reads this L.A. Times headline (with “narrowly” instead of “barely” on the Web version). The opening paragraph reads, “By bare majorities, Californians reject the state Supreme Court’s decision to allow same-sex marriages and back a proposed constitutional amendment aimed at the November ballot that would outlaw such unions, a Los Angeles Times/KTLA Poll has found.”
It’s only in paragraph 6 that reads learn that the amendment “was leading 54% to 35% among registered voters.” It’s true, as the paragraph says, that “ballot measures on controversial topics often lose support during the course of a campaign” and therefore “strategists typically want to start out well above the 50% support level.” But despite this 54%-35% doesn’t strike me as “barely”; likewise, the 52%-41% disapproval of the California Supreme Court decision doesn’t seem likely “barely reject[ing]” to me.
So while 52% and 54% are indeed not much above 50%, they are much more than barely or narrowly above 41% and 35%. Formulating both the headline and the opening paragraph in terms of “barely” or “narrowly” and “bare majorities,” without noting the large margins, strikes me as not the best way of presenting the data to the reader.
I should stress, by the way, that my point here is about the coverage of the poll, not about the likely November results. I suspect that the proposed amendment banning recognition of same-sex marriages will pass (assuming, as seems likely, that it will get on the ballot); but now is not November, and the voters haven’t seen the campaigns on both sides. That the view “As long as two people are in love and are committed to each other, it doesn’t matter if they are a same-sex couple or a heterosexual couple” polls at 59%-35% in favor suggests that public opinion may well be quite movable, if the issue is framed in that way.