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Re: polyphyletic Alvarezsauria assemblage

Alvarezsaurids show a number of bizarre characters which appear to unite them. One of them is the caudally expanded, anteriorly tapered iliac blade, seen in Alvarezsaurus and the Mongolian material, nothing else looks like it in the Theropoda. Another is the strongly procoelous, ball-and-socket caudals which are anything but common in theropods, and the digital proportions are just bizarre: the second and fourth digits are more robust than the third which is almost unique, other than having evolved convergently in jerboas and Borogovia (I checked out the possibility that Borogovia was an alvarezsaur, however the laterally compressed second metatarsal and the well-developed medial condyle of the astragalus indicate that it is in fact troodontid).
Its also worth noting that fusion of the carpals is notoriously variable. Protarchaeopteryx for example has distal carpals 1 and 2, unfused, capping metacarpals 1 and 2. The holotype of _Oviraptor philoceratops_ preserves a full fusion of the carpals and metacarpals, forming a carpometacarpus, which has not been reported in other oviraptorids. So should we now decide that Oviraptoridae is really polyphyletic and Oviraptor goes with Mononykus, Avimimus, and pygostylians, other "oviraptoridae" are more primitive, and Protarchaeopteryx is a basal form related to therizinosaurs, all based on this "key character" (all the other evidence being homoplastic noise)?

I've been looking at the characters that supposedly unite Alvarezsauria, and all I can see is a bunch of homoplasic "noise".
The first two (small cervical epipophyses and neural spines) seem to be very subject to convergence and found in other groups. Procoelous caudals and sacrals pop up here and there in all kinds of archosauromorphs (incl. the bird Patagopteryx), and they grade into slightly procoelous-to-amphiplatyan forms in a variety of neotheropods. I find nothing convincing in this list of so-called synapomorphies. The similarities appear to be pretty superficial and homoplasic.

I'm not clear, how is this process different from the work of those who would say "I've been looking at the characters which supposedly unite birds and dinosaurs, and all I can see is a bunch of homoplasic 'noise'," and then argue that each supporting character is highly homoplastic or easy to evolve convergently, so it can be conveniently dismissed without an analysis?
The problem with manually picking and choosing characters is we can get absolutely anything we want if we have the will to ignore the counterevidence. Take a set of animals, find characteristics that unite them, and call those "key characters" or "good characters", and everything else can be dismissed as homoplasy. And lo and behold: all the evidence supports my hypothesis, except forthat evidence which doesn't.