A political formula is the justification for political power. The classic example is divine right monarchy, where the king is said to rule due to be chosen by God. Democracy's political formula is consent of the governed.
Due to the iron law of oligarchy, any ruling group is a small minority. The majority must make peace with this fact somehow, and the political formula is the tool the oligarchy uses to allow this. The formula allows the subject to believe that the easy route, obedience, is doing the right thing. It addresses the pride of the adult male, allowing them to believe it is not cowardly submission, but rational assent that drives their obedience. It provides a Schelling point. It pacifies the rebellious subject by making them doubt the justification of their rebellion. It appears to provide a test whereby legitimacy of a regime can be checked.
Coercion is defection. The political formula is a justification for why this defection is nevertheless prosocial. A king is licensed by God to defect on the citizen. A democratic regime claims it is not really defecting - that the rules were in fact consented to by the populace.
The idea of the formula is accredited to Gaetano Mosca.
I was dissatisfied with all major search engines' offerings for the term political formula, hence this piece.
Some discussion, necessarily biased by my own conclusions, but regardless useful for illustration of the concept and its uses:
Using the idea of a concrete political formula, we can do transformations to search for equivalences. Democracy is, precisely, not the consent of the governed but consent of the majority governed.  There is a particular mob of citizens whose will is supposed to be carried out on any particular issue. Thus, we have something very similar to the divine right of kings - we have the divine right of mobs. Vox populi, vox dei, after all. If the divine right of kings is illegitimate, it would seem, rationally, that the divine right of mobs is also illegitimate. Or, conversely, both can be legitimate - if God says so. Why don't we ask Him?
In practice, citizens understand the legitimacy test in a degenerate form. Democracy is supposed to provide consent, because a suitable mob may withdraw their consent at the voting booth. However, citizens do not check whether their consent can be meaningfully withdrawn - it would be dangerous and responsibility-invoking if they found it could not, after all. Instead, they convert [consent of the governed] to [can I vote]. Regardless, it is difficult to impossible to determine how many, if any, other citizens in fact consented.
 In modern times, includes certain so-called fundamental rights which supposedly supercede democracy and are not subject to the will of the governed. It almost included the right to property, but they noticed this would prevent them from doing any actual coercion.