In Short (Preview)
According to the 2008 laws, a poll pretty much determines what is or is not a logical alternative. Further analysis ("It seems like a bad bid", "I wouldn't consider that alternative") are pointless. An AC could review whether the procedures of a poll were appropriate, but it could not appropriately over-rule a poll.
1997 Versus 2008 Laws
The 1997 laws did not define the term "logical alternative". Therefore, it presumably takes its meaning from the natural meaning of
"logical": A logical alternative is an alternative that is logical to select. ( I do not know what Regulating Authorities may have done to
clarify the meaning.)
In the 2008 laws, "logical alternative" is given a technical definition: "A logical alternative action is one that, among the class of players in question and using the methods of the partnership, would be given serious consideration by a significant proportion of such players, of whom it is judged some might select it."
I suspect this change has subtle but important implications for how we make judgments about what is or is not an LA. I am interested in the particular situation where a director has performed a poll, has concluded that a call is an LA, and this is being appealed.