Democracy is defined by two core tenets: voice and pluralism. Within these constraints, a wide variety of regime types can be designed. We show that the only new, untested form of democracy is when every citizen is governed by the political party of his/her choice. Multiple full-edged governments would coexist in the same national territory at the same time, each one sovereign only over the people who chose to vote for it - hence the name: Choice Democracy. Choice Democracy can be regarded as pure polyarchy, the broadest form of political competition, and a robust mechanism for disciplining government agencies. We argue that this system makes democracy more stable by reducing the risk of revolutionary and financial crises. We develop a theory for the optimal number of governments per countries, where the answer is determined by a trade-off between cooperation and competition. We also provide evidence indicating that Choice Democracy would be viable in the real world.