Strengthening elements of direct democracy has become a hotly debated issue especially in purely representative democracies where distrust in political institutions and policymakers has been continually growing in recent years. We develop a compensation model of interest groups seeking a majority for their projects by compensating potential losers. Assuming a centre-left government backed by a parliamentary majority, we apply the model to interest groups of varying size and ideology acting in democratic systems with and without faction discipline. With faction discipline in a representative system, direct democracy is comparatively advantageous and efficiency-enhancing if a leftist interest group initiates a project. For rightist project proposals, direct democracy performs better only if the winning group is small; this obeservation that indirect democracy has a comparative efficiency advantage for medium-sized and large winning groups can be seen as a demonstration of OlsonÃÂÃÂ´s encompassing group effect. With faction discipline removed, direct and indirect democracy are generally equivalent. The case in which all members of the governing faction have to be compensated constitutes the only exception for which indirect democracy is superior.