The literature on referendums comes to conflicting assessments: for some authors referendums are equivalent to direct democracy, for others, a poor and unfounded substitute. In addition, existing classifications use very diverse criteria, and theoretical models lead to different results depending on whether the underlying assumptions reflect a single- or multi-dimensional policy space: single-dimensional models lead to specific policy predictions, while multidimensional models typically identify paradoxes connected with referendums. We present a multi-dimensional model of referendums that leads to generalizations of the single-dimensional models. This multi-dimensional model makes predictions about how various provisions for referendums affect policy stability and the relationship between voter preferences and policy outcomes. To assess the relevance of these predictions we present information about referendum procedures all around the world on the basis of our model. Linking this information with existing empirical work on the effects of referendums suggests that our theoretical predictions are largely borne out.