Shootout at the Candidate Corral

By Jim Tankersley

Consider, if you will, a deceptively political question: Three sharpshooters step outside at high noon. Each has a gun and a single bullet. Only one heads back to the ranch alive. So -- who shoots whom?

In game theory, the scenario is called a "truel," a duel with three participants. In politics, it's called "the 2008 Democratic primary."

The shots are now flying furiously on the presidential campaign trail as the calendar shows five weeks to the Iowa caucuses. After months of relatively genial politicking, the candidates are in effect choosing their enemies -- deciding whom to strike and how hard.

Game theory -- a branch of mathematics that examines the smartest choices for people in strategic situations -- can help explain who's blasting whom, and why. The Democratic primary, for example, has a classic truel look to it, said Steven Brams, a professor of politics at New York University and the author of several books and papers on game theory including "The Presidential Election Game."

Target: The top gun

One variation of a truel pits one deadly accurate shooter against two others whose aim is less true. In that case, Brams said, the math suggests the two less-accurate shooters should both fire at the top gun -- or in political terms, as Brams puts it, "get rid of the most prominent candidate and then worry about each other."

Hillary Clinton, Brams said, started the fall as the sharpest shooter in the Democratic field. So it's no surprise that her two leading rivals, John Edwards and Barack Obama, have trained their fire on her almost exclusively.

The Republican field is harder to sort out, largely because there are so many top contenders. It's tough to call any of the candidates the strongest. Rudolph Giuliani leads national polls. Mitt Romney leads in New Hampshire and is formidable in Iowa, where recent polls showed Mike Huckabee gaining fast.

During a Republican debate this week, Giuliani and Romney tangled repeatedly; Romney attacked Huckabee; Fred Thompson criticized Huckabee, Romney and Giuliani; and John McCain jabbed Romney and Ron Paul.

The Republican field's quick shifts mean that voters are seeing different attack combinations almost daily. If they appear random -- why, you might ask, would Romney hit McCain on immigration in an Iowa mailing in late November? -- political communication pros suggest thinking about this question: Which voters is each candidate trying to win, and how to get them?

Consider Huckabee, who is surging in Iowa by rallying social conservatives. "If I were Gov. Huckabee, I would make sure that the voters in the Iowa caucuses know Mitt Romney's many and varied positions on abortion and that Rudy Giuliani is pro-choice," said Tim Dickson, a Virginia-based Democratic political consultant. "Because the caucusgoers Huckabee is talking to are not pro-choice."

On the Democratic side, he continued, Clinton could be looking to score with older voters when she criticizes Obama's health-care plan for leaving millions of Americans uncovered.

Sometimes candidates attack just to stop a rival's momentum, which would explain Romney's rip on Huckabee this week. And sometimes not attacking is the best strategy.

Firing into the air

In a truel, the shooter who fires into the air could watch his rivals kill one another. Think Iowa 2004, when Howard Dean and Richard Gephardt nuked each other on television and watched John Kerry scoot past them both.

Candidates know voters often punish the perpetrator of attacks, so they take pains to look innocent even when they go on the offensive. Asked recently why he was breaking his pledge to stay positive in the campaign, Giuliani replied, "It's because they criticized me. Notice I haven't criticized anyone who hasn't criticized me."

Still, count on voters complaining about negativity. The game theorist has a solution for this too. In multicandidate elections, Brams would let people vote for as many candidates as they deem acceptable -- creating, he said, an incentive for everyone to play nice.

"Negative campaigning is probably our biggest problem today in multicandidate races like primaries," he explained. "You win by attacking others."