Earlier I suggested that anyone writing about the electoral implications of Obama's support of gay marriage needed to think rigorously about some key questions. This is in lieu of flabby statements about how Obama's endorsement "could" lead "some voters" in "key battleground states" to "reconsider" their support for him. Etc. The upshot of that post was: don't necessarily expect big effects on voters.
Let me illustrate why I think that expectation is reasonable. I am going to simulate improbably massive changes in attitudes toward same-sex marriage and see what would happen to Obama's vote share in a head-to-head race with Romney.
I'll begin by stacking the deck in favor of a big effect of same-sex marriage. Let's assume that only two things matter for people's votes: (1) what party they identify with and (2) their views of same-sex marriage. In a May 5-7 YouGov poll, respondents were asked "Do you favor or oppose allowing gays and lesbians to marry legally?" 30% said strongly favor, 17% said somewhat favor, 12% said somewhat oppose, and 33% said strongly oppose. 8% were not sure, and I exclude these people from the analysis. In a model of support for Obama vs. Romney, both party identification and attitudes toward same-sex marriage are statistically and substantively significant. Needless to say, the most favorable one's attitude toward gay marriage, the more likely one is to favor Obama over Romney.
Now imagine a world in which every person who opposes same-sex marriage now "somewhat favors" it. How much would Obama's vote share increase? 4.7 points.
Of course, other things matter for vote choice besides party identification and same-sex marriage. Let's add a variable for black respondents. And let's loosely proxy other issues that might affect vote choice by adding a measure of respondent's self-reported ideology on the liberal-conservative scale. Now the apparent effect of same-sex marriage shrinks by about a quarter -- in line with my earlier point about how you have to consider the possible effect of gay marriage alongside the effect of other things.
Now imagine this same world in which all same-sex marriage opponents change their minds. Obama's vote share would increase by 2.5 points.
What if we pick a more reasonable counterfactual? What if only that 12% who "somewhat opposed" gay marriage changes their mind and decides they "somewhat favor" it? Now Obama's share increases only by 0.6 points -- even though I'm still stacking the deck in favor of a larger increase by assuming that only a small handful of factors might affect voter choices.
One can nitpick any counterfactual, of course. For example, if all Americans supported same-sex marriage, both parties would support it and it wouldn't be an issue at all. But these counterfactuals still serve an important purpose: disciplining our thinking about what is really plausible in a presidential campaign where most votes aren't up for grabs and very few single events and issues are game-changers