Brooks Kraft / Corbis for TIME Republican presidential candidate Mitt Romney and his vice-presidential candidate Paul Ryan campaign in Lancaster, Ohio, on Oct. 12, 2012

As his standing in the polls improves, Mitt Romney is piling up public endorsements from a new cohort of voters: the celebrity-train-wreck set.

The latest celebrity to climb aboard the Romney bandwagon is actress and Page Six piñata Lindsay Lohan. “I just think employment is really important right now,” Lohan said. “So, as of now, Mitt Romney.” She joins Clueless actress Stacey Dash, wrestler Hulk Hogan and adult-film star Jenna Jameson on the Celebs for Romney booster squad. How much does this matter? Narrowly speaking, not at all. None of these people live in competitive states, it’s unlikely their opinions will sway a soul, and wealthier people tend to vote Republican anyway based on their economic self-interest. (If you don’t buy those charts, take it from Jameson: “When you’re rich, you want a Republican in office.”)

But the celebrity migration to the Romney camp, as Walter Hickey of Business Insider noted, may be a symptom of a potentially serious problem for Barack Obama: an indication that so-called low-information voters, many of whom supported Obama in 2008, will abandon the President’s re-election bid. The conviction that undecided voters will break late against the incumbent has always been a pillar of the Romney campaign’s strategy.

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In political handicapping, the belief that voters who remain undecided late in the race ultimately swing toward the challenger is known as the “incumbent rule.” The soundness of the theory is up for debate. The incumbent rule was broken in 2004, when George W. Bush and John Kerry split undecided voters fairly evenly. But the demographics of this year’s group of undecided voters may in fact favor Romney. One survey jointly conducted by one Democratic and one Republican pollster for the Wall Street Journal/NBC News found that of voters considered “up for grabs” — either undecided or leaning slightly — 68% are white, 53% are male, and 60% disapprove of Obama’s performance.

Which isn’t to say Romney can count on undecided voters breaking his way. UCLA political scientist Lynn Vavreck has been tracking a large group of uncommitted voters since December 2011. As they’ve made up their minds, those voters have gravitated in roughly equal numbers to Romney and Obama. Obama “has the advantage among undecided voters who are making choices as Election Day draws near,” Vavreck wrote recently.

Regardless of where you sit on the political spectrum, there is reason to lament the attention lavished on a relatively tiny cadre of undecided voters, many of whom are ambivalent or indifferent because their grasp of the facts is hazy. Ezra Klein wrote recently about a Saturday Night Live bit that lampooned undecided voters. “We’re not impressed by political spin and 30-second sound bites,” says one of the skit’s actors. “Before you get our vote, you’re going to have to answer some questions. Questions like, ‘When is the election?’ ‘How soon do we have to decide?’ ‘What are the names of the two people running?’ ”

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This satire is laced with kernels of truth. There are, of course, plenty of intelligent and engaged voters who have studied the candidates’ positions and remain genuinely torn. But the bulk of undecided voters are undecided because they are not trying very hard. The vast gulfs between Obama and Romney — on taxes, social-welfare programs, the budget, energy, immigration, abortion and so forth — are so pronounced on so many policy issues that it seems difficult for an informed voter to struggle with his or choice. As Newsweek‘s Michelle Cottle writes:

Ask the political scientists, pollsters, and other professional analyzers of the electorate who parse these sorts of things. They will tell you — as they have told me repeatedly over the years — that undecideds or swing voters or whatever you want to call them tend to be low-information folks who cast their ballots based on whichever candidate gives them the last-minute warm-and-fuzzies.

Take, for example, another celebrity Romney fan whose endorsement caused a hullabaloo recently. Buzz Bissinger is the author of Friday Night Lights and a native, he wrote in his endorsement, of the nation’s “nexus of liberalogy,” [sic] the Upper West Side of Manhattan. “There is a part of me that feels like a traitor,” Bissinger wrote, in a kind of hyperbolic confessional designed to imbue his opinion with the gravitas of the converted. “I fear that I will lose friends, some of whom I hold inside my heart.” And yet there he was, bravely risking the wrath of his wife and the brie-and-Chardonnay set by outing himself as a Mitt Romney supporter.

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So how did Romney win him over? In sum, he spoke faster at the debate in Denver. “Romney did not simply act like he wanted to be president. He wants to be president,” Bizzinger said, with no evidence at all. “He showed vigor, and enthusiasm, and excitement, a man who wants to lead.” And Obama? He “dipped into the podium as if avoiding the smell of something rotten, acting above the very idea that a debate does provide a pivotal referendum on his first term,” Bissinger wrote. “I am not sure Obama really wants to be president in any practical way.”

This is the kind of trenchant analysis that moves undecided voters toward a candidate. Mocked for the flimsiness of his logic, Bissinger penned a follow-up piece to defend himself against an onslaught of criticism that dubbed him a classic l0w-information voter. His retort? “I spend five to six hours preparing for [a radio show] each day and do nothing now but read politics from a variety of differing viewpoints,” he wrote. “I may be a misinformed voter but I am not a low-information one.” Misinformed or ill informed, this is the type of voter that both sides need to win.

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