I thought I would throw my 2 cents into the current discussion since my view seems to be different than those who have posted so far.
I have to first say something about how I think political philosophy should be done. On this score, I should admit, I am old-fashioned. I believe that one must first specify the ideal society (one that is completely just) and then—and only then—consider how to move from one’s non-ideal society to the ideal. I don’t think one merely finds injustices and seeks to correct them; we should do that, but cannot do it if we do not know what justice is—and that is a matter of ideal theorizing. This view seems to be somewhat unpopular these days.
My libertarian principle(s) of justice—which I admittedly have yet to fully articulate—are, I think/hope, fact-insensitive (a la G.A. Cohen). They are also the principles that would guide those in the ideal society—meaning a society wherein there is full compliance with the principles of justice (a la Rawls). They are, that is, a matter of ideal theory (in at least those 2 senses). They do not directly guide action in the real world—and I am, in fact, often unsure what to suggest should be done in the real world (I want the world to be ideal and want to encourage practices in the real world that lead to that, sometimes even if those practices might not be permitted in the ideal world). Indeed, it is a standard criticism of ideal theory that it is not action-guiding. I think the criticism is mistaken, but there is an element of truth to it. Principles of ideal theory do not provide us direct action guiding advice, but they are (or so I believe) necessary for such action-guiding advice. My principles don’t provide action-guiding advice directly, but they are a way of describing what an ideal society would be. For action-guiding advice one uses something like rules of regulation (a la G.A. Cohen), where these should be rules that are meant to bring us—in whatever society we are currently in—closest to the ideal society.
So, mine is a two level theory and I am perhaps more interested in working out the ideal theory than the non-ideal theory. By contrast, all three of Matt’s types of BHL strike me as being of non-ideal theory.
OK, why am I a BHL? My ideal theory is concerned to prevent suffering and promote human flourishing for all—and, of course, that includes the less fortunate. Suffering is to be prevented, wherever it occurs, to whomever it occurs, in whatever form it occurs. In the real world, of course, suffering is most likely to occur to the least advantaged. Hence, the non-ideal theory (which I tend to sort out a bit on this blog) is concerned with the least advantaged. Does that make me a contingent BHL or a strong BHL? I’m not sure. In the ideal theory, libertarian institutions (like markets, rights, etc., all thinly defined) are justified independently and sufficiently on the basis of suffering and flourishing, and “would still be justified even if they were not good for the poor and vulnerable.” (After all, in a society where there were no poor or vulnerable people, the institutions would still be justified—even though they didn’t help anyone poor or vulberable.) So that may mean that my ideal theory is a form of contingent BHL. On the other hand, in the non-ideal theory libertarian institutions (like specific, thickly-defined sorts of markets and rights that we have or that I think we should have given the empirical facts) “actually depend in part for their moral justification on the extent to which they serve the interests of the poor and vulnerable.” That may mean my non-ideal theory is a form of strong BHL.
Putting this all a bit differently, the social and economic facts (including the fact that there are social and economic classes, some of whom are extremely wealthy, some of whom are extremely poor, and some of whom are neither) are facts that must be taken into account when considering the way the fact-insensitive principles of the ideal theory are put to use in the non-ideal theory, which is itself meant to be action-guiding in the real world. The point is to bring us closer to the ideal world, but when doing so, we must take care not to cause suffering or harm, and so, de facto, the least-advantaged figure prominently.