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Master of the Game: Henry Kissinger and the Art of Middle East Diplomacy, by Martin Indyk. New York: Knopf, 2021. 633 pages. $35.

The pure realist picture of world politics combines the demand for power with the problem of cooperation. In a more up-to-date, less austere variant, power is no unqualified asset: a state can profit from a unilateral loss of power, all else equal. And mutual cooperation is often achievable, thanks in great measure to the shadow of the future. My newer, richer variant enlarges and combines those two features of anarchy: sometimes a loss of power by a single state not only is advantageous to that state but enhances mutual cooperation, and when that happens the motives to cooperate—which turn out to be quite varied—only have to work in a one-sided way.

The widespread use in legislative studies of the one-dimensional model and its median-stability consequence raises a question: Do stability and one-dimensionality rest on evidence drawn from observed votes? They do not and cannot. I prove that every possible legislative history is compatible with a transitive majority preference (hence stability), and except in very special circumstances with a cyclic majority preference (hence instability) as well: observed votes can never refute and almost never confirm stability. One-dimensionality fares worse: any legislative history is compatible with the one-dimensional model if it includes no two votes with overlapping pairs of alternatives, but otherwise, I show, it is almost certainly incompatible with the model, even in those rare cases that ensure transitivity. Voting evidence aside, the one-dimensional model is unduly restrictive, and arguments in its defense do not survive scrutiny. Adapted from the source document.