Structural theories of international peace among democratic regimes have relied on two distinct explanatory logics: democratic institutions may cause a state's foreign policy to tend toward peace by exposing policymaking elites to pressure from ordinary citizens (the popular logic) or to pressure from other governmental agencies (the elite logic). These logics are often conflated in scholarly studies of war and peace, but we attempt to isolate the popular logic for empirical testing by developing a novel measure of institutionalized popular influence, the Institutional Democracy Index (IDI). Whereas previous usage of the Polity index to operationalize democratic structures has succeeded in testing the elite logic more than the popular logic, we use the IDI to analyze long-established democracies' involvement in international conflict between 1961 and 2001. What we find are significant differences within the family of democratic regimes that point to a monadic structural explanation of peace: more popular democracies are less warlike with respect to all other regimes, not just other democracies. By capturing variance among democratic regimes in their structures of inclusion (especially formal rules pertaining to voter access, electoral formulae, and cameral structures), the IDI enables us to observe crucial differences between the conflict propensities of more popular and more elite types of democracy.