This book presents a number of ideas for drawing up new rules to improve the functioning of democracies. The first part examines ways of combining incentive contracts with democratic elections. Such a judicious combination can alleviate a wide range of political failures without impairing the principles on which democracies are founded. The second part presents new rules for decision-making, agendas and agenda settings which can transcend the limitations of prevailing democracies in achieving desirable outcomes. An example is flexible majority rules where the size of the majority depends on the proposal. The book comprises a sequence of simple models and intuitive explanations of the results they yield.