用公平投票法提升民主，让少数声音被听见。

Voting methods are instrumental design elements of democracies. Citizens use them to express and aggregate their preferences to reach a collective decision. However, voting outcomes can be as sensitive to voting rules as they are to people's voting choices. Despite significance and interdisciplinary scientific progress, several democracies keep relying on outdated voting methods that do not fit modern, pluralistic societies well, while lacking social innovation. Here, we demonstrate how one can upgrade real-world democracies, namely by using alternative preferential voting methods such as cumulative voting and the method of equal shares designed for a proportional representation of voters' preferences. We rigorously evaluate the striking voting outcomes of these fair voting methods in a new participatory budgeting approach applied in the city of Aarau, Switzerland, including past and follow-up evidence. Results show more winning projects with the same budget. They also show broader geographic and preference representation of citizens by the elected projects, in particular for voters who used to be under-represented. We provide causal evidence showing that citizens prefer proportional voting methods, which possess strong legitimacy without the need of very specialized technical explanations. We also reveal strong underlying democratic values exhibited by citizens who support fair voting methods such as altruism and compromise. These findings come with the momentum to unleash a new and long-awaited participation blueprint of how to upgrade democracies globally.