Fixed-Composition Legislative Systems with Cross-Validation and Mutual Deterrence: A Mechanism Design Approach to Constitutional Engineering and Coalition Stability

Contemporary multiparty democracies frequently suffer from two symmetrical institutional pathologies: legislative hyper-fragmentation driven by open-list personalistic incentives, and executive governability crises that necessitate costly post-electoral coalition bargaining via ministerial patronage and budgetary side-payments. Conversely, purely majoritarian or closed-list reforms often suppress ideological diversity, insulate party oligarchies, and exacerbate affective polarization. Drawing on mechanism design, spatial voting theory, and cooperative game theory, this paper introduces the Fixed-Composition System with Cross-Validation and Mutual Deterrence. The proposed constitutional architecture partitions a 513-seat legislature into four fixed functional roles: a Government Block (S_G = 257 seats, 50.1%), an Official Opposition Block (Sₒ = 206 seats, 40.2%), and two orthogonal Neutral Arbitration Blocks (S_N₁ = 25 and S_N₂ = 25 seats, 9.8% combined), with members of the opposition and neutral blocks constitutionally barred from holding executive branch offices. Crucially, the seats of the Chamber of Deputies are apportioned directly from the same unified ballot vector that elects the Head of the Executive, preventing a segregated tally between the Executive and the Legislature and ensuring macroeconomic and institutional State stability. Party eligibility and coalition stacking are governed exogenously by an empirical spatial alignment index Iₚ ∈ [-1, +1] derived from weighted roll-call voting records over two legislative terms, enforcing a presumed federalization rule for parties exhibiting at least 85% legislative convergence (ΔI ≤ 0.30). On the ballot, each voter submits a four-row vector allocating parties to the four constitutional blocks (Screen 1) and gains the cross-validation right to reorder candidates within the closed lists of those selected parties (Screen 2). By computing intra-block seat shares symmetrically across the primary government and opposition preference rows (L₁ + L₂), the mechanism transforms strategic voting from an instability factor (as in the Gibbard-Satterthwaite framework) into an incentive-compatible Mutual Deterrence Nash Equilibrium that systematically rewards moderate parties and candidates. We demonstrate the mathematical properties of the model through a full numerical simulation of the Brazilian Chamber of Deputies and examine its broader institutional extensibility to intra-party governance in one-party socialist states.