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When it comes to trying to end long-standing conflicts, Barack Obama was off to a good start this week. He had snuffed out the last embers of the Vietnam War by ending a 50-year-old military embargo. He removed the last vestiges of dehumanizing racism from U.S. policy by signing a bill that banishes the word "negro" from the criminal code. And, on top of that, he killed the leader of the Taliban.

Well, someone else, piloting a drone from a military base inside the United States, killed Akhtar Mansour, by firing a laser-guided missile into the Taliban chief's vehicle as it cruised down a northern Pakistan road.

But it was the President's kill. First, because he personally authorized it. By ending the life of an extremist leader who refused to enter into peace talks, he announced, he hoped that the Taliban, after pulling itself together, would come to the table.

Second, because leadership decapitations, as these strikes are known, are Mr. Obama's signature policy. The tightly geared killing of Osama bin Laden was the definitive move by a President who has generally backed away from the full-scale occupations that turned the previous decade into such a catastrophe.

That's the Obama approach: Skip the war and kill the chief bad guy, in hopes that his whole organization will collapse around him. It's an appealing strategy.

Who didn't cheer Mr. bin Laden's demise? A leadership decapitation doesn't sound so bad when its victims are men who are responsible for scores of actual, literal decapitations.

But does it work?

One reason why Mr. Obama's Taliban-termination received hardly more attention than his other acts on Monday is because people increasingly feel like it doesn't. The Taliban appointed another leader, its third. Al-Qaeda has sprung back to life. Some have likened decapitation policies to Whac-a-Mole games: Bash a bad guy, and another one springs up.

Boss-offing is not a mysterious topic: In recent years, an entire science of decapitation analysis has sprung up.

The most influential number-crunching was conducted in 2009 by Jenna Jordan, a researcher at the University of Chicago (she is now at Georgia Tech). She analyzed 298 incidents of "leadership targeting" over six decades and looked at their impact on the organizations whose leaders were the recipients of these abrupt terminations.

Her results were far from encouraging. Her data showed that decapitation, on average, "does not increase the likelihood of organizational collapse beyond a baseline rate of collapse for groups over time."

In fact, the extremist groups most likely to fall apart (that is, to stop being able to commit attacks and wage war) are actually those whose leaders have not been killed: Hitting the head honcho actually seems to help groups keep fighting longer – perhaps because it rather literally injects some fresh blood into the organization.

More recent analyses have questioned these findings. Certain groups have indeed self-imploded following the untimely demise of their figurehead: Peru's Shining Path faded into irrelevance after its leader Abimael Guzman was captured; Italy's Red Brigades did not outlast its founding leaders; the capture of Abdullah Ocalan disempowered Turkey's Kurdistan Workers' Party for a decade.

In a big-data study last year, Bryan Price of the U.S. Military Academy analyzed 207 terrorist groups from 1970 to 2008, but instead of looking at their effectiveness, he examined their longevity.

He found that taking out the executives "significantly increases the mortality rate of terrorist groups, even after controlling for other factors" – but it often takes longer than we'd like. Counterterrorism, he concluded, is a long game. He also found that the groups most likely to implode after things blow up in the head office are nationalists. Groups that see themselves as religious, he found, are more tolerant of bloodbaths at the top. Of 53 religious groups, only 19 have ended – 16 of them after their boss was wiped out. But of the 34 such terrorist groups still in existence (including al-Qaeda and the Islamic State), 20 have endured a decapitation strike.

There are other good reasons to knock off the kingpins: Inspiring morale in your troops, hurting jihadi recruitment by looking all-powerful, sowing moments of chaos that can be exploited. But there's no reason to think they'll make the fight any easier, or the world less bloody.

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