The selectorate theory is detailed in The Logic of Political Survival, authored by Bruce Bueno de Mesquita of New York University (NYU), Alastair Smith of NYU, Randolph M. Siverson of UC Davis, and James D. Morrow of the University of Michigan.
In selectorate theory, three groups of people affect leaders. These groups are the nominal selectorate, the real selectorate, and the winning coalition. The nominal selectorate, also referred to as the interchangeables, includes every person who has some say in choosing the leader (for example, in an American presidential election, all registered voters). The real selectorate, also referred to as the influentials, are those who really choose the leaders (for example, in an American presidential election, those people who cast a vote). The winning coalition, also referred to as the essentials, are those whose support translates into victory (for example, in an American presidential election, those voters that get a candidate to 270 Electoral College votes). In other countries, leaders may stay in power with the support of much smaller numbers of people, such as senior figures in the security forces, and business oligarchs, in contemporary Russia.
The fundamental premise in selectorate theory is that the primary goal of a leader is to remain in power. To remain in power, leaders must maintain their winning coalition. When the winning coalition is small, as in autocracies, the leader will tend to use private goods to satisfy the coalition. When the winning coalition is large, as in democracies, the leader will tend to use public goods to satisfy the coalition.
In The Dictator's Handbook, Bueno de Mesquita and Smith state five rules that leaders should use to stay in power: (1) The smaller the winning coalition the fewer people to satisfy to remain in control. (2) Having a large nominal selectorate gives a pool of potential people to replace dissenters in coalition. (3) Maintain control of revenue flows to redistribute to your friends. (4) But only pay friends enough that they will not consider overthrowing you and at the same time little enough so that they depend on you. (5) Don't take your friends' money and redistribute it to the masses.
A public good is one that everyone enjoys non-exclusively such as national defense or clean water. A private good is a good that is enjoyed exclusively by a select few, usually within the winning coalition, and cannot be shared. An example of such a good would be anything exclusionary, such as cash or legal impunity.