Prominent theories of political representation consider ideology to be a central concept that links political elites and citizens. However, studies usually rely on different data and measures to operationalize this concept. This paper presents a two‐step estimation strategy for measuring the ideological positions of parties and population subsets in the party competition space using observational data on Swiss direct democracy. I first use a (dynamic) Bayesian Item‐Response‐Theory model to define the party competition space. Then, I impute this space to segments of the population based on their support for direct democratic proposals. I then show how this yields different results from an existing estimation strategy. Finally, I introduce an R package designed to disseminate publicly available data on direct democracy and the parameters of the party competition space for academic research and teaching purposes.