It is really a somewhat peculiar idea that scientists would gather input on how to decide a scientific question by conducting a poll. Surely science would not get very far if the age of the earth or the efficacy of homoeopathy were decided by public vote as opposed to based on the evidence.
However, viewing it like that is somewhat missing the point. This is, after all, the Angiosperm Phylogeny Group, and they make clear right at the beginning that the recognition of natural groups in classification is non-negotiable. It can be safely assumed that they put the question whether stability or monophyly should be prioritised in there to see where the individual poll participant is coming from, not because they will say, hey, perhaps we should accept non-monophyletic groups after all now that 52% have voted for that. (In actual fact, at the moment 75% of the participants prioritise a natural classification over a stable one, as they should if they are scientists.)
No, what this survey is really about is what to give second priority, so to say. Apart from describing biological diversity correctly, a classification of vascular plants can aim to fulfil several other criteria, and often one will have to be traded off against the others:
- Stability, already mentioned above, means that one tries to minimise disruptive changes in the classification even as our knowledge advances. When faced with the decision whether to reclassify many species or few species, one would prefer the second option.
- Recognisability of the taxa. In the present case, there is clearly a concern that plant families be defined by some clear, preferably exclusive characters that make it easier for students to learn about the groups and for end-users of the classification to understand it. Uniting the Orobanchaceae with the Lamiaceae, for example, would pretty much make it impossible to explain how to recognise the family.
- Conversely, one would like to avoid making many small groups that don't really differ from each other by any obvious character.
But that is also one of two possible sources of frustration with the APG's poll: the family rank is taken entirely too seriously by many of us botanists. Instead of obsessing about where to draw the line for this category perhaps we should acknowledge that there are simply clades inside of clades. I have the feeling that most zoologists are way ahead of us in this regard (although admittedly entomologists tend to think in terms of insect orders).
The second source of frustration is the one mentioned by Bort in his comment. The APG solicits opinions on questions without providing sufficient information to the participants of their poll. How am I supposed to know the clade support and character distribution in, say, Dioscoreaceae, Tecophiliaceae or Restionaceae? Ultimately, unless more data are provided the only people qualified to have an opinion in those cases are a handful of phylogeneticists working on those groups which, as Bort pointed out, kind of defeats the purpose of the poll.
In some cases, however, the description of the problem itself makes clear that there is currently insufficient support in the phylogeny to decide how to circumscribe natural groups. I find it strange that such cases even need to be discussed; it seems obvious that one should not make any taxonomic changes until more data are available.