The Romney campaign’s new ad targeted to women voters, released during last night’s debate, begins with footage from an Obama ad targeted to women voters. Like a great many ads this season—from both campaigns—it’s an ad about an ad.

In it, a woman named Sarah Minto explains how she discovered by searching the Internet that, contrary to what Obama campaign ads will tell you, Romney “doesn’t oppose contraception.” (Romney does oppose federal funding of Planned Parenthood, something Obama mentioned four times in last night’s debate.) And, she is relieved to discover, his position on abortion is not “extreme” at all, because the Governor is willing to consider that abortion might be O.K. if a woman had been raped, or was the victim of incest, or if continuing the pregnancy would lead to her death. This issue is important, Minto continues—voicing over a scene in which she is supervising her two children doing homework at the kitchen counter—but the national debt is more important, because it affects her children’s future.

Romney’s latest ad is a reply to ads like one produced by the Obama campaign over the summer, called “Important.” It features two women, Dawn and Alex, explaining that “contraception is so important to women,” alongside footage of Romney, promising, at a campaign stop, “I’ll cut off funding to Planned Parenthood.” Mostly, though, we hear from Dawn (“I think Mitt Romney would definitely drag us back”) and Alex (“This is not the nineteen-fifties”).

Unsurprisingly, the history of Planned Parenthood and its relationship to the Democratic and Republican parties, as I wrote about in the magazine last year, is far more twisted than either of these ads imply. Much has changed in American politics since Planned Parenthood got its start, in 1916, four years before women gained the right to vote. And much has changed since 1952, when votes cast by women carried Dwight Eisenhower to the White House. But, as I remarked in a lecture at the New Yorker Festival earlier this month, something that hasn’t changed is the way political advertisers sell candidates to women voters.

The very first television ad targeted to women was produced by the Eisenhower-Nixon campaign in 1956. It includes footage of a woman supervising her children doing their homework at the kitchen table. It features ordinary women explaining why they like Ike. “So much of our future rests with the women of our country,” the ad’s host insists. But that ad, like every ad targeted to women voters for the last half century, including those made by both campaigns this election season, assumes that women are wholly different species of citizen than men. The political imagination of American women, at least according to American political advertisers, begins with our cervixes and ends at the kitchen door.

“We fixed that,” Obama said last night, talking about pay inequity and Lilly Ledbetter Act. There’s more to fix than that.