Suppose I propose an analysis of X (welfare, say) in terms of some more basic phenomenon Y (e.g. desire satisfaction). One might try to object to this by pointing to various paradoxes that result. But it is important to check whether the analysis is really contributing to the alleged problem here. Often, I find, it is not. The problem derives from the underlying phenomena, and is nothing to do with the proposed analysis. The analysis merely enables us to redescribe an old problem in new terms. It doesn't really introduce any new problems. So it is unobjectionable (at least in this respect).
Here's a test: If we can replace all instances of 'X' with the proposed reduction basis 'Y', and the paradox still remains, then there's no objection to the analysis here. What's problematic is the underlying phenomenon Y, but that's going to be a problem for everyone who accepts the existence of Y, regardless of whether they believe that Y can ground X or not.
Examples of this fallacy in action:
(1) Claims that the desire paradox is a special problem for preferentist analyses of wellbeing. "I desire to be poorly off", if we accept preferentism, is just a redescription of the more basic paradox, "I desire that most of my desires be thwarted." It's clearly no objection to a view that it allows old paradoxes to be restated in new terms. It's only objectionable if a view introduces new paradoxes!
(2) All those objections to consequentialism that really derive from the difficulty of evaluating certain states of affairs (see, e.g., infinite spheres of utility, the population paradox, etc.). The consequentialist claim that right action maximizes the good does not add any further paradoxicality to our theorizing about the good. As R.M. Hare once wrote:
It is worth saying right at the beginning that this is not a problem peculiarly for utilitarians... The fact, if it is one, that there are other independent virtues and duties as well [as beneficence] makes no difference to this requirement. Only a theory which allowed no place at all to beneficence... could escape this demand. Anybody, therefore, who is tempted to bring up this objection against utilitarians should ask himself whether he is himself attracted by a theory which leaves out such considerations entirely.
So here's a handy methodological principle: when faced with an objection to a theory that relates X to Y, first check - via my above test - whether it isn't really just a "derivative objection" to Y itself. The theory of X may be a red herring, distracting the discussants from what's really at issue.