In a connected world where people influence each other, what can cause a globalized monoculture, and which measures help to preserve the coexistence of cultures? Previous research has shown that factors such as homophily, population size, geography, mass media, and type of social influence play important roles. In the present paper, we investigate for the first time the impact that institutions have on cultural diversity. In our first three studies, we extend existing agent-based models and explore the effects of institutional influence and agent loyalty. We find that higher institutional influence increases cultural diversity, while individuals' loyalty to their institutions has a small, preserving effect. In three further studies, we test how bottom-up and top-down processes of institutional influence impact our model. We find that bottom-up democratic practices, such as referenda, tend to produce convergence towards homogeneity, while top-down information dissemination practices, such as propaganda, further increase diversity. In our last model – an integration of bottom-up and top-down processes into a feedback loop of information – we found that when democratic processes are rare, the effects of propaganda are amplified, i.e. more diversity emerges; however, when democratic processes are common, they are able to neutralize or even reverse this propaganda effect. Importantly, our models allow for control over the full spectrum of diversity, so that a manipulation of our variables can result in preferred levels of diversity, which will be useful for the study of other factors in the future. We discuss possible mechanisms behind our results, possible applications, and implications for political and social sciences.