ten support (three strongly) it and three are negative.¹ And two of these negative ones are based on indirect inferences from complex statistical manipulations of many variables, themselves indirectly measuring the relevant concepts. There are five important (in the scope and relevance of the data and analyses) studies, all of which support the proposition (two strongly; Babst, 1972; Rummel, 1979: Appendix I, Project 48; Barringer, 1972; Vincent, 1977a, 1977b, 1979; and Small and Singer, 1979). It is fair to say, therefore, that in general the evidence supports the idea that violence will not occur between libertarian states.

In evaluating this evidence, including that to be presented here, keep in mind the unusual nature of this proposition. It is not a statement of correlation, association, or relationship. It is an absolute (or "point') assertion: There will be no violence between libertarian states. One clear case of violence or war unqualified by very unusual or mitigating circumstances falsifies the proposition.²

As for the Freedom Proposition, the evidence in the literature described in Rummel (Vol. 4: War, Power, Peace) is mixed but tends to support it. Of 25 relevant studies, 13 favor (4 strongly) the proposition and 10 are opposed (6 strongly). However, when only directly relevant studies are considered, those in favor number the same, while those that oppose the proposition drop to 8 (with 5 strongly negative). Finally, if only important studies (covering large historical periods, large samples, or many variables) are counted, 6 are positive (4 strongly), while only 3 are opposed (one strongly). The result is that the more directly relevant and important the published study, the more likely its findings will support the proposition.

Freedom is best measured by the degree to which governmental power is decentralized and limited and society is based on exchange. Here it suffices to measure the level of economic freedom (from governmental ownership, control, and regulation). Thus the two definitions are:

• Political freedom = civil liberties + political rights
• Freedom = political freedom + economic freedom

The Freedom House publication Freedom at Issue presents annually a 7-point scale of all states on their political rights and civil liberties.³ To paraphrase Freedom at Issue (1981: 6), political rights are defined by an open, competitive electoral process through which leaders are clearly elected. States rated 1 have these characteristics; those rated 7 have none--those at the top believe they have the right to govern without challenge and are not constrained by public opinion or tradition. Civil liberties comprise the freedom of the press and the independence of the major media from government dictation; the protection of the individual by the courts; the freedom to express individual opinions without fear of imprisonment; the respect for private rights and desires in religion, occupation, residence, education, and the like; and the individual's ability to engage in rational political activities without fear for his or her life. States rated 1 have all these civil liberties; those rated 7 have complete censorship; political prisoners; no right of assembly; restricted travel, residence, and occupation; pervading fear tied in to a police-state environment; and swift and sure execution. I will operationalize political freedom, then, as the sum of these two scales,⁴ where the higher the combined scale value, the less the political freedom. Thus for 1980 the United States is 1 + 1 = 2; Indonesia is 5 + 5 = 10; Kuwait is 6 + 4 = 10, and Vietnam is 7 + 7 = 14.

Freedom at Issue also classifies states by their economic and political systems (see Wright, 1982, for a useful refinement of the economic classification). According to my estimate of the economic freedom under each subclassification, I distributed scale values 1 through 14 in the following manner:

Scale Value = Type of Economic System (all examples for 1977)

1 = industrial and preindustrial capitalist, decentralized (e.g., the United States, Botswana, Cyprus)

2 = all other preindustrial capitalist (e.g., Fiji, Gambia, Honduras)

3 = all other industrial capitalist (e.g., Costa Rica, France, Surinam)

5 = preindustrial capitalist-statist (e.g., Rhodesia, Iran, Zaire)

6 = industrial capitalist-statist (e.g., Malta, Taiwan, Ghana)

8 = preindustrial capitalist-socialist (e.g., Burma, Sudan, Peru)

9 = industrial capitalist-socialist (e.g., Austria, Egypt, Yugoslavia)

11 = preindustrial socialist (e.g., Angola, Laos, Tanzania)

12 = industrial socialist, non-Communist (Algeria only)

14 = industrial socialist, Communist (e.g., Albania, Czechoslovakia, USSR)

Freedom is then measured as the scale values for political freedom plus those for economic freedom, which gives equal weight to political and economic freedom. Thus freedom for Belgium in 1977 equals 2 + 1 = 3; for Sweden 2 + 9 = 11; for Senegal 8 + 9 = 17; for Poland 11 + 9 = 20; and for East Germany 14 + 14 = 28.

I need also to group states and dyads by their degree of libertarianism and to keep distinct the two definitions of a libertarian state. The most objective way of doing this is to divide the political freedom and freedom scales into the types listed in Table 1. These scales and types are now the basic data on libertarianism for testing the propositions.

In application to the event data, each variable (with one exception) is scaled from 1 to 8 by judging the hostility involved, severity of underlying conflict, values, and stakes at issue, and the possibility of escalation to more intense conflict, including violence and war. The full definitions cannot be given here, but, for example, the

warnings-and-threats variable is scaled as

0 = none;

4 = warning or threat of hostilities short of war, or warning or threat of significant negative sanctions;

8 = ultimatum (or threat of war).

The economic sanctions variable is scaled

0 = none;

2 = politically significant, showing coolness of relations;

4 = politically significant, showing cold and somewhat antagonistic relations (or part of coercive diplomacy); and 8 = severe sanctions (or strongest possible economic sanctions outside of boycott, embargo, or blockade).

The alert variable is scaled as

0 = none;

2 = politically significant expectations of military action and low, simple preparation for a contingency;

4 = an alert preparing for likely military action but of lesser magnitude than a war alert;

8 = an alert threatening or involved in preparations for war (or complete and highest alert possible).

And the war variable is scaled as

0 = none,

1 = a minor, limited war fought in a remote area, or a declaration of war or statement of war involvement without much military action following;

2 = border war, high intensity, but clearly limited to the border,

4 = war, but not fought totally (if lost, revolutionary domestic change not threatened);

8 = a total war, from the state's perspective (or revolutionary domestic change threatened by a loss).

The number killed scale needs to be given completely. It is

0 = none killed in official dyadic violence;

1 = 1 to 5 killed;

2 = 6 to 25 killed;

3 = 26 to 225;

4 = 226 to 1,125;

5 = 1,126 to 5,625;

6 = 5626 to 28,125;

7 = 28,126 to 140,625;

8 = 140,626 to 703,125;

9 => 703,125.

Where this is roughly a logarithmic (to the base 5) scale selected and, adjusted to index the step-up in political intensity with increased casualties, and to give scale values comparable to those for other variables.

I tested the reliability of the above scaling procedures on 1,500 news reports involving 37 dyads and 24 states. The independent scalings of two untrained volunteers were compared to that used here. The t-test of the difference between the mean scalings for each variable was nonsignificant (p <.73; .70); the product-moment correlations^6a were .87 and .76. [On the nature of this correlation, see Understanding Correlation] The mean absolute scale difference on the 8-point scales were .63 and 1.0. All this suggests the scales are fairly reliable.

The dyad profiles across the seventeen variables need to be collapsed into one scale of nonviolent conflict/ violence/war. Figure 1 presents a Scaling Transformation Chart for the seventeen conflict variables. The scale values of a variable were aligned from left to right in the chart according to the underlying intensity of conflict, in comparison to the scale values of the other variables. Thus it can be seen that the scale values of the accusations variable are usually to the left of the same values for the protests variable; values for protests are to the left of the same ones for threats and warnings. And considering the dimensionality of the groups of variables as one moves from negative communications variables at the top to the military action variables at the bottom, the scale values for the variables move to the right. Actually, as a result, the Foreign Conflict Scale of Figure 1 is roughly divisible into left to right segments, corresponding to these dimensions, as shown at the bottom. One can convert from a variable scale value to the Foreign Conflict Scale as follows:

1. Determine the profile scale values across the seventeen conflict variables for dyad for a year.

2. Of all scale values for all variables, isolate the one furthest to the right 0: the Transformation Chart.

3. Define for this one value the corresponding (vertical) Foreign Conflict Scale value. This is then the measure of conflict for a state or dyad for a year.

The selected, symmetrical dyads listed in Table 2 provide examples; for each a Foreign Conflict Scale value is shown. For India and Pakistan this is determined by referring to its profile in Figure 1, where the value of 4 for the accusations variable has the highest (is furthest to the right) Foreign Conflict Scale value, 10. For the Iran-Iraq dyad, both war and number killed variables give the same maximum Foreign Conflict Scale value of 47. Such Foreign Conflict Scale values for 1980, as well as those for the other dyads, are the conflict data for the tests to be conducted here.

Reliability tests were done on the Foreign Conflict Scale using the event data scalings independently generated for the assessment described above. There was no significant mean-scale difference from the final scale scores used here (p <.92; 98);⁷ the product moment correlations were .99 and .99. For the scale length of 52 units, the percentage mean absolute difference was 2.1 and 3.2.

Overall, then, this approach to measuring conflict produces one ordinal scale measuring the intensity of conflict with clear demarcations between violent and nonviolent conflict and between war and nonwar.^7a Moreover, very intense war, as well as minor conflict, can be discriminated. This Foreign Conflict Scale thus avoids the distortion created by adding weighted or unweighted event data counts across variables: Many low-level accusations can then equal an embargo; some combination of low-level conflict can sum to a high level, making states that are verbally conflictful appear to have conflict as intense as that of those having clashes or military action.

More important, the Foreign Conflict Scale helps to overcome data bias and unavailability. Because of interest and a free press, data are more easily available on the low-level conflicts of Western and open societies. As conflicts become more intense they tend to be reported, even for totalitarian states. The invasion of Afghanistan by the USSR could not be hidden, but a sanction against North Korea by China would likely be unknown outside their elite circles unless publicized for propaganda purposes. To sum weighted or unweighted counts across conflict variables therefore biases the resulting scale downward for closed (such as Albania), remote (such as Gambia), and uninteresting (such as Rwanda) states. My scale helps to avoid this, since the more intense an action, the more likely it is that it will be reported, and one clash between, say Albania and Yugoslavia, is sufficient to place this dyad above any other without violence, irrespective of their negative sanctions or communications.

Finally, the Foreign Conflict Scale is appropriate and conservative in testing the propositions of concern here, since both focus on the occurrence of violence. Rightly, then, any one act of violence or of war automatically creates a high Foreign Conflict Scale value, whereas no matter how many negative communications or sanctions, the Foreign Conflict Scale value will be low or moderate.

Table 3 lists the wars and campaigns of violence (the systematic use of violence for political ends) reflected by the Foreign Conflict Scale values of Figure 1 for the 1976-1980 period. Not shown are the many violent incidents, involving a singular confrontation, clash, or attack, that also are scaled. For other purposes, some of these incidents might be omitted, such as the firing by Iranian soldiers on the ships of Panama and Japan caught in the Shatt al Arab waterway when the Iran-Iraq war broke out. Such were included in the scaling so that any occurrence of violence between free states, however minor, could be caught.

Data were coded for all legally sovereign and independent states, and for all directed, interstate dyads for the years January 1, 1976, to December 31, 1980.

By nature of the propositions to be tested, directed dyad data (e.g., U.S. threats against Cuba) were converted to symmetrical dyad data (e.g., the threats between the United States and Cuba).⁹ It is these symmetrical data that were transformed into the Conflict Scale values of Figure 1 for dyads.

Hypothesis 1: Libertarian states have no violence between them.

Recall that "libertarian" is alternatively measured as political freedom or freedom. "Violence" means official violence, i.e., that between or involving government forces (the Soviet-Afghan war is an exception; see Note b to Table 3). This in mind, Table 4 presents the relevant theoretical and empirical frequencies.

Focusing on the frequencies for all cases, by Hypothesis 1 the expected (theoretical) frequency of violence is zero. And empirically there is no instance of violence between politically free or free states. Thus Hypothesis 1 is not falsified.

This lack of falsification may be only a lucky result. One way of testing for this is to consider the probability that the theoretical and empirical frequencies would be as close (or closer) than they are, were they truly from separate distributions. To test for this, consider the following null hypothesis.

Null Hypothesis 1: Libertarian states have violence between them.

This may be tested using the goodness-of-fit chi-square (²), which for the frequencies of Table 4 and 1 degree of freedom (the zero violence for libertarian dyads and all violence for other dyads is predicted by theory)¹⁰ is zero for both P-P and F-F samples. The probability of getting this chi-square were the Null Hypothesis true is p <.005 for both samples. Clearly, on this test the possibility of chance should be rejected.

However, the chi-square goodness-of-fit test is problematic here because of the expected zero violence--even for large samples the theoretical expectations should be at least 5 for 1 d.f. to avoid misjudging the Null Hypothesis, although the very small p seems safe enough. An alternative without this problem is the binomial test. Let each case of violence equal a "success," each P-P (or F-F) dyad per year be a "trial," and the empirical probability of violence for each dyad for each year be the number of cases of violence divided by the total sample, or 121/ 62,040 = .00195. Also let the Null Hypothesis be that P-P (or FF) dyads are as likely to have at least as much violence as are other dyads. Then, for the P-P (or F-F) dyads the probability of zero violence for 3,530 (or 1,690) trials is .001 (or .037). Since both binomial tests are significant, this test also enables us to reject (for the Null Hypothesis) the possibility that chance explains the zero violence for P-P (or F-F) dyads.¹¹

In their article on the war-proneness of democracies, Small and Singer (1976) tested the belief that democracies are more peaceful than are other states.¹² Using their list of 50 interstate wars (occurring between 1816 and 1965), they find that, except in two "marginal" cases,¹³ democracies had no wars between them. However, Small and Singer explain this mainly as a result of the lack of common borders between democracies and try to show that a large percentage of wars involved neighboring states. Aside from difficulties with their percentages, ¹⁴ they raise an important point.

Table 4 also presents the cases of violence for contiguous P-P and F-F dyads. Of course, since this is a subsample, we will also find zero violence as expected. However, the question here also is whether this is a random result, especially since the sample size is so much smaller than the one for all cases. If chance can explain the zero violence for contiguous libertarian states, this would suggest that the significant zero violence for all libertarian states is really due to their lack of common borders. As for the all-case sample, the goodness-of-fit chi-square test for the contiguous cases is zero at 1 d.f.; p <.005. The hypothesis of chance should be rejected.

The binomial test should also be applied here, especially because of the zero expected values. Defining "success" and "trials" and the Null Hypothesis as before, and the probability of success as 86/1,164 = .074, the binomial distribution gives the probability of zero violence for P-P contiguous states as p <.0003, and for F-F states as p <.018. For both meanings of libertarianism, therefore, and with both chi-square and binomial tests, we can prudently reject the hypothesis that the significant results for all cases are due to the lack of contiguity among libertarian states.

Such are the direct tests of Hypothesis 1. The conclusion is that it cannot be rejected by virtue of a negative case, and that it is highly unlikely that this lack of any violence is due to chance or to the lack of borders between libertarian states.

While Hypothesis 1 asserts an amount (zero) and not a correlation or association between libertarianism and violence, the credibility of the hypothesis will be increased if we also find that violence between states scales upward the less they are libertarian. This is because the underlying theory implies that there is a gradient of restraining effects on the intensity of foreign violence correlated with the degree of libertarianism within a state. We would surely be troubled if libertarian and partially libertarian states are more violent toward one another than are wholly nonlibertarian states, or if nonlibertarian states are, next to the libertarian ones, the least violent toward one another.

The tests to be presented for the Freedom Proposition (below) will give positive evidence for this gradient. Here it should suffice to show this. The percentage of dyads of each type with violence or war, moving through the six types of dyads from P-P (or F-F) to those involving the least libertarian NP-NP (or NF-NF), for the 1976-1980 period is shown in Table 5. Note that the last three types include no politically free (or free) states at all and have the highest percentage of violence; the last type has the highest of all. These percentages can be correlated with the level of libertarianism in a dyad. Let P (or F) = 0, PP (or PF) = 1, and NP (or NF) = 2. Then give a dyad type the joint score of its members as shown in Table 5. The resulting product-moment correlations between the decreasing libertarianism in the dyad and the percentage of violence are given at the end of Table 5, along with their significance. Clearly, decreasing libertarianism means increasing violence.

The violence for political freedom and freedom samples is plotted in Figure 2 and Figure 3. They show violence obviously scaling upward to the right, as we would expect from the above correlation. Especially important is that, for both plots, the best-fitting function (compared to power, logarithmic, and linear functions) is an exponential, or growth, curve. It bends upward toward higher violence as libertarianism decreases; as libertarianism increases it declines and crosses the violence threshold into nonviolence in the region of libertarian dyads. Although indirect, these plots and functions are among the most important results of this study. They show the great power of the underlying theory.

The growth functions for the above plots are fitted to the variance for all cases of violence, and the coefficient of determination (R²) is therefore not itself an indirect test. Only the direction and shape of the curve are. R² is an appropriate indirect test, however, for the maximum violence reached for each scale value of political freedom or freedom. This will indicate the extreme range of violence likely per decrease in libertarianism and can be plotted in Figure 2 and Figure 3 by connecting the highest points reached for each freedom value.

Figure 4 shows the best-fitting curves to these maxima. For political freedom, a growth curve is still best, accounting for 85% of the variance (p <.4 x 10^-52). This is strong, indirect support for Hypothesis 1. For freedom, the best fit is a power curve, reflecting the bunching of several wars among the middle freedom values in Figure 3; but it still moves upward even for the lowest nonlibertarian values. The R² is also very highly significant, accounting for 43% of the variance (p <.4 x 10^-20).

Not only violence, but if the underlying libertarian theory is correct, war also should increase with decreasing libertarianism in the dyad. We do find this for the 1976-1980 period, as can be seen from Table 5. The least libertarian states had the highest percentage of wars, and the correlation between a dyad's lack of political freedom (or freedom) and percentage of war is .81 (.74), both significant.

Note also from Figure 2 and Figure 3 that wars do not occur even near the region of Politically Free or Free dyads. For example, while a scale value of 8 is the threshold for political freedom, the dyads with war that are closest to it have a value of 24. This is, of course, consistent with the gradient we are testing for here, and which can be seen so well in the right triangular shape of the plots in Figure 2, and to a lesser extent, in Figure 3.

This result for war is so important that I have tried to broaden the sample beyond that used here. I have already mentioned the Small and Singer (1976) list of 50 interstate wars between 1816 and 1965. Table 6 presents the total number of dyads engaged in these wars from 1816 to 1918, the end of World War 1, and from 1919 to 1965. Overall, 325 dyads were involved in these wars, but with only the 11 marginal exceptions, they included no democracies fighting other democracies. This is true even though Small and Singer used a less restrictive definition for democracy than I did for libertarianism, which includes not only having the franchise and an effective legislature, but many additional civil liberties and political rights. Unfortunately, I do not have the data to determine the number of democracies in the world for the 1816-1965 period, and so the significance of the distribution in Table 6 cannot be tested. This aside, the distribution gives considerable indirect, subjective weight to Hypothesis 1.

Bueno de Mesquita (1981: 209) updated the Small and Singer list of wars to 1974. No democracies, as Small and Singer defined them, on the updated list had war. Considering my list of wars (from 1976 to 1980) in Table 2, the Small-Singer-Bueno de Mesquita list (from 1816 to 1974), and the fact that no war between democracies occurred in 1975 (and including the marginal exceptions noted above) we have not had a real war between democracies in over a century and a half, from 1816 to 1980.This gives more indirect, subjective support to Hypothesis 1.

Pride (1970) provides a classification of 14 democracies in terms of a democratization index and the stability of this index for the twentieth century. This gives us a very conservative (some of the democracies were marginally so, and lasted for only a few decades) way of testing the significance of the Small-Singer list of wars, as shown in Table 7. Clearly, using Prides sample of democracies, there has been a significant lack of war between them.

What about this possibility being due to the lack of borders between democracies? The number of dyads with and without war who share borders is also shown in Table 7. Unfortunately, because of the very low expected values for the top row of the table and the marginal values for the significance of the resulting chi-square, we cannot base a clear decision about the significance of this distribution on it. In this case, then, we can use the binomial test, which gives us a significance of p <.03 (one-tailed).

In sum, whether controlling for borders or not, the lack of wars between democracies is unlikely to have occurred by chance, and Hypothesis 1 is indirectly supported.

By theory we should expect not only a gradient of violence with decreasing libertarianism, but also that libertarian states make no preparations for violence or war regarding each other--the undefended border between the United States and Canada should be paradigmatic of libertarian states.

This point is also important methodologically. It may be that, tests for chance aside, the 1976-1980 period just happened to have no violence between libertarian states, but later periods will. If we find even no preparations for war or violence, even no activity warning of violence or war (such as shows of strength, alerts, troop movements) between libertarian states, the probability decreases that, relevant to Hypothesis 1, 1976-1980 is an aberrant sample of violence.

As will be shown for the Freedom Proposition (below) there are no warning and defensive acts between politically free or free states for the 1976-1980 period. Interestingly, when the maximum conflict behavior for each value of the Political Freedom or Freedom Scale is plotted, the best-fitting plots are logarithmic, dipping sharply down below violence and toward zero at the greatest freedom. This is shown in Figure 5 (to be clear, the difference between Figure 4 and Figure 5 is that in the former the functions fit only the maximum violence; in the latter the functions fit the maximum conflict behavior, violence or not, for each value of the libertarian scale). Relevantly, both curves decline steeply into the region of libertarian dyads at the threshold of warning and defensive acts.

As for war, it is important to determine whether other periods will also indirectly support this gradient extending to the threat of, or preparation for, violence. Table 8 presents 20 years of data on conflicts involving the threat or actual use of force. As shown, there were no such conflicts between democratic states, as defined by Feierabend and Feierabend (1972, 1973). And this is highly significant (p <.004), even when controlling for common borders (p <.027). This is a critical result, although indirect. It uses the definitions and data of others to arrive at the same conclusion as Hypothesis 1. The only reason the results must be considered indirect, however, is that threats of force were also involved, and such threats are not specifically part of the hypothesis.

H2: The more libertarian a state, the less its foreign violence.

H3: The more libertarian two states, the less their mutual foreign violence.

The first is a restatement of the operational expression of the proposition at the national level; the second states the proposition's implied operational meaning for dyadic relations. While obviously related, these hypotheses are separate and make distinct assertions about freedom.

As for the previous tests, "libertarian" will be alternatively defined here as political freedom (which comprises political rights and civil liberties) and freedom (which also includes economic freedom--a free market). Moreover, recall that by theory freedom is the preferred definition, since it defines the maximum freedom within a state; it is, indeed, what libertarians (or classical liberals) usually mean by freedom. Where possible, tests will be performed for any significant differences in results between the two definitions.

The first, which I will call the Max Violence Sample (N = 112), will consist of the maximum conflict behavior of each state between 1976 and 1980. This will avoid weighting the tests by the several states involved in continuous violence for the five years. These data, then, really will gauge the relationship between libertarian freedom and the highest intensity of conflict behavior reached during this period.

The second sample will comprise all cases of violence for each year, summed over the five years. Thus, if state i had a Conflict Scale value (as defined earlier regarding Figure 1) of 12 in 1976, 41 in 1977, and 21 in 1980, each of these values is a separate case (for the Max Conflict Sample, only the 41 in 1977 for state i would have been included). I will call this the Full Sample (N = 334). Although separate years with violence for the same state are thus considered different cases, this should not create a problem of dependent cases. Theoretically and mathematically, there is no necessary relationship between nonviolence in one year and violence or nonviolence in the previous or following year: Two states may be at peace one year, at war the next, and at peace the year after, or peace or war may extend over many years. Of course, there may be a temporal correlation in the occurrence of violence that can influence the tests. But this may work for or against the hypotheses, and there is no reason by theory that it should go either way. In any case, the Max Violence Sample does not have this problem and thus serves as a check for those who remain concerned about possibly dependent cases.

Table 9 presents the two samples, cross-classified by political freedom and freedom types, and the range of conflict behavior. The tabulated numbers are frequencies. To be sure the table is clear, for the Max Conflict Sample over the 1976-1980 period, only one politically free state (P) had conflict behavior no more intense than negative communications; four other politically free states had conflict behavior as intense as warning and defensive acts; and another politically free state was involved in a war. For the Full Sample and nonpolitically free (NP) states, there were a total of 32 cases of states having conflict behavior reaching the level of negative sanctions over the five years, i.e., [(number of NP states reaching the level of negative sanctions for 1976) + (those for 1977) + . . . + (those for 1980) = 32]. Now for Hypothesis 2.

The hypothesis first asserts a negative relationship between the libertarianism of states and their foreign violence. Table 9 gives the appropriate frequencies; the relationship between libertarianism and violence can be seen to be largely negative (the major exception being the nonwar violence for F cases in the Max Sample). However, the differences in these frequencies may be due simply to there being fewer P or F cases to have violence, for example. Table 10, therefore, presents the proportion of cases with violence. As can easily be seen, the proportions are in the hypothesized direction, and the correlations at the bottom of the table measure this (they are positive because the higher number for the nation type, the less libertarian it is). The correlations by themselves, or their significance, are not a sufficient test of Hypothesis 2, however; they are linear measures, while the relationship specified in Hypothesis 2 may be nonlinear.

The appropriate tests are provided in Table 11. Given (see above) that the data show the hypothesized direction of relationship, the question the table should answer is whether this is a significant contingency. Can we, with fair confidence, reject the possibility that these data favor Hypothesis 2 by chance? First, the Null Hypothesis.

Null Hypothesis 2: Violence is not less the freer a state (violence is either greater the more libertarian a state, or is independent of its libertarianism).

To reject this null hypothesis requires that the contingency table show a negative relationship between violence and libertarianism and that this be significant. The appropriate coefficient is the chi-square (²), which is shown for the two samples and each of the definitions of freedom. The significance level is one-tailed, due to the null hypothesis being directional.

First, the contingency is in the opposite direction to that specified in the null hypothesis, as shown in Table 10. Second, all the ² results are highly significant. Therefore, the null hypothesis should be rejected with confidence; we can say that for the 1976-1980 period, the more libertarian a state, the less violence.

Is freedom a significantly better fit to the hypothesis than political freedom? Clearly, both definitions yield significant results. And the ² for freedom is higher. Moreover, as can be seen from the difference in the ² t-test, this is a significant difference for both samples.¹⁵ Therefore, I can conclude that there is significantly less violence when a state's economic freedom is added to civil liberties and political rights. The above constitute direct tests. There are indirect tests that also can be applied that should affect our confidence in Hypothesis 2.

If the theory underlying the hypothesis is valid, we also would expect that the more libertarian states are, the less they have wars. The data support this, significantly. The appropriate contingency table (like Table 11, with war in place of violence) can be calculated from Table 9 and Table 10, and would yield four ² tests, all significant in the hypothesized direction at p <.002, one-tailed. Moreover, freedom would still do significantly better than political freedom at p <.007, one-tailed.

By theory, we also would expect that, relative to their nonviolent conflict behavior, the more libertarian states are, the less their violence. This is because the very forces that limit violence--greater activity among divergent interest groups, the greater pluralistic dynamism of open societies, the greater segmentation of interests, and the greater cross-pressures--also promote internal and external (nonviolent) conflict. This can be tested by cross-tabulating nonviolent conflict behavior and violence separately against the nation types for both samples. The contingencies would be then in the proper direction; the four ² calculated for such a 3 x 2 table would be all significant at p <.003, one-tailed. That is, relative to their nonviolent conflict, the more libertarian a state, the less its violence. There is, however, no significant difference between these results for political freedom and freedom.

Second, this symmetrical dyadic data will be organized by year, so that the frequency counts will be of the number of dyads with given conflict behavior per year, over the five years. This is comparable to the Full Sample used above. A Max Sample is not employed because of the greater refinement in cross-classifications (for example, now instead of just a classification for free states F, there are F-F, F-PF, and F-NF subclassifications of dyads), and thus a reduction in subsample sizes (and expected values for a contingency table).

Third, since the hypothesis posits a general relationship between freedom and violence, one should avoid letting a dyad with violence over the five years and having the same joint political freedom or freedom score skew the tests. The conservative approach to the hypothesis, given that the test of Hypothesis 2 already shows a tendency for violence to be associated with nonlibertarian states, is to omit those years of data for a dyad for which the dyad's joint political freedom or freedom score is duplicated, keeping only the year of highest conflict behavior. This will combine the virtues of both the Full and Max Samples used above and make any positive results for Hypothesis 3 more robust. That is, it is a conservative procedure.

To make sure this procedure is understood, consider the data on violence for Ethiopia-Somalia. For those years having conflict behavior between these states, joint political freedom scores and Conflict Scale values of Figure 1 were for the years 1977, 1978, 1979, and 1980 respectively:

Joint Political Freedom: 28, 28, 28, 28;
Conflict Scale Value: 49, 47, 45, 45.

Therefore, since the joint PF were the same for these four years, only the data for the highest Conflict Scale value of Figure 1, which is for 1977, will be used. Had 1976 had conflict behavior, but with a different joint-PF score, it would have been also included. The year 1976, however, will be a case of no violence.

In total, 680 symmetrical dyads had conflict behavior over the five years 1976-1980 (that is, those dyads with conflict behavior in 1976 + those in 1977 + . . . + those in 1980 = 680). The sample for political freedom, omitting all but the highest conflict data for a dyad base whose joint political freedom scores were duplicated, is 510; for freedom it is 527. Therefore, the elimination procedure drops 23% to 25% of the cases.

Table 12 presents the data, subdivided as finely as the frequencies permit. These will be the basic data for testing the Hypothesis 3. Table 13 shows the hypothesis-relevant data on violence that were omitted.

One can see from Table 12 that there is a tendency overall for the raw frequency of violence to increase as joint political freedom and freedom decrease (note the clustering of zero violence in the upper right). This is even more obvious in Figure 2 and Figure 3, which plot this violence for the joint political freedom and freedom scores. To measure this increase in violence here, Table 14 gives the proportion of violence to total dyads. As for Hypothesis 2, the problem now is to determine the probability that the direction of relationship those proportions show and the contingencies also given in Table 14 are due to chance.

The Null Hypothesis to be tested is:

Null Hypothesis 3: Violence is not less between two states the more libertarian they are (violence is either greater between two states the more libertarian they are, or is independent of their libertarianism).

The correlation coefficients in Table 14 show the contingencies to be in the wrong direction for the null hypothesis; the ² is highly significant for both definitions of libertarian. We must therefore reject the null hypothesis as being very highly unlikely (less than two in a billion probability) and accept alternative Hypothesis 3.

Are my data elimination procedures responsible for rejecting the null hypothesis? The answer can be seen in Table 13, in which the elimination of data on violence associated with duplicate political freedom or freedom scores tends to favor those dyads involving the least libertarian states (empirically they tend to have stable scores while also having the most violence, as for example, Vietnam; the freest states also tend to have stable scores, but with little violence), which would work for the null hypothesis. To prove this, I recalculated the ² results for Table 14 using all data on violence (N = 121). The ²s are 75.2 (182.3), which are 57% (97%) higher than those in Table 14. Therefore, for all the data the null hypothesis also would be rejected, but with even much greater significance. This is why I say that my data procedures are conservative.

Freedom, as it should by theory, clearly does better in rejecting the null hypothesis than does political freedom, and the difference is highly significant.

For the Hypothesis 1, I tested the possibility that lack of common borders between libertarian states may be causing the significant results. This may also be true here. Table 15, therefore, presents the violence data of Table 14 only for those dyads whose members are contiguous. If the increase in violence with the decrease in libertarianism is due to contiguity--it may be that the least libertarian states commonly share borders, while the most libertarian have few--then the distribution of violence in Table 15 should not enable us to reject Null Hypothesis 3. However, as the proportions show and correlations measure, the direction of relationship between violence and dyad type is opposite to that specified by the Null Hypothesis; and the ² proves that this is highly unlikely to be random. Therefore, Null Hypothesis 3 should be rejected. Even when controlling for common borders, the less libertarian two states are, the more mutual violence there is.

Also as shown in Table 15, freedom still is the significantly better definition: Economic freedom does make a difference, even when controlling for contiguity.

There is another kind of direct test of Null Hypothesis 3, but this time using curvilinear regression. If the null hypothesis is correct, we should find anywhere from a horizontal line fitting a plot of violence against joint political freedom or freedom to a curve of decreasing violence with decreasing joint political freedom or freedom. The best regression curves among the linear, logarithmic, power, and exponential types are shown in Figure 2 and Figure 3. For political freedom and freedom these curves are:

y = 28.9e^.014x₁

R² = .28 p <.6 x 10^-11, one-tailed

y = 31.3e^.005x₂

R² = .21 p <.6 x 10^-7, one-tailed

where

y = violence score on the Conflict Scale of Figure 1

x₁ = joint dyadic political freedom score

x₂ = joint dyadic freedom score

R² = coefficient of determination

N = 121 (see Note 16)

For both political freedom and freedom these are growth curves that cross the violence threshold beyond the region of jointly free dyads and curve upward in violence as the dyad's joint freedom declines. This contradicts Null Hypothesis 3, and, judging by the R², very significantly so. Therefore, for this kind of test also, alternative Hypothesis 3 must be accepted.

So far, only the central tendency of violence, which was found to lie along the above curves, has been tested. However, if Hypothesis 3 is correct, we would also expect that the peak violence would increase with decreasing political freedom or freedom scores. Since the curvilinear test for the central tendency was based on minimizing the squared deviations from the curve (i.e., least squares regression analysis), it is possible for the peak violence (defined by the top points in the plots, as shown in Figure 2 and Figure 3) to remain the same or even decrease with decreasing libertarianism, inconsistent with Hypothesis 3. Were either to occur it would question the hypothesis, regardless of the central tendency. Therefore, a regression analysis was done on the highest level of violence reached for each scale value of political freedom (N = 19) and for transformed scale values¹⁷ of freedom (N = 20).¹⁸ The reason for the transformation, which uses the highest violence on adjacent scale values, is that the freedom scale is twice that for political freedom, and I want to make the two regressions comparable.

The best-fitting regression curves (among linear, logarithmic, power, and exponential) for these maximum intensity data are these:

y = 25.97e^.025x₁

R² = .85 p <.2 x 10^-7, one-tailed

y = 18.3e^.3x₂

R² = .53 p <.0002, one-tailed

where

y = maximum violence (Conflict Scale value of Figure 1) reached by any dyad

x₁ = joint dyadic political freedom score

x₂ = joint dyadic freedom score

N₁ = 19

N₂ = 20

Both curves are plotted in Figure 4. Note that these curves are of different types. The one for political freedom is a growth curve, with the maximum violence between states curving upward as their joint political freedom decreases; the other is a power curve, which has its greatest slope upward in maximum violence between states when they are partially free. Because of the jump in magnitudes of violence in the middle ranges of freedom, the curve crosses the violence threshold just within the region of jointly free dyads in spite of their having no violence. Moreover, the difference between these curves shows that the decrease in civil liberties and political rights increases the intensity of violence most when they are all but eliminated. But the added decrease in economic freedom increases the intensity of violence most at the early or middle stages--that is, when free market economies become mixed socialist or statist. In sum, since both curves contradict Null Hypothesis 3 with high statistical significance, it must be rejected.

As with Hypotheses 1 and 2, there are several indirect tests that also can be made--these get more at the implications of the underlying theory and the sense of Hypothesis 3 than at its operational meaning.

If the ² tests of Table 14 are recomputed for a contingency table with the number of cases of no war and war cross-tabulated for nation types, the contingencies are in the proper direction and with a ² of 26.09 [86.38], significant for both political freedom and freedom at p <.00005 (one-tailed). And freedom does significantly better (at p <.3 + 10 ¹⁰, one-tailed). That is, the implication that the inverse relationship between libertarianism and violence should also hold for even extreme violence--war--is strongly supported.

There is also the theoretical implication that violence between states will be higher the less they are libertarian, even relative to their overall conflict behavior. That is, nonlibertarian states should have higher violence even in proportion to their conflict behavior. If nonviolent conflict behavior and violence are separately cross-tabulated against the nation types, the ² results are 39.66 [29.02], both significant in the correct direction for political freedom and freedom at p <.00002 (one-tailed).

Earlier in this section, the curves of violence were found to fit Hypothesis 3. By theory, we should also expect a curvilinear regression to do equally well for the maximum conflict behavior, whether violent or not. By only specifying violence, Hypothesis 3 allows for the empirical possibility that it may well fit the maximum violence, when violence occurs. However, for many joint political freedom or freedom .scores there may not be any violence at all, and if this lack of violence is at the nonlibertarian end, it is contrary to theory. Accordingly, curves were fitted to the Maximum Conflict Scale Value (of Figure 1) per political freedom, or freedom, score. The results are shown in Figure 6 and Figure 7, where for comparability, the transformed scores are used for freedom (see Note 17). Their equations are:

y = -26.2 + 23.2nx₁

R² = .87 p <.5 x 10^-11, one-tailed

y = -26.7 + 24.1nx₂

R² = .83 p <.5 x 10^-9, one-tailed

where

y = score on the Conflict Scale of Figure 1

x₁ =joint dyadic political freedom score

x₂ = joint dyadic freedom score

n = natural logarithm

N = 25

As should be expected, the maximum conflict behavior per political freedom or freedom score is well represented by continually rising curves, logarithmic in each case. This is shown by the coefficients of determination R², both of which are highly significant. Freedom, however, is not a significantly better fit than political freedom. But when the results get this good (accounting for at least 83% of the variance), even greater significant improvement becomes very difficult.

Nonetheless, as theory predicts, when the curves of Figure 6 and Figure 7 are overlayed, as shown in Figure 5 the freedom curve is higher. That is, for the same political freedom and (transformed) freedom score, freedom predicts to a higher level of violence.

All this aside, the plots and shape of the curves in Figure 6 and Figure 7 in the region of those dyads involving libertarian states sum up the theory underlying Hypothesis 1 and Hypothesis 3. Clearly, freedom makes a critical difference in conflict behavior and marks a fundamental threshold between violence and nonviolence. Note especially that the greatest increase in the maximum conflict behavior along the curves happens when freedom is beginning to be lost, and the maximum violence occurs when both members of a dyad are no longer free at all.¹⁹

Contiguity is not an intervening variable: Contiguous or not, libertarian states do not exert violence on each other; and whether having common borders or not, the less freedom in states, the more violence between them.

Whether libertarian is defined by political freedom or freedom, the data are highly supportive of the propositions. However, while economic freedom does not significantly detract from the Joint Freedom Proposition, it is clearly important for the Freedom one. To add economic freedom to civil liberties and political rights is to reduce significantly the level of violence for a state overall, or between particular states. For the Freedom Proposition, the libertarian's (or classical liberal's) faith in the peaceful effects of economic freedom appears" according to these data, well justified.

The best check against normative bias involves two stages. One is presenting clear and precise data and methods, using systematic and objective techniques, and making tests and conclusions intersubjectively verifiable. The second is even more important. It is the actual attempt to refute through reanalysis or new data what one believes to be biased or wrong. It is, in short, through the dialectical process of presenting controversial results and the attempts at their public refutation that we check bias.

(2) The sample is too limited, and does not include the period when democracies were heavily involved in war, such as the Suez or Vietnam War periods. First, in including all violence for five years, the sample is hardly limited. Second, other samples were drawn on, such as of all wars between 1816 and 1974, and all threats or actual use of force between 1945 and 1965, which all show the same lack of violence or wars between democracies. Third, such wars as Vietnam are irrelevant to the Joint Freedom Proposition, for that is a case of a libertarian state versus a nonlibertarian one. In any case, one must make one's tests with one sample at a time. The real question is whether this sample is important and these tests well done.

(3) Violence is misconstrued. This study severely neglects the violence of the rich or imperialist nations against the poor, or what is called "structural violence." "Violence" as physically attacking the life, limb, and property of others is the consensual meaning in both field and libertarian theory. This criticism would really want to use another theory and meaning, one based on a socialist and equalitarian perspective. Fine. But then the onus is the critic's to show that the concept of "structural violence" will yield better results, in some sense, than the one given here.²¹

(4) The theory is too sketchy--its logic and properties need detailing, especially regarding economic freedom. I agree, but the purpose here is to test the two propositions and not to present the theory that I have elaborated elsewhere in greater detail (e.g., Vol. 4: War, Power, Peace).

With regard to economic freedom, the basic idea is that intervention of centralized, coercive power--government--into a social field has certain social effects, among which is an increase in the polarization of interests (forces) and a reduction of cross-pressures. By theory and holding other things constant, this should increase the level of violence in the social field (Vol. 2: The Conflict Helix: Part VIII) and decrease inhibitions in the foreign policy behavior of the elite. That mixed capitalist-socialist democratic systems like Sweden or Denmark, therefore, should be more violent than the United States or West Germany may strike some as silly. But then among the mixed democracies are also Israel, the United Kingdom, and Portugal; and also among the capitalist are Iceland, Switzerland, and New Zealand. For these two groups the claim that the former should and does have more violence is not at all strange. All this says, of course, is that the theory should not be left to socialist or liberal predispositions, but must be tested systematically. And this I have tried to do here.

(5) But you still should have carried out a sensitivity analysis. What would be the result if say, Sweden's freedom values were changed from partially free to free? Ordinarily, I think it methodologically unwise to change the values of a case alone in a sensitivity study, for then it is not clear what unique or common aspects of a case are causing the resulting effects. A better approach is to vary uniformly a variable or group of cases based on some theoretical or hypothetical principle. Here, I have in fact done this. For although mixed capitalist-socialist democracies like Sweden, Denmark, and Norway are coded partially libertarian on the freedom scale (and these are the cases that I believe will most bother some readers), their values are all changed to libertarian for the political freedom scale. That is, on the principle that political and civil rights completely dominate economic freedom, Sweden, Norway, and others are treated as free. Thus we have the two sets of results for political freedom and freedom, where those for political freedom in comparison to freedom can be considered methodologically a sensitivity analysis of the role of economic freedom.

(6) Contiguity should have been measured on a many-valued scale to take account of the impact of near contiguity. Perhaps, but I do not believe the scale will make much difference. Politically, the threshold condition is a common border; lack of such contiguity is, however scaled, of a different order. In other words, scaling contiguity should only marginally, if at all, alter the present results.

(7) Statistical tests were done without a well-defined sample, in a sample survey sense. The population is of interstate, dyadic violence, anywhere, anytime. The sample is of all such violence between 1976 and 1980 and was selected randomly with regard to the hypothesis. It is arguable whether this sample represents well the relevant characteristics of the historical population, but the working assumption is that it does.

Clearly, more samples must be taken and much more work be done before this question can be shelved; however, recall that other and larger samples of war and violence were used also.

But there is another answer. The statistical tests also assess whether for the given sample the particular combination of results (i.e., no violence falling among libertarian dyads) could occur by chance. And if the critic does not like my answer about sampling, he should nonetheless accept the statistical tests as valid on these second (not secondary) grounds.

(8) The variance in violence that libertarianism explains is low (see Figure 2 and Figure 3). Therefore, while the results are statistically significant, they are for practical purposes insignificant. True, the variance explained is low in some cases (but note also the high variance for the functions fitting the highest magnitudes of violence), but explaining variance is not the essence of this study. It is determining whether the prediction of no violence, or of decreasing violence with increasing libertarianism, holds true, and if so, whether this result could be due to chance. As to practical significance, the policy importance of establishing the credibility of these propositions should be obvious.

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