Constitutional democracy can be modeled as a complex game involving two general stages of political decision making. One stage (sometimes labeled the constitutional phase or higher track) is a cooperative game in which moral (i.e., rational and fair-minded) players jointly agree to promote their common good by unanimously accepting a (written or unwritten) constitutional code. The code typically sets out fundamental political institutions (including legislative procedures, modes of election and appointment, amendment processes, and the like), delineates a system of checks and balances (though not necessarily one that undergirds an American-style separation of powers), and lists some basic rights of the people. Unanimous consent to some such constitution is effectively guaranteed through suitable definition of what it means to be a moral agent. For example, it might be supposed that, for this higher track of politics, any moral agent is an expected utility maximizer who imagines himself in a hypothetical position (or state of nature) behind a veil of ignorance, where he is uncertain as to his actual position in society and thus assigns equal probabilities to occupying each of the possible positions. Given these assumptions, moral agents will consent to a utilitarian constitution whose rules of conduct maximize the general welfare.

The second stage (also called the postconstitutional phase or lower track) is a noncooperative game in which the veil of ignorance is lifted and each moral player freely pursues his particularistic interests in competition with other people under the constitutional rules chosen at the first stage.