US President Barack Obama shakes hands with Republican presidential candidate Mitt Romney on October 22, 2012 at the start of the third presidential debate. (SAUL LOEB/AFP/GETTY IMAGES)

The president is having Mitt Romney over for lunch today. What will transpire over clinking china and awkward silences is anyone’s guess. Will there be anything more than exchanged pleasantries? The start of discussions about a job for Romney in an Obama administration? Some kind of real friendship between the two rivals?

I doubt there’s much chance of the last two. Obama and Romney had a clear dislike for each other on the campaign trail, and, whatever tradition may state, there’s little evidence many presidential rivals go on to be friends. That’s especially the case when the loser is not a defeated incumbent. When both men have been president, as in the case of Jimmy Carter and Gerald Ford who went on to become lifelong friends, their egos start with more equal footing, however bitter the fight may have been.

Still, despite the brutal campaign and the remote relationship the two appear to have, Romney does have something to offer the president, even if it is simply ideas for the country rather than an actual role in the administration. He is noted for his “legendary appetite” for data, his turnaround skills and his standing in the business community. As a result, wasting the lunch by making it little more than a photo opp is not the answer, either. As the elected leader, it is Obama’s obligation to put substance on the menu.

First, as the host, he should try to defuse the setting as much as he can. When Romney walks through the White House’s historic halls and sits across from the president in his dining room, it will be hard for him not to fixate on what might have been. I can’t help but wonder if they should have met a more neutral setting—a private club, perhaps, or the home of a nonpartisan friend of both men—that would have put Romney more at ease, though the logistics would have been tremendous. Since the lunch will be in the private dining room of the White House, keeping it as informal as possible would help. Too bad they can’t start off with a beer.

Next, he should focus the discussion on ideas rather than roles, future jobs or the past campaign. The president has said Romney “presented some ideas during the course of the campaign that I actually agree with,” and that “there are a lot of ideas that I don’t think are partisan ideas but are just smart ideas about how can we make the federal government more customer-friendly.” If indeed there is a job for Romney to do in an Obama administration—which, again, seems unlikely—it’s not the time to start talking about it quite yet. Instead, the president should first try to improve the relationship by finding common ground and talking up some of Romney’s ideas. There are few better ways to build relationships than by offering sincere praise.

Finally, the president should seek Romney’s advice. This may seem contradictory, given Romney appears to be persona non grata to Republicans already and has become the stuff of jokes by some former supporters. But again, there are few better ways for leaders to bridge their divide with former opponents than by soliciting their thoughts. It shows humility, appreciation and respect. What does Romney think will help negotiations in the fiscal cliff? What does he think is the single worst contributor to partisanship in Washington? Were there any advisers he met on the trail who might be willing to work in a bipartisan fashion?

Romney may stand the most to gain from today’s lunch at the White House. His last public impression, some have noted, was the bitter-sounding leak about “gifts.” But as the president, it is Obama’s job as a leader to try to gain something from the meeting, too.

Jena McGregor is a columnist for the Washington Post’s On Leadership section.

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