Examples aren’t hard to come by. Shiites seek revenge on Sunnis for the revenge they sought on Shiites; Irish Catholics retaliate against the Protestants who retaliated against them; and since 1948, it’s hard to think of any partisan in the Middle East who has done anything but play defense. In each of these instances, people on one side claim that they are merely responding to provocation and dismiss the other side’s identical claim as disingenuous spin. But research suggests that these claims reflect genuinely different perceptions of the same bloody conversation.

If the first principle of legitimate punching is that punches must be even-numbered, the second principle is that an even-numbered punch may be no more forceful than the odd-numbered punch that preceded it. Legitimate retribution is meant to restore balance, and thus an eye for an eye is fair, but an eye for an eyelash is not. When the European Union condemned Israel for bombing Lebanon in retaliation for the kidnapping of two Israeli soldiers, it did not question Israel’s right to respond, but rather, its “disproportionate use of force.” It is O.K. to hit back, just not too hard.

Research shows that people have as much trouble applying the second principle as the first. In a study conducted by Sukhwinder Shergill and colleagues at University College London, pairs of volunteers were hooked up to a mechanical device that allowed each of them to exert pressure on the other volunteer’s fingers.

The researcher began the game by exerting a fixed amount of pressure on the first volunteer’s finger. The first volunteer was then asked to exert precisely the same amount of pressure on the second volunteer’s finger. The second volunteer was then asked to exert the same amount of pressure on the first volunteer’s finger. And so on. The two volunteers took turns applying equal amounts of pressure to each other’s fingers while the researchers measured the actual amount of pressure they applied.

The results were striking. Although volunteers tried to respond to each other’s touches with equal force, they typically responded with about 40 percent more force than they had just experienced. Each time a volunteer was touched, he touched back harder, which led the other volunteer to touch back even harder. What began as a game of soft touches quickly became a game of moderate pokes and then hard prods, even though both volunteers were doing their level best to respond in kind.

Each volunteer was convinced that he was responding with equal force and that for some reason the other volunteer was escalating. Neither realized that the escalation was the natural byproduct of a neurological quirk that causes the pain we receive to seem more painful than the pain we produce, so we usually give more pain than we have received.