Strictly speaking a Fatwa is opinion letter on a question of Islamic law issued by a Islamic law scholar. The popular media accounts of this kind of instrument, however, focuses on the subtype of Fatwa in which opinion letters on Islamic law authorize some sort of extra-governmental self-help action by a representative of the victim or members of the general public to punish someone for a violation of Islamic law in a partular way for particular conduct. In short, some Fatwa's authorize private violence since Islamic law, which isn't statist and isn't united in a bureacratic hiearchy that derives its power from a sovereign, doesn't have the capacity to compel state action to enforce its edicts. Islamic law when used in this manner goes almost beyond libertarian visions of the role of government in securing legal justice to a basically anarchist theory of the state (which is not to say that there isn't a role in Islamic political theory for a state - indeed a state in which church and state are unified).
This kind of activity isn't as alien as it seems. Medieval Iceland has a period of time when it had courts that likewise authorized private individuals to carry out judgments, but had no enforcement mechanism of their own. The Article 9 of the Uniform Commercial Code authorizes creditors who comply with a certain set of requirements to seize and dispose of collateral for their loans through private action, without resort to the courts, so long as this can be accomplished without a "breach of the peace." U.S. Presidents have long been entitled, in fact, even if the law has sometimes been muddy, to authorize the use of military force in the furtherance of a variety of ill defined national security ends, such as the recently exercised authority to authorize the assassination of a particular U.S. citizen abroad without any court process, in furtherance of the authorization for the use of military force that is the legal basis for the war in Afghanistan and the "war on terror." The U.S. Constitution makes provision for the issuance of Letters of Marque and Reprisal (i.e. authorization for the owner of a private vessel to capture enemy vessels and goods on the high seas, a Congressional right abrogated in the Declaration of Paris in 1856, but which could be overturned by a simple statute passed by Congress). Bailbondsmen have extraordinary authority to take actions that would constitute kidnapping and certain other crimes if committed by someone else, to produce the persons whom they have posted bond for in court. Legislative authority to engage in self-help hacking targeted at suspected hackers (e.g. intentionally sending computer viruses to their computers) is a regular subject of debate in Congress today, and the self-help remedy of the non-judicially authorized "take down notices" to Internet institutions like You Tube, have become a part of every day life in the 21st century.
Historically, the right to use force to discipline and control one's children or one's spouse or one's slave or one's indentured servant or one's military subordinate, and to force those people to return to you if they ran away, was another large domain in which the private use of force was authorized and supported by state authority, but this right is now much diminished in theory as well as practice. As Pinkerton has noted in his recent book, "The Better Angels of Our Nature," support for corporal punishment of children is greatly diminished. Legal toleration of domestic violence has dramatically declined within my own lifetime. Reforms in the military justice system and in how military discipline is maintained generally in the last seventy years or so have greatly reduced the caprice of force directed at military subordinates in the U.S. military (some countries, like Russia, have lagged further behind in this regard). History views the fugitive slave act as an instance of historic, collective shame. Government authorities still help parents recover their runaway children, but the cutting edge of modern social criticism is increasingly calling attention to the fact that even runaway children may have good justification for running away even though that means rejecting the parental economic support that they rely on for all of their economic needs.
Many countries authorize trial in absentia for crimes, although under U.S. law this is pretty much limited to cases where a criminal defendant absconds during the course of a trial already commenced in the defendant's presence. U.S. law certainly authorizes default judgments, however, which in cases where the object of the case is property rather than a civil judgment (a.k.a. a license to steal under the watchful eyes of sheriffs and/or courts), can sometimes issue without actual notice that a case is pending to a defendant. Closely related is the somewhat obscure and perhaps misunderstood concept of "wanted dead or alive" bounties.
Of course, the private use of violence for self-defense has been recognized since ancient times and is frequently considered a form of natural justice, although debates on the requirements for invoking the privilege of self-defense, for example, to defend a business when retreating from the business would have been a viable alterantive, is an issue being debated by Colorado's state legislature in 2012. For about a century, combat by agreement (i.e. dueling) was a defense to charges of murder and assault, a defense only removed by constitutional amendment in many states.
Louisiana recently considered (and rejected in a 54-39 state house vote) a law that would have reduced the criminal penalties available in the case of assaults directed as someone who is burning an American flag to $25. The idea has a lot in common with the notion that "heat of passion" murders (e.g. of a spouse or "other man" found engaged in the act of adultery by a husband) are less culpable than premediated murders.
A ruling in a Mechanicsburg, Pennsylvania case by Judge Mark Martin in which assault charges were dismissed against a man caught on videotape attacking an atheist Halloween parader dressed up in a way that mocked the Prophet Muhammed in a ruling that breated the parader for being offensive raise the specter of the harm that can be done not with state action, but with state inaction in the face of what would otherwise be illegal private violence that would usually be (and in this case was) prosecuted and would usually result in criminal punishment for the person engaging in intentional private violence.
In general, in U.S. law, unlike German law, for example, there is also no per se duty of the state to enforce criminal laws for the benefit of citizens who have been victims of crime. The political structure of U.S. law enforcement and criminal prosecutions ensures that usually law enforcement officials errs on the side of overkill in trying to enforce criminal laws, and federalism in the U.S. means that there are usually there are several officials who have the independent authority to bring criminal charges arising from a particularly instance of criminal conduct. But, absent an almost impossible to prove case of discrimination on the basis of race or some similarly prohibited reason, prosecutors and law enforcement have no legally enforceable duty to attempt to protect citizens from crimes or to prosecute crimes they know to have taken place no matter how solid the case, even in the face of state law authorized and court issued restraining orders that purport to create such an obligation (see Castle Rock v. Gonzales).
As I've noted before, this lack of duty to use the criminal justice system and law enforcement to protect people from private violence is perhaps the strongest policy argument for an individual right to bear arms for self-defense under the Second Amendment in the U.S. Constitutional scheme. If people can't rely on the state to defend them, they must be allowed adequate means to defend themselves through self-help. U.S. law also generally allows suits for civil damages arising from most kinds of common law crimes committed against an individual by an alleged victim of the crime or their heirs even in the face of an acquittal of the same charges in a trial by jury (the most prominent such case being the O.J. Simpson civil case for wrongfully causing the death of his wife).
There are times when we don't often do so, when authorizing private violence, i.e. making someone a stranger to the protections of the law, might make a certain amount of sense in foreign policy settings, as an intermediate step between making only diplomatic protests to some actions in a foreign state, and directing our own covert agents and military to themselves use force against that state. For example, one could imagine Congress or the U.N. Security Council, declaring that anyone or any country or any organization who kills specified leaders of the regime in Syria that is raining down artillery on its own citizens indiscriminately in violation of international human rights standards, or sabatogues that regime, may do so with impunity notwithstanding international laws that normally afford the highest levels of respect to sitting sovereigns. To some extent, this already happens through consultations between intelligence agencies of various foreign governments.
Still, on balance, I am inclined to think the the lack of limitations in the U.S. Constitution and state constitutions in the United States, laws that have the effective of authorizing or minimizing private violence without compelling justifications for that authorization, are a defect born of the short sightedness of Founding Fathers whose political theory was so concerned about active abuses of state power, that the more more subtle theat of abuses of state power through inaction were simply overlooked. The Founding Fathers did not have fresh in their minds as they drafted the Bill of Rights, the experience of institutions like informally state sanctioned death squads of Latin America, the Lynch Mobs of the Reconstruction South, the full fledged Middle Eastern institution of honor killing, or the organized brownshirt organizations of the Third Reich through which private citizens carried out state encouraged private violence to inform their deliberations.
Our system of criminal justice is based on the bedrock assumption that prosecutors and law enforcement will make their best efforts given their practical limits in resources and likelihood of conviction to prosecute cases where they have bona fide probable cause to believe that crimes have been committed. When that assumption is absent, legal due process protections for criminal defendants can look like rules that simply further the end of official corruption and abuse of power. The only institution in American law, other than political incentives and federalism (including federalism within states) that limits this kind of problem is the rarely invoked notion of a "special prosecutor" appointed in cases where the person with official authority to act may have a conflict of interest (for example, in the case of crimes committed personally by an elected district attorney such as the case Colorado recently saw in Montrose County). But, that doesn't cover cases where there is not a personally self-interested kind of conflict of interest involved.
There are a couple of distinct problems with private violence authorized by Fatwa-like authority that are in theory distinguishable.
One is a due process concern. U.S. criminal law generally requires in person participation by defendants in cases that invoke criminal-like punishments, and a Fatwa-like process (not at all specific to Islamic law as I have illustrated above) makes it possible to go through the motions without the level of due process secured by in person participation in key events of the process combined with a right to counsel if one can't afford it. These concerns can be just as great when the President authorizes an assassination or airstrike that will likely lead to civilian casulaties as it is when an Islamic scholar in Pakistan or Iran declares that it is acceptable to murder a Scandinavian cartoonist, although the concern that there might be multiple conflicting rulings by people with equal authority is much greater in the latter case than the former one. In many cases, self-help remedies put someone in the position of being the judge of their own case, a fundamental prohibition of ordinary judicial proceedings.
The second is the concern associated with lack of state involvement in the carrying out of the remedy. The idealized basic bargain of Western political theory is that the state has a monopoly on the use of violence (or any breach of property rights as well) that comes with a duty to use that monopoly to suppress private violence against those who are under the protection of the state, a duty to protect those who are under its protection from violence from foreign sovereigns, and a duty to dispense justice so that self-help not supported by sovereign authority is unnecessary or at least undesirable. Exceptions to this basic bargain delegate the state's monopoly on the use of force to private individuals in cases where the state is incapable of fulfilling its duty (e.g. self-defense or a posse), and only in cases justified and provoked by someone else's actions that themselves abridge the state monopoly on the use of force. Citizens are, in turn, protected from state abuses of its monopoly by the rule of law, and by violations of their rights under the color of law, with a set of rights enforceable against the state in the event that its agents deviate from the requirements of the rule of law (e.g. in a civil rights action). The idea of this political theory is to create a utopia where non-consentual activity by private parties is rare, violence is minimized, and both private and public interests are tamed so that they act on the basis of consent and rational, well informed decision making processes.
This second concern isn't deeply implicated in cases where due process concerns are for some reason associated with the scope of a particular grant of self-help authority are minimial, remedies for misuse of the authority to engage in self-help activities are ample where it occurs, and the force in question would in reality have been little different had it been carried out with perfunctory state supervision or where the private parties carrying it out as deputized as "officers of the court" or the "public trustee" some such quasi-public title with corresponding obligations associated with acting under color of state law (which to be clear, U.S. law generally often doesn't actually treat as such for purposes of civil rights lawsuits).
But, this political theory breaks down most severely when the state authorizes private individuals the right to use force in circumstances when it would not have been authorized to use force itself (and hence cannot be said to be delegating to private individuals), or establishes punishments that are mitigated on grounds that it would be improper and contrary to the rule of law for it to considerate itself. This concern gets to the heart of the legal prohibition on vigilantism beyond the delegations of power to private citizens to use force for the defense of others, or to make a "citizen's arrest" for a range of offenses much narrower than those which a law enforcement officer may make absent very special circumstances.
Fortunately, legislators, jealous of their monopoly on the use of force and intuitively understanding the grand bargain of the Western political and constitutional system even when it isn't expressly stated, generally don't authorize private individuals to use force or act non-consentually in circumstances when the state couldn't jusifiably do so. This doesn't mean, however, that sometimes they might do just that, because partisan policy agendas frequently trump larger process concerns based in political theory in the political process when courts don't restrain them.