This article shows how fair voting methods can be a catalyst for change in the way we make collective decisions, and how such change can promote long-awaited upgrades of democracy. Based on real-world evidence from democratic innovations in participatory budgeting, in Switzerland and beyond, I highlight a trilogy of key research results: Fair voting methods achieve to be (i) legitimacy incubator, (ii) novel impact accelerator and (iii) safeguard for risks of artificial intelligence (AI). Compared to majoritarian voting methods, combining expressive ballot formats (e.g. cumulative voting) with ballot aggregation methods that promote proportional representation (e.g. equal shares) results in more winners and higher (geographical) representation of citizens. Such fair voting methods are preferred and found fairer even by voters who do not win, while promoting stronger democratic values for citizens such as altruism and compromise. They also result in new resourceful ideas to put for voting, which are cost-effective and win, especially in areas of welfare, education and culture. Strikingly, fair voting methods are also more resilient to biases and inconsistencies of generative AI in emerging scenarios of AI voting assistance or AI representation of voters who would be likely to abstain. I also review the relevance of such upgrades for democracies in crisis, such as the one of Greece featured in the recent study of `Unmute Democracy'. Greek democracy can build stronger resilience via higher representation of citizens in democratic processes as well as democratic innovations in participation. Fair voting methods can be a catalyst for both endeavors.