For a concise definition of Rule Utilitarianism

The detractors of utilitarianism are very good at presenting endless cases and situations, wherein the path of greatest apparent utility is clearly contrary to the intuitive judgment of most well meaning, moral human beings. Indeed, such situations arise frequently. These situations often involve sacrificing the most sacred rights of the individual for what appears to be a greater good. Rule utilitarianism competently deals with these situations. Rule utilitarianism is the best version of utilitarian theory because it allows for the establishment of a system of basic individual rights and freedoms whose preservation takes precedence over utility.

With act utilitarianism, the moral rightness of every action and every decision is based solely one factor: That it results in the greatest happiness for the greatest number of people, and the least pain. When a choice arises, both the quality and quantity of pleasure are weighed against the quality and quantity of pain for each possible course of action, and inevitably a single choice stands out as 'best'. Take the following example from Ayn Rand, arguing for Libertarianism: "Human beings who lose an eyeball lose much less happiness than the total happiness obtained by a human being without eyeballs who receives a new eyeball. Therefore, the state should redistribute eyeballs." Within the strict confines of act utilitarianism this is the only acceptable path. It is most likely, however, that the majority of people would find the proposition utterly repulsive.

Rule utilitarianism offers a rational solution to this and other similar dilemmas, which preserves utility and agrees with our intuitive moral sense. Rule utilitarianism is based primarily on one assumption. The assumption that in order for a society to function, it’s citizens must all obey a universal set of laws. These laws must be obeyed without exception or the system doesn’t work (there are, of course, avenues for adding, removing or modifying the laws, but only through the proper processes). Therefore, in any situation where the course of action providing the greatest immediate utility runs counter to the law, the law must still be obeyed to achieve the greatest overall utility. The most important interpretation of this allowance is that it permits the establishment of a system of basic, immutable human rights and freedoms, whose preservation always takes precedence over utility. The specific definition of these rights is, naturally, beyond the scope of this essay. One basic property should be mentioned, however. In no way can the rights of one individual or group, permit them to infringe upon the rights of another individual or group. Therefore external preferences cases (Whereby an action might be considered wrong solely because the thought of someone committing it might cause someone else mental anguish) are invalid.

In this way rule utilitarianism refines utilitarian moral theory, humanizes it. Let us, for instance, apply rule utilitarianism to the aforementioned example. In most societies, individuals are guaranteed a right to health, and to infringe on someone else's health, without their consent, is unlawful. Therefore, an eyeball redistribution program, even if it produced greater immediate utility, could not be rightly implemented, unless every donor agreed to it.

At this point, objections may be forming in the skeptical mind. Chief among them is doubtless the issue of complexity. Some will say that the system of rules necessary to deal with every possible situation where rule utilitarianism might need to be applied in an individuals regular existence would be far too great for that individual to retain, and too complex to be applied in an efficient manner. For instance, police have found themselves on several occasions required to deal with a single person threatening a group of people. Sometimes the most reliable option available for dealing with this person involves physically harming them. To incorporate the rights of the person threatening, and the necessity to protect those being threatened, into a conclusion which adheres strictly to the principles of rule utilitarianism could be time consuming and impractical, given the immediacy of the situation.

Rule utilitarianism is, in any case, a vast improvement over the terrible bluntness of strict act utilitarianism. It easily tackles the greatest problem with act utilitarianism. That is, the way in which it often seems to trample blindly over the rights of individuals; Something we are naturally inclined to object to, being individuals ourselves. It does so by easily incorporating a respect for those rights into itself.

Please bear in mind I've argued in this node that rule utilitarianism is the best form of utilitarianism.
Utilitarianism is still, I believe, fundamentally flawed, for the same reason all totally rational approaches to moral theory are. They leave no room for our intuitive sense of what is right.