Consider two approaches—
The Stick. If the United States and other countries simply blew up any ship captured by pirates, including the crew and the pirates themselves, then, after a few demonstrations, piracy would no longer be a profitable activity. The pirates, rational profit-maximizing agents that they appear to be, would conduct backward induction and then find something else to do with their time. After the short term costs are incurred, the sea lanes would be safe until memories faded.
The Carrot. Pay the pirates to stop engaging in piracy. That was the approach of the United States and other maritime powers in the early nineteenth century; for a number of years, they paid ransom as necessary; eventually, the process was formalized as tribute payments, which made the initial capture of the ship and crew unnecessary. As Michael Oren's recent book makes clear, this practice was entirely rational; when the United States finally decided to destroy the pirates, the naval costs were far greater than the tribute payments had been. The various U.S. administrations paid the ransoms as long as they could but eventually bowed to popular pressure incited by a sense of national shame.
Each approach has characteristic costs and benefits. The stick lacks credibility. The pirates know that no government will kill its own people, nor can governments or shipping companies refuse to pay ransoms. The problem is not so much the doctrine of double effect as the political difficulty of inflicting harm on innocents even to advance the greater good. The carrot gives pirates incentives to invest in more destructive capabilities and draws more people into the labor market. Depending on just how costly piracy is for the pirates, the implicit tax imposed on shipping could end up significantly suppressing economic activity. At approximately $100 million per year, however, we are far from reaching that point.
One significant problem is the low cost of entry into the piracy business. It would be much better if a single pirate leader controlled entry. Then we could do business with him, paying him a tribute (we might prefer to call it a "toll") in return for a promise not to molest our ships. As a monopolist, he would have an incentive to limit "production" of piratical activity, relative to the unregulated market we currently live in. The monopolist essentially would be selling passage off the coast of Somalia, and would be constrained by competition from people who control alternative routes (which, unfortunately, seems limited). We might even expect the pirates to start organizing, or fighting among themselves, in an effort to establish a single firm that could obtain these monopoly rents. In the happy event that an organization emerged, we could call it a "state" and deal with it as we deal with any other state—paying it or pressuring to act as we want it to act, in light of its interests and capacities. We could even call this state "Somalia." If the gains from rational management of this newly discovered resource—the power to block important sea lanes—provide sufficient incentives for Somalia's warring clans to make a deal and reestablish a state that can control entry into the market, we should be sure to keep paying Somalia money (we might call it "foreign aid" if "tribute" or even "toll" is too irksome) rather than yield to the temptation to smash it to pieces. In the state system, sometimes you do better with an enemy than without one.
But that outcome is a long way off. In the meantime, governments will have to employ an unsatisfactory combination of carrots and sticks—mounting expensive patrols that spot and pick off pirates on occasion, while paying ransoms to those pirates who succeed.
Everyone thinks that President Obama will put together an international coalition that will solve the piracy problems. So far skeptics have emphasize the costs of patrolling, which are extremely high. But there are other reasons for skepticism. Clearing the sea lanes is a public good, and no state has much of an incentive to help others. Indeed, we have already seen that states take their own nationals far more seriously than the nationals of other states. The French attempted to rescue a French crew. Piracy was considered a joke among the American public until an American crew was captured; now President Obama is "personally involved," according to the papers, as he never was before. These conflicting incentives will contaminate all aspects of an international operation. Some states may hope to pay tribute payments to pirates so that the pirates will go after other states (akin to putting bars over your windows so that burglars will go next door). The current practice of responding more forcefully when one's own nationals are involved will have a similar effect. Obama will have no more luck persuading states to overcome these incentive problems than he has had in so many other areas—economic stimulus, contribution of troops to Afghanistan, assistance in relocating Guantanamo Bay detainees.
Obama has good reason to become personally involved in the current hostage crisis. Despite the relative insignificance of the problem up till now (ransom payments of $100 million per year are a pittance), the pirates' main tactic—hostage-taking—has a way of capturing the public imagination. It also has a way of sucking the air out of normal politics and destroying presidencies. That is what happened to President Carter, when Iranian militants took over the U.S. embassy in Tehran. And that is almost what happened to President Reagan, who launched his cockeyed arms-for-hostages scheme in order to secure the release of a handful of hostages in Lebanon. The scandal nearly destroyed his presidency. President Obama has every reason to be concerned.
He also has little room to maneuver. Having just returned from a trip promoting internationalism, he has raised expectations that any anti-piracy endeavor will have an internationalist flavor. This will mean costly, time-consuming negotiations for the sake of largely symbolic contributions by other countries, if history is any guide. Having also raised expectations that his administration will act with the utmost respect for legality, Obama will either have to direct American forces to walk on eggshells or risk exposing his words as empty. If the pirates continue to take American hostages, he will have trouble maintaining these commitments while giving satisfaction to the inevitable nationalist backlash driven by the mounting sense of powerless and humiliation that we haven't seen since the Carter years.