Why is it so hard to get opposing elites to work together rather than to seek partisan gains and/or political survival? While the credible commitment problem is widely known, there are a number of lesser known obstacles to building trust and trustworthiness between opposing elites. This article presents an account of how some of those obstacles interact through time. Common institutional types, particularly winner-takes-all and power-sharing institutions, force trade-offs between agile responses in the short term and medium-term trust between elites, on the one hand, and between trust among elites in the medium term and the adaptability of agreements in the long term, on the other. We call this the ‘time horizon trilemma’. As an alternative approach, we consider a variant on the two-person consulate used by the Roman Republic for more than 400 years as Rome rose to prominence. In our variant, a ‘turn-taking institution’, opposing executives take short alternating turns as the ultimate decisionmaker within one term. We conduct behavioral games in the experimental lab to provide an initial estimate of the impact of these institutional types – winner-takes-all, requiring consensus only, requiring turn-taking only, or requiring both – on overcoming obstacles to agile responses in the short term, trust among elites in the medium term, and adaptability of agreements in the long term. We find that turn-taking is a promising alternative to solving the time horizon trilemma.