The theory operates on two fundamental groups, the Winning Coalition and the Selectorate, both drawn from the overall populace of a state. The Winning Coalition is a subset of the Selectorate, and the Selectorate is a subset of the overall population. The Selectorate is simply those within the state that have a say in policy outcome (in the United States, for example, it would be all citizens over the age of 18 eligible to vote). The Winning Coalition is a portion of the Selectorate sufficient to choose and sustain a leader in office.
It can be said, then, that everyone in the Selectorate (including the Winning Coalition) reap the benefits of public goods while only those within the Winning Coalition enjoy private goods.
In a monarchy, where the Selectorate is small and the Winning Coalition is even smaller, provides the challenger with a greater opportunity to overthrow the current leader. This is because the proportion of Selectorate members who are also in the Winning Coalition is relatively large. That is to say if a new leader comes to power, chances are a given member of the Winning Coalition will remain within the coalition. The incentive for defection in order to attain a greater amount of goods offered by a challenger is not, in this case, outweighed by the risk of not being included in the new Winning Coalition. Here, the proportion of private goods in relation to public goods is seen declining.
A scenario where both the Winning Coalition is large and the Selectorate is even larger provides the least amount of stability to a leader’s occupancy of power (such a system is a Democracy). Here, the proportion of public goods outweigh private goods simply because of the sheer size of the Winning Coalition; it would be far too costly to provide private goods to every individual member of the Winning Coalition when the benefits of public goods would be enjoyed by all. Because of this fact—that the leader cannot convince Winning Coalition members to remain loyal through private good incentives (which are in turn cost-restrictive)—the challenger poses the greatest threat to the incumbent. Furthermore, this degree of loyalty to the incumbent leader—whatever the government structure may be—is called the Loyalty Norm.
A scenario where the Winning Coalition is large and the Selectorate is small is logically impossible since the Winning Coalition is a subset of the Selectorate.
Bueno de Mesquita, Bruce; Smith, Alastair; Siverson, Randolph M.; and Morrow, James D. The Logic of Political Survival.(Book review)
Sep 22, 2006; Bueno de Mesquita, Bruce; Smith, Alastair; Siverson, Randolph M.; and Morrow, James D. The Logic of Political Survival....