The threat posed to Iraq's Yazidi community was one of the stated rationales for the United States to begin a series of airstrikes against the militants of the "Islamic State of Iraq and Syria" (ISIS). ISIS sees the Yazidis as polytheists who have no place within an Islamic state and are to be presented with the traditional alternatives of death or conversion. Given the thousands who have already been killed or who have died as a result of being driven from their homes into inhospitable country, there was sufficient grounds to make a credible claim that immediate military action was justified to blunt the ISIS offensive and to give the refugees some breathing room to make their way to safety, as well as to assist the on-the-ground Kurdish militias (peshmerga) in halting the ISIS attack on their territory.
Yet the air option was also politically acceptable to decisionmakers in Washington because it continued the "low cost, no casualty" model that was on display in Libya in 2011. The United States would not directly insert land forces on the ground or undertake a risky intervention; instead, superior U.S. air power plus intelligence and targeting capabilities could be used to great effect against ISIS military formations and to aid the Kurds in their efforts--following the same playbook used in Afghanistan in 2001. In the absence of a credible Kurdish peshmerga force, U.S. airstrikes would have been far less effective. Yet Washington (and other countries) would probably not have substituted their own forces to provide a more effective barrier for the Yazidis.
ISIS, in turn, is altering its tactics to minimize the impacts of airstrikes, which raises the question of their utility if ISIS moves to methods that are harder to stop using air power alone and which would require ground interception and engagement. There is a point, it seems, where ISIS can raise the cost for U.S. action which would be beyond Washington's willingness to pay. In such circumstances, the United States may instead decide that support for proxies--in this case, the peshmerga, is a more cost-effective way to pursue its security goals.
There are also other limits. More Yazidis may survive than if the U.S. had done nothing at all, but beyond airstrikes, the U.S. does not appear prepared to take steps to help them regain their homes, or to push for the return of Iraqi Christians also displaced from their traditional homes. Perhaps efforts will be taken to help resettle the Yazidis in other parts of Kurdistan where they can be protected, or the U.S. or other countries will make offers for refugee resettlement in their own territories. There are compelling political and ethical reasons for such a step; the previous U.S ground intervention, even if undertaken for the best of motives, ended up being quite destructive; accepting Yazidi dispossession (if accompanied by active measures for sustainable resettlement) may be a lesser evil than supporting the return of a massive U.S./coalition land force to resume fighting in Iraq.
The U.S. thus has claimed a limited responsibility to protect the Yazidis--essentially using its air power only, with the hope that the Kurdish authority will be willing to take on more of the job. How this develops over the next few weeks may present us with an interesting evolution of the doctrine of R2P: one where states accept a responsibility to act, but deliberately limit the means and costs associated with such a venture--and where if the responsibility to protect is not achieved using that limited menu of options, further efforts will not be forthcoming.