Democrats thought they had a winning campaign theme in the “war on women.” Yet the president’s fall in the polls among women voters shows this strategy isn’t working. This campaign theme’s failure is a big victory for women.

According to a recent Associated Press-GfK poll, Gov. Mitt Romney is pulling even with President Barack Obama among women voters at 47-47. Just a month ago, Mr. Romney was lagging by 16 points, and Mr. Obama seemed destined to repeat his 2008 performance of commanding 56 percent of the female vote.

The Romney campaign adopted a different strategy to appeal to female voters, aiming to convince women, like all Americans, that Mr. Romney’s preferred policies will improve the economy and that fostering job growth will be his top priority if elected.

Which appeal has succeeded in winning women? According to the Associated Press-GfK poll:

“A month ago, women favored Obama over Romney on the economy 56 percent to 40 percent. Now, the split has shifted to 49 percent for Romney and 45 percent for Obama. Similarly, Obama’s lead among women as the candidate who better understands the people’s problems has narrowed considerably, from a 58-36 Obama advantage last month to a 50-43 Obama edge now.”

For everything we hear in the news about the gender gap Republicans face for women voters, this most recent poll really is incredible.

While Mr. Romney has been offering women a vision of economic freedom, opportunity and prosperity, the Obama campaign has continued to push the tired idea that women are all victims and that anyone who questions further expanding government power is party to a “war on women.”

Such arguments are plainly insulting to women. Rather than treating women as strong, independent individuals, those perpetuating the idea of a “war on women” advocate policies that cast women as helpless without government support. As if this wasn’t bad enough, the other campaign tactic has been to reduce women to their body parts.

The Obama campaign’s troubling depiction of women came into focus earlier this election cycle with the release of the Life of Julia, an infographic detailing how women will supposedly benefit from Mr. Obama’s policies from ages 3 to 67. Website visitors are invited to “take a look at how President Obama’s policies help one woman over her lifetime—and how Mitt Romney would change her story.” In Julia’s life, government is the solution—providing tax credits, student loans, health care, business loans, retirement benefits and more.

This Life of Julia infographic grabbed national headlines because it raised questions about how the Obama campaign viewed women and the relationship between women and the government. At each major stage in her life, Julia is dependent on the government, apparently unable to do things on her own.

Then there was the Obama campaign’s Tumblr, which sought to appeal to women with an image that read, “Vote like your lady parts depend on it.” And most recently, we have a new ad by the Obama campaign, “Lena Dunham: Your First Time,” which compares a young woman’s “first time” with her first time voting.

Is this really what Mr. Obama thinks appeals to women?

Mr. Romney’s approach sharply contrasts with Mr. Obama‘s. The Romney campaign cut an ad featuring women who were Cabinet members while he was governor ofMassachusetts, called “Cabinet Members — Humanity.” There were no celebrities, sexual innuendoes or attempts at peer pressure — just women who had worked hard to reach high levels in their careers.

The difference in ads demonstrates the different visions these two candidates offer for women. One candidate offers a vision of women dependent on government who vote based on their body parts, while the other offers a vision of independent women who make their own choices about careers and family. Based on this poll, it looks like more and more women are choosing the latter. That’s not just good news for Mr. Romney, but for all American women.

Karin Agness is a senior fellow at the Independent Women’s Forum and founder of the Network of Enlightened Women (NeW).