Results

Main Specifications

We estimated two sets of models for all pairs of states for every year over the 1900 to 2010 period with the democratic peace hypothesis represented as the democracy score(s) of the stronger country, that of the weaker country, the interaction of these two, and several control variables. In the first set of models, we entered the five indicators of constraint one by one along with our control variables. Figure 3 summarizes the results from these models. Complete estimation results in table form with all control variables are found in Table SF-3.

The first model (called electoral accountability) enters the electoral accountability index scores of both members of the dyad and their interaction along with control variables. The estimates from this model are printed in black color at the top of the figure. The points represent the estimates and the whiskers their 95% confidence interval. The two main terms are both positive, although for the weaker country it is not statistically significant. The interaction between the index values for the two countries in the dyad, on the other hand, is negative and highly significant—when both countries score highly in terms of electoral accountability, the risk of a fatal dispute is much lower than if either have low scores. In line with expectations, we show in Table SF-6 that the effect of electoral democracy is driven by the “Schumpeterian” core dimensions tapping into contestation—whereas suffrage does not play an independent role in promoting peace.

The second model enters the horizontal accountability terms. The third model adds the social accountability variables to the controls. In both of these models, the interaction terms are negative and significant, whereas the main terms are positive and significant. Each of the three sets of individual indices are related similarly to interstate peace.

Figure 4 shows that the net effect for each of these indicators is consistent with the democratic peace. In the left panels, the dashed line plots the estimated log odds of a MID when the weaker country j is at the mean of the index, as a function of the score for the stronger country (along the x-axis). The metric for the y-axis is log odds relative to the case where both countries have scores of 0 for the index. The dotted and solid lines show the same when the index is one standard deviation below or above the mean.17

The graph on the right plots the marginal effect of this relationship—it shows the change in the estimated probability of a fatal dispute when comparing a pair of countries where the weaker country has a value for the index one standard deviation below the mean and one standard deviation above, respectively, as a function of the index for the stronger country. Both these graphs show a clear dyadic democratic peace in terms of all our indices of constraint—a more democratic weaker country means a clearly lower risk of fatal MID if the stronger country is relatively democratic.18

All of our individual indicators of constraint reflect the democratic peace when entered on their own. Given the high correlation between them, we investigate their relative impact in two different ways. The first is to estimate models with all the individual terms entered simultaneously. In Figure 5, we show the results of a “joint constraint model” that contains all terms.19 The electoral accountability index terms are not distinguishable from zero in this model. It should be noted that this result cannot be explained by multicollinearity, since the variance inflation factor is not particularly higher for this index or its interaction effect.20 The horizontal accountability variables, on the other hand, retain separate contributions to the democratic peace. The interaction term is negative and significant. The variable that retains the most of its impact on the probability of a fatal dispute is the social accountability index. The democratic peace seems to rest in particular on horizontal constraints on the executive and the presence of strong and active CSOs.

The second route is to compare the models in terms of their overall fit to the data. A set of different metrics is reported in Table 2 for the six models reported in Figures 3 and 5 as well as some additional models in Table SF-9. The Akaike information criterion (AIC) values for each model discussed so far are reported in the “AICfull” column. The civil society model has the lowest AIC values, indicating as above that this variable provides the best fit within the estimation sample. The table also reports how well the different models do in terms of out-of-sample predictive performance.21 To obtain these estimates, we first reduced the size of our data set by removing at random 95% of all the non-MID dyad years.22 We then drew half of all dyads at random, estimated the models on this partition, obtained predictions for the nonestimation partition, and compared with the actual record of fatal MIDs for the nonestimation partition. We repeated this for twenty independently sampled divisions of the sample. The “AICds” column in Table 2 shows the average (in-sample) AICs for the twenty reduced-sample estimations. The “AUROC” and “Brier” columns show the area under the receiver operator curve and the Brier scores averaged over the twenty out-of-sample partitions. Models that predict well out of sample have high scores on the AUROC and low Brier scores. The two statistics indicate similar rankings of the models.

Table 2. Model Summary Statistics.

The out-of-sample evaluation of predictive performance further strengthens the impression that the electoral accountability mechanism is weaker than the other two. The AUROC is lower and the Brier is higher for this model than for the other models. The horizontal and social accountability models perform the best. The model including all the three indicators performs considerably better than the three models in Figure 3 across all metrics, suggesting that the conclusions drawn from Figure 5 are still valid.

Figure 6 illustrates the implications of the joint constraint model compared to the electoral accountability only model for selected dyads in 2010. For each pair of countries, we calculated the extent to which “joint democraticness” in each alters the risk (measured as log odds) of conflict in comparison to what is explained by the control variables. We plot the marginal effect of the electoral accountability model along the horizontal axis and that of the joint constraint model along the vertical one. Democratic pairs such as Great Britain and India (IND-GBR) have a low risk of conflict according to both models and are located in the lower left corner.23 Pairs with one democracy and one nondemocracy such as Great Britain and North Korea (GBR-PRK) have a high risk and are found in the upper right. The diagonal line represents the case where the two models yield similar predicted effects.

The figure shows that models that reflect multiple dimensions of accountability give a more nuanced picture of interstate conflict risk. The electoral accountability model indicates that autocracies such as North Korea, Turkmenistan, and Myanmar have equally high risk of conflict with democracies. The joint constraint model distinguish much better between them—the predicted risk of conflict between GBR and North Korea is twice as high as between GBR and Myanmar.24

Our results suggest that the democratic peace rests less on electoral accountability than on horizontal and social constraint. Illiberal democracies, hybrid regimes, and electoral authoritarian regimes such as Turkey and Venezuela in 2010 continue to hold competitive elections but harass CSOs and undermine horizontal constraints on their ambitious executives. The joint constraint model indicates that the pairs of countries they form are more bellicose than the electoral accountability model suggests. Figure 6 shows, for instance, that the electoral accountability index values for Turkey–Venezuela dyad (“TUR-VEN”) translates into a reduced log odds of conflict of .7 relative to what is implied by the control variables. The combined effect of the joint constraint model is to increase log odds by 0.1. The difference in the predictions from the two models is less marked for Venezuela than for Turkey however because V-Dem rates Venezuela as having a much stronger civil society in 2010.

Similarly, a number of weaker at-risk democracies, such as Kenya or Tanzania, despite their low level of vertical electoral accountability should have a lower risk of conflict with other democracies than these two illiberal examples. Pairs of countries including Ghana or Tanzania, for instance, score relatively better on civil society participation than on electoral accountability. Figure 6 shows that these pairs have very low predicted risk of conflict by the joint constraint model but are placed close to the middle by the electoral model.

Our theoretical argument implies that social accountability should contribute to the democratic peace even in political systems where elections are absent or meaningless. However, it also suggests that electoral and social accountability reinforce each other. To explore this, we estimated a model with interaction terms between electoral and social accountability (see Table SF-4 for complete results). This model performs better in terms of in-sample and out-of-sample fit to data than all the other models (Table 2).

Figure 7 shows the interpretation of this interaction model. Both panels show estimated log odds of fatal MID as a function of electoral accountability in the stronger country, with separate lines for low (solid line), medium, and high (dashed line) electoral accountability in the weaker. The democratic peace implies that log odds is lowest when both countries have high accountability. The upper panel shows this relationship when social accountability is low for both countries. In that case, the estimates do not support the hypothesis that joint electoral accountability reduces the risk of conflict. The lower panel, on the other hand, shows the same when social accountability is high in both countries. Under these conditions, there is a clear “electoral peace.” In addition, the figure shows that log odds of conflict is lower overall when social accountability is high.

By implication, the vast expansion of electoral accountability during the twentieth century demonstrated in Figure 2 may have considerably less positive implications for international peace than the steady improvement in all three indices of constraint seen from 1990 onward. Our analysis has important bearings for the “decline of war” thesis (Gat 2006; Pinker 2011; Gleditsch et al. 2013). After the end of the Cold War, the Uppsala Conflict Data Program (UCDP) records a much lower frequency of interstate wars than in preceding decades (Petterson and Eck 2018). Our analysis suggests that the strengthening of civil society participation and executive constraints are important contributors to this trend.25