This post assumes familiarity with my old post on utility, equality and priority. I've previously argued against egalitarianism; I now want to do the same for prioritarianism, i.e. the view that "benefiting people matters more the worse off these people are."
First we need a standard measure for quantifying benefits. I will employ the notion of a 'util' or unit of utility (i.e. individual welfare) to serve this end. I stipulate that all utils are of equal worth to the person who receives them. If the welfare value of my life increases from 2 to 3, this is exactly as good for me as an increase from 99 to 100 would be. They are also to be standardized between individuals, so a one util benefit for you is just as good for you as a one util benefit is good for me.
This is clearly wildly different from how material goods behave. $100 is worth a lot more to a starving man than to a millionaire. More generally, material goods are less valuable to you the more of them you have. We call this "diminishing marginal utility" (DMU). For example, the $100 might be worth 20 utils to the starving man, but only 1 util to the millionaire. Given a choice between giving the money to one or the other, utilitarianism recommends we favour the starving man with material goods; that is what will maximize total welfare in this imagined case.
Now, suppose we can either give a large benefit (in utils, not merely dollars!) to someone who is already well off, or else a smaller benefit to someone less fortunate. Which should we do? For utilitarians, the answer is simple: give the greatest benefit, without regard for who receives it. On the priority view, however, we might instead opt for the more egalitarian option.
I think that would be a mistake. It's a tempting mistake, insofar as our intuitions are more familiar with material goods and so find it difficult to ignore DMU. But ignore it we must, for recall that utility benefits - by definition - do not suffer from diminishing returns. We tend to assume that helping the worse-off will "make a bigger difference", i.e. benefit them more than offering similar help to someone more fortunate. It is important to be clear that this is not the case in the scenario I have described. The well-off person really would gain the greater benefit, in real (and not merely material) terms.
Here is why it's a mistake: consider a similar option but all within the life of just one person. He can receive a mild benefit when he is badly off, or else a larger benefit at a different stage of his life when things are going better for him. Which option is better for him? Well, by definition, the greater benefit is better for him. So if offered the choice, he should - if rational - prefer that you benefit his well-off self, rather than prioritizing his worse-off self.
But recall the definition of prioritarianism: "benefiting people matters more the worse off these people are." This suggests that giving the lesser benefit might matter more (be "better") than giving the greater benefit, in the case just discussed. Considering only this person's welfare, it might be better to do what is worse for him. This is an absurd and contradictory result.
So the priority view, as stated, is not universally true. In particular, it is not true within an individual's life. Defenders might hope to modify it into a purely inter-personal form, e.g. "benefiting distinct people matters more the worse off each person is." This restriction seems ad hoc, but never mind that for now. The problem is that it seems open to an analogous objection to the above.
Recall that benefits have been defined in terms of 'utils' which are an inter-personal standard measure of welfare. Each util I gain is just as good for me as each util you gain is for you. This much is stipulated. Also, let us define the welfare value of a life relative the zero baseline of a life that is barely worth living (for the person living it).
Now, let's say Ana currently has a welfare value of 100, and Bob's is 10. Suppose you have a choice between giving a benefit of +10 to Bob, or else +11 to Ana. Which is best, from a neutral point of view? Simply enough, +11 is better than +10, which is all it comes down to when giving equal weight to the interests of both involved. If you put the agents behind a "veil of ignorance", so they didn't know which person they were, they would (if rational) prefer you to choose the +11 benefit to Ana rather than the +10 to Bob. The fact that Bob is worse-off to begin with is irrelevant. What matters is how much better off each of them could be.
But prioritists would have us believe that the benefit to Bob matters more, because he is worse off to begin with. Although our only consideration is the welfare of these two individuals, we're supposed to believe that it might be better to do what is worse from their combined point of view. Again, this is an absurd and borderline contradictory result.
So we should reject the Priority View. Benefiting people matters more the greater the benefit is to the beneficiary. Their prior welfare level has no intrinsic relevance here. It is only relevant insofar as, say, it might be easier to benefit worse-off people, e.g. if the same material investments would yield greater benefits for them. But of course such factors are already taken into account by utilitarian principles. A preference for egalitarian or prioritarian principles may rest on a failure to understand this point.