This Bloomberg Politics article authored by Steven Yaccino notes problems with the Fox News Republican debate criteria. Fox News still has not said which polls it will depend on to determine which Republicans will be invited into its August 6 debate. By contrast, CNN, which will host the September debate, has already said which polls it will use.
The article also quotes statisticians who say that using polls to determine the top ten, at a time when many polls show ties for eight, ninth and tenth place, is arbitrary. One statistician is quoted as saying, “Methodologically, they might as well be drawing straws.” Also the story explains that some presidential primaries are open, some are semi-closed, and some are closed. Yet a national poll can’t account for differences in the various state primary systems. Therefore, the decision of various polls to either include or exclude certain classes of voters (such as independents, or members of other parties) may determine the results; there is no obvious best way to handle this in a nationwide poll.
UPDATE: also see this story, in which a Fox spokesperson says the network will use “a range of quality polls”, which does not answer any of the objections mentioned in the Bloomberg story.