Simulating Electoral Systems: from open-list to single-member districts in Brazil

Open-list electoral systems provide a complete rank ordering of all candidates-parties in a race covering a large area. Thus, we can observe a complete rank ordering of candidates-parties for any sub-area of that race. This allows us to simulate a single-member majoritarian electoral system based on the preferences revealed by an open-list proportional system with relative easy. We simulate the 2022 election in the Brazilian state of São Paulo. We simulate thousands of counterfactual intra-state constituency boundaries based on existing legal boundaries. For each simulated constituency map we compute the district winner by four different methods. The non-ideological rank method produces results that have a similar ideological breadth as the open-list system. The party aggregation method delivers a two-party system. The Left-Right aggregation method produces complete dominance by right-wing parties. The Left-CenterRight-Right aggregation does not identify a clear third party, suggesting instability.