Coalitionwise Electoral Inversions in Brazil’s Chamber of Deputies (1998–2022)

This paper studies coalitionwise electoral inversions in Brazil’s Chamber of Deputies under open-list PR, where apportionment constraints and integer seat allocation can generate representation reversals at the coalition level. I assemble and standardize federal deputy election data for 1998–2022 and implement a processing pipeline that produces party vote shares, seat shares, quotas, and seat differentials. Using these quantities, I identify inversion candidates via coalition diagnostics grounded in the Miller/Kurrild-Klitgaard framework and map how inversion risk concentrates across parties and blocs. I then evaluate inversion patterns within two substantively meaningful coalition families: (i) observed ministerial coalitions derived from cabinet composition over time, and (ii) ideologically admissible coalitions defined by established party-bloc classifications. This structure distinguishes arithmetically possible reversals from politically plausible alternatives and from realized governing arrangements, and clarifies the contribution of federal apportionment to coalition-level distortions in representation.