Deliberative democracy is a project that has strong normative implications for constitutional design, but its procedural nature leads to preoccupations about how fundamental rights might be ensured. Rawlsian perspectives highlight the importance of core principles that deliberation cannot override, while Habermas defends that an optimal procedure leads to an endogenous observation of minorities rights. In this paper, I present a game-theoretical model to analyze whether variations in the costs for deliberation and heterogeneity in society might cause welfare enhancements. If there are no minorities – all groups have the same probability of being non-majoritarian in an important issue – lower costs of deliberation always increase social welfare. Nonetheless, if there are minority groups, it is not possible to ensure they will not suffer from distortions in the deliberation process led by elites unless costly Rawlsian consensus rules are enacted.