Republican presidential candidate Mitt Romney (R) and U.S. President Barack...

Republican presidential candidate Mitt Romney (R) and U.S. President Barack Obama greet each other following the third presidential debate at Lynn University in Boca Raton, Florida. (Oct. 22, 2012) Credit: Getty Images

The stage may have been in Boca Raton. The contest may have been broadcast worldwide, but both presidential candidates spent their last debate Monday night playing to the same crowd: Suburban women in Ohio, Florida and other so-called "war" states, where votes are still up for grabs in the close race.

The debate between President Barack Obama and Republican Mitt Romney at Lynn University was supposed to be about foreign policy in a mean, scary and much-too-often cruel world. But at every opportunity Romney and Obama made their pitch to a smart, sensible demographic that pollsters say prefer peace to war.

"We can't kill our way out of this mess," Romney said early on in response to a question about the Middle East and the changing face of terrorism.

What else would he do as leader of the free world? "Well, my strategy is pretty straightforward," Romney said. "I'd go after the bad guys . . . " He'd also help the Muslim world gain better education and "gender equality," Romney said.

Obama picked up some of the same threads a few minutes later. "We do have to make sure that we're protecting religious minorities and women because these countries can't develop unless all of the population -- not half of it -- is developing."

Both candidates worked hard to convey that they want to give peace a chance -- no small thing for women voters who, experts say, rightly cringe at the notion of sending their children off to war.

"We want a peaceful planet," Romney said in answer to a question about how he would have handled the crisis arising from former President Hosni Mubarak's treatment of his countrymen in Egypt.

"We want people to be able to enjoy their lives and know they have a bright and prosperous future and not be at war," Romney said. "That is our purpose."

The nation's purpose also is to help young people who rose up against Mubarak, according to Obama.

"The notion that we would have tanks run over those young people who were in Tahrir Square, that is not the kind of American leadership that John F. Kennedy talked about 50 years ago," Obama said.

At one point, the debate veered off onto a 10-minute discussion of education policy and teachers. "Let's get back to foreign policy," moderator Bob Schieffer said.

The candidates did, agreeing more than disagreeing on Egypt, Afghanistan, Iran, Syria, Israel and China.

But on almost every point, Obama and Romney veered back home, talking about restoring the economy, keeping the nation safe, ensuring that the U.S. remains a world leader, bringing back American jobs and taking care of U.S. veterans along the way.

Did the final debate firm up either candidates' base? It's hard to imagine that the notions of world peace or building gender equity in the Middle East would light a fire under some voters in either camp.

But smart, suburban women? Gender equity's just fine. The prospect of world peace? That's even better.