In its crudest form, geopolitics is a zero-sum game. The United States recognizes mainland China and breaks official ties with Taiwan; Washington leans toward Karachi and away from New Delhi. A gain along one axis is offset by a loss along a second. But diplomacy is usually too complex an amalgam of relationships to evaluate so starkly on a balance sheet, and there are often opportunities for simultaneous improvements between mutually antagonistic countries. Take, for example, the surprising improvement in U.S. relations with both China and Taiwan over the past three years. Alas, the flip side to win-win diplomacy is lose-lose diplomacy. Since 2000, when U.S. relations with both halves of the Korean Peninsula seemed to be on the upswing, Washington has managed to unravel its incipient relationship with Pyongyang while tangling its ties with Seoul.

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