This article attempts to examine the relationship between the most important political institutions and direct democracy in 23 modern OECD democracies by expanding Lijphart’s concept of majoritarian and consensus democracy. The article updates Lijphart’s data collection for the most recent period (1997–2006); it responds to criticisms of Lijphart’s measurement of a number of variables and of case selection, and it integrates direct democracy as an additional variable. Based on factor analysis, the main finding is that there are not just two, but three dimensions of democracy in advanced democracies. The horizontal dimension comprises the disproportionality of the electoral system, the number of parties, the executive–legislative relationship, the interest groups, and the degree of central bank independence. In the vertical dimension of democracy, we find federalism, decentralization, bicameralism, the rigidity of constitutional provisions, and the strength of judicial review. The top-to-bottom dimension of democracy comprises the type of cabinet government and the strength of direct democracy. In contrast to earlier research, our empirical analysis furnishes the hypothesis that direct democracy is not a variable that is independent of all other political institutions. While active direct democracy goes hand-in-hand with broadly supported multi-party governments, purely representative constitutions frequently appear in conjunction with minimal winning cabinets.