<p>The competence of individuals in cooperative activities can be measured through various channels. A football player is sometimes evaluated by their solo-performances, and at other times evaluated by their cooperative performances with other players with related roles. A familiar way to compare two individuals is to consider their performances ceteris paribus—that is, to see what happens if two players are substituted with one another under fixed conditions (the same teammates). However, such substitution does not make sense if the individuals have fundamentally different roles (e.g., an offensive forward and a goalkeeper). Thus, appropriate patterns of comparison can differ from context to context. The present paper formulates such comparison schemes as the set of all pairs of coalitions that are taken into consideration. Two theoretical results are demonstrated. The first is the characterization of majority rule with respect to a particular comparison scheme. The second is the determination of admissible comparison schemes under which the majority rule becomes transitive. These findings provide new insight on the method of comparison itself, showing the necessary information on coalitions to determine the achievement ranking of individuals.</p>