WELL: I came across this bit in the Montaigne I quote somewhere below:
"'What ought I to choose?'--'Anything you wish, so long as you choose something!' A daft enough reply! Yet it seems to be one reached by every kind of dogmatism which refuses us the right not to know what we do not know."
What I thought when I read this was the similarity it has to what is often said about voting--"make sure you vote, doesn't matter who for, just so long as you vote." Now Montaigne is playing devil's advocate in this particular passage (he's supporting Pyrrhonism as a philosophical doctrine if one refuses to believe in God), but his essential point is that when looking for explanations physical and metaphysical about the world around us, it makes no sense to cling to a position just so that you have a position to defend.
Similarly, it seems to me, with politics. If you think that which parties, candidates and propositions you support will actually make a difference in what ends up happening in government (and well you should, if you want to take politics seriously), then contending that taking any old position will somehow be beneficial to the process is silly. It's far better, if you have no opinion on a contest, to take no position at all on it; or, at least, this will give a marginally more rational final result.
I do wonder whether GOTV efforts rely on a similar scheme, only they advocate that people who have no position themselves take up a certain position. Then again, I imagine the people who are brought to the polls by GOTV are people who have positions but wouldn't be (otherwise) voting for other reasons. Then again, I'm not an Americanist, so I couldn't say for certain.