Forming stable coalitions: The process matters

Players are assumed to rank each other as coalition partners. Two processes of coalition formation are defined and illustrated:

• Fallback (FB): Players seek coalition partners by descending lower and lower in their preference rankings until some majority coalition, all of whose members consider each other mutually acceptable, forms.
• Build-up (BU): Same descent as FB, except only majorities whose members rank each other highest form coalitions.

BU coalitions are stable in the sense that no member would prefer to be in another coalition, whereas FB coalitions, whose members need not rank each other highest, may not be stable. BU coalitions are bimodally distributed in a random society, with peaks around simple majority and unanimity; the distributions of majorities in the US Supreme Court and in the US House of Representatives follow this pattern. The dynamics of real-life coalition-formation processes are illustrated by two Supreme Court cases.