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The electoral formulas to choose presidents differ in the degree they restrict the number of parties competing in presidential elections. While simple plurality rule tends toward two-party competitions, qualified plurality and majority rule tends toward multi-party contests for the presidency. This article argues that the bargaining power and the electoral expectations of the political actors with control over constitutional design explain the choice of these rules. Using this analytic framework, the article shows that the recent shift in Latin America from plurality to more-than-plurality rules of presidential elections reflects the risk-averse choice of multiparty assemblies and military rulers. The explanation is supported with data on 35 cases of major constitutional reforms in 18 countries of Latin America and with the study of the most recent reforms in Colombia, Venezuela, and Argentina. [ABSTRACT FROM AUTHOR]