A hidden facet of democratization in the world over the past two centuries has been the increased weight of people's voice in electing presidents. On the basis of new data on all presidential elections in the world since 1789, we show that they evolved from systems in which the final decision was made by someone other than voters, to systems in which the choice of voters was decisive only if it generated a majority, to systems in which the final decision is made by voters. This means that in countries where presidents have executive powers, elections may not be the mechanism by which the people, as a collectivity, always selects its rulers, thus violating the fundamental norm of democracy. We document the history of presidential election rules, offer some tentative explanations, and explore the consequences of particular systems.