Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they “fall back” on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the players common to them, or kingmakers, determine which fallback coalition will form. The first player(s) acceptable to all other members of a fallback coalition are the leader(s) of that coalition. The effects of different preference assumptions—particularly, different kinds of single-peakedness—on the number of coherent coalitions, their connectedness, and which players become kingmakers and leaders are investigated. The fallback procedure may be used (i) empirically to identify kingmakers and leaders or (ii) normatively to select them. We illustrate the model using data from the U.S. Supreme Court, 2005–2009.