Ceteris paribus majority for social ranking

We study the problem of finding a social ranking over individuals given a ranking over coalitions formed by them. We investigate the use of a ceteris paribus majority principle as a social ranking solution inspired from the classical axioms of social choice theory. Faced with a Condorcet-like paradox, we analyze the consequences of restricting the domain according to an adapted version of single-peakedness. We conclude with a discussion on different interpretations of incompleteness of the ranking over coalitions and its exploitation for defining new social rankings, providing a new rule as an example.