This paper presents a novel explanation for political alternation in democracies, rooted in the benefit for the median voter of keeping policy from drifting too far to either extreme. Central to this argument is the idea that policy change is gradual and that this gradualism depends on the institutional flexibility/rigidity of the country. Built on this idea, we propose a model of dynamic elections and show that institutional rigidities cause alternation. We also show that, though institutional rigidities prevent governments from implementing extreme policies, they incentivize parties to polarize as much as they can. However, more flexible institutions can foster moderation. Last, we analyze the resilience of equilibrium policies to players’ impatience and discuss extensions of our model, including office-motivated parties, the cost of alternation, alternation every two terms, and asymmetric policies.