NEW HAMPSHIRE — Over the weekend, media coverage of the Republican presidential race focused on the lack of conflict in Saturday night’s debate, which baffled commentators, and the sharper exchanges in Sunday morning’s debate, which thrilled them. Here in New Hampshire, the Concord Monitor’s headlines changed from Sunday’s “Romney rivals hash it out” to Monday’s “Rivals ramp up criticism”.

Many reporters and pundits seem confused that the other candidates haven’t ganged up on Mitt Romney more aggressively. But there’s a simple explanation, which the Daily Caller’s Matthew Lewis identified: the non-Romneys are stuck in a prisoner’s dilemma. While they might collectively benefit from a joint attack on the frontrunner, each has an individual incentive to defect from such an attack and avoid the resulting damage to his own reputation. It’s far better to let another candidate go negative while you remain above the fray.

Even when the candidates do mix it up on stage, though it’s not clear how much effect their sparring will have on the race. Though debates can sometimes have important consequences (including destroying Rick Perry’s campaign), their importance in presidential primary and general elections is often overstated. However, the format remains enticing to journalists because it (sometimes) creates conflict between the candidates that can be turned into dramatic narratives and “decisive moments.”

But if the debates are unlikely to sway voters, is there a format where attacks can shape the primary campaign? Yes—television advertisements, which are seen by a wider and more diverse group of people than debates. As Georgetown political scientist Jonathan Ladd pointed out on Twitter, negative ads may be especially potent in primary campaigns since voters lack party cues or an incumbent record to vote on, and there are often vast resource discrepancies between rival candidates.

Viewed through this prism, the most significant campaign news of the last few days was not the debates over the weekend, or even today’s New Hampshire primary, which Romney should easily win. Rather, it was the report that a super PAC backing Newt Gingrich will air millions of dollars in negative ads against Romney in South Carolina, the site of the next Republican primary after New Hampshire. But while the media hasn’t ignored this development—the news was reported on the front page of Monday’s New York Times, among other places—it hasn’t yet gotten the broad attention it merits.

Romney remains the overwhelming favorite to win the nomination, but those ads could damage him in a state that is considered more difficult for him to win. More importantly, they raise serious questions about the role that outside spending will play in our post-Citizens United democracy. For both reasons, the coming South Carolina onslaught deserves more coverage than it’s getting.

Brendan Nyhan is an assistant professor of government at Dartmouth College. He blogs at brendan-nyhan.com and tweets @BrendanNyhan.