Democracy is perhaps the best form of government known to the human kind, but it is in serious trouble these days. Various approaches are taken to try to help democracy; I will speak about recent advances in the analysis of algorithms that enable, e.g., to replace existing representative democracies with direct, participatory decision making mechanisms. As concrete examples, I will review recent techniques for writing laws and constitutions in a collaborative way and mechanisms for participatory budgeting, in which the distribution of mutual funds is decided in a democratic way. To make this dream come true, I would argue that societies shall utilize techniques such as liquid democracy, which uses online social networks to shift representative democracy closer to direct democracy, as well as other ideas and tools developed by the artificial intelligence research community.