Prioritarianism, also known as "priority view" is a modern varient of the Utilitarian school of thought which represents the most popular attempt to reconcile results-based consequential ethics with equality. Prioritarian ethics improves on Hedonic Calculus by synthesizing utility with priority, judging an action first and foremost by its effect on the wellbeing of the worst off rather than all people equally. Some of its chief proponents include Derek Parfit and Harry Frankfurt, (author of On Bullshit).
 Basic concept
Prioritarian ethics gives more moral weight, or "priority," to the benefit of the needy, so what one deserves is inversely proportional to what one already has, addressing the problem that measuring welfare alone can lead to great disparity. Prioritarian beliefs is often summed up as follows: "Benefiting people matters more the worse off these people are." In this way, Prioritarians are rather unique among consequentialists: they believe in two, rather than one, source of intrinsic good: utility (pleasure/flourishing) and priority (equality).
Prioritarians are distinguished from other related schools of thought by the way they handle inequality. Imagine three scenarios involving a majority and a minority: in the first, the majority is modestly well off and the minority is just a bit better off; in the second, both are equally poor; in the third, the majority is extremely well off and the minority is much worse off. A prioritarian would prefer the first scenario, which is intuitively the best, while a strict egalitarian would choose the second because of the equality and a utilitarian might choose the third because the majority and minority combined would have a greater total. Prioritarianism is very appealing because its conclusions almost always "feel" right but do not rely on faith, duty, or intuition.
 Applications and criticism
Prioritarianism is especially appealing to socialists and progressives because of its redistributive and egalitarian nature. As a secular ethical system, it is also sometimes associated with Secular humanism and atheism. One might say that prioritarianism is the philosophical/ethical equivalent of social democracy in the way that Ethical egoism is the equivalent of Objectivism.
Prioritarianism is criticized for some of the same problems of utilitarianism, most importantly the practical difficulty in determining what outcome an action will produce. It is also unable to explain exactly how much more weight to give benefit to the less well off. Although it is the most popular  variant of consequentialism, it is nonetheless one of the least well known and thus only occasionally comes under the usual attack from crazed proponents of Divine command theory. It is not very popular among the religious because it presents an alternative to God-based morality.