Equality or priority about competing claims?

According to the Competing Claims View (CCV) we decide between alternatives by looking at the competing claims held by affected individuals. The strength of these claims is a function of two features: how much they stand to benefit (or lose) by each alternative, and how badly off they would be in its absence. The view can be, and is, endorsed by both egalitarians and prioritarians. For the former the second condition will concern looking at how badly off the person is relative to others, whereas for the latter it will be how badly off she is in absolute terms. In this paper I want to argue that neither should be endorsed. The egalitarian version of CCV breaks down when attempting to assess the competing claims of possible persons who may never exist. Also, the view, on at least one plausible interpretation, leads to intransitive judgements. The prioritarian version of CCV, in turn, is vulnerable to its own unique objection, namely delivering an anti-prioritarian and rather implausible verdict in certain Single Person Cases.