MONTPELIER — For David Contrada, a board member of the liberal advocacy group “VT Priorities,” the ill effects of Citizens United were writ large last week on the Democratic primary for attorney general.

Save for a nearly $200,000 mass-media campaign launched by a federal super PAC on behalf of Bill Sorrell, Contrada said in a press release last week, the seven-term incumbent would likely have lost to challenger TJ Donovan.

“It is clear that large sums of out-of-state money have already had an effect on Vermont’s elections,” Contrada said. “In Vermont we want our elections to be decided by ideas and values, not dollars.”

In a hard-fought race in which only about 700 votes separated the Democratic rivals, it’s a tempting conclusion to draw. But did the $194,000 expenditure by the Committee for Justice & Fairness really tip the scales for Sorrell?

“That’s just always an amazingly complicated question,” says Bob Biersack, senior fellow at the Center for Responsive Politics, an elections watchdog in Washington, D.C., known best for its “Open Secrets” campaign finance database. “There’s still a debate among political scientists over campaign spending, period, and the relationship between what candidates spend and elections outcomes. And there’s certainly nothing straightforward and linear about it.”

In a study published last month, Brett Gordon and Wesley Hartmann, of Columbia University and Stanford University, respectively, try to ferret out the impact of television advertising in the 2000 presidential race.

Their study of county-level vote shares found “significant positive effects of advertising exposures,” and their conclusion won them more than a few headlines.

“If advertising were set at zero and all other factors held constant, three states’ electoral votes would have changed parties in 2000,” they wrote in their paper, titled “Advertising Effects in Presidential Elections.” “Given the narrow margin of victory in 2000, this shift would have resulted in a different president.”

Biersack, however, says that isolating the impact of advertising in a hypothetical universe where certain variables are set at zero is far different from parsing its effect on real-world elections.

The universe of factors involved in determining winners and losers — name recognition, incumbency, economic trends, etc. — make it incredibly difficult to draw “but for” conclusions” about the role of super PACs, Biersack says.

“Take the presidential primaries, for example,” says Biersack, who, prior to joining the Center for Responsive Politics in 2011, spent 30 years at the Federal Elections Commission, where he specialized in reforming disclosure laws. “In the early days of the Republican race, everybody had their super PAC, and it didn’t seem like (casino magnate) Sheldon Adelson’s millions on behalf of Newt Gingrich were all that effective in gaining votes for him, ultimately.”

However, Biersack says, that isn’t to say that super PACs might not have had outsized influence on the outcome of the Republican presidential primary.

“Maybe super PAC spending on behalf of Mitt Romney that came out and attacked Gingrich and Rick Santorum was effective,” he says. “All those things are possible. All those things are partially true. But being able to say the next $10,000, or $100,000, or $1 million gives you 1 percent or 2 percent or 3 percent, you can’t make that determination.”

Even Gordon and Hartmann concede that the “conclusive evidence of the efficacy of advertising is still quite elusive.”

Sorrell, who has staked out an odd middle ground in the new super PAC landscape — he said he thinks they’re terrible for democracy, but welcomed the support of the one spending on his behalf — wouldn’t hazard a guess as to what would have happened last Tuesday without the Committee for Justice & Fairness.

The group seized on a loophole in Vermont elections law that allowed it to avoid disclosing its donors before the primary. Vermonters won’t know until Oct. 15, the next quarterly filing deadline for federal PACs, who had such a vested interest in seeing Sorrell re-elected.

“I think their ads heightened the general awareness of the fact there was a primary, and I certainly appreciated that they said good things about my contributions as attorney general,” Sorrell said.

The ad featured a voice-over by former Gov. Howard Dean, saying positive things about Sorrell’s record.

“On the other hand, I’m sure it sort of energized the Donovan base, and they were able to play up this whole David versus Goliath thing,” Sorrell said.

Paul S. Ryan, senior counsel at the Campaign Legal Center, a Washington, D.C.-based elections watchdog, says the post-Citizens United era is still in its infancy.

“Super PACs are a very new creature, and the research usually lags considerably behind the advent of new creatures in the political landscape,” Ryan says.

Even in cases when the super PAC-backed candidate wins the race, Ryan says, the PAC shouldn’t necessarily get the credit.

“There’s a very large body of research about candidate spending, for example, and it is certainly the case, and demonstrably so, that the candidate who spends the most money wins,” Ryan says.

“But all that research is pushed back on by others who say that’s because the winning candidates were also more popular and more qualified, and therefore likely to raise more money. When it comes to money in elections, it’s really tough to track the causal effect.”

In the absence of hard evidence quantifying their effect, why all the fuss over super PACs?

“It’s because of that uncertainty, and the potential they have to be shaping campaigns,” Biersack says. “If we’re in a position where a very small number of people or organizations control the dialogue in politics in a meaningful way, then at a minimum we would need to know that.”

Todd Bailey, director of the campaign division at the Statehouse lobbying firm KSE Partners, says money may not guarantee a win, but it certainly improves the prospects.

“The New York Yankees spend more than any other team every year, but they don’t always win the World Series,” Bailey says. “Money certainly plays a role in the electoral process, and to have that much money spent, you would assume in some years there’s going to be an effect on the outcome of the race.”

The Committee for Justice & Fairness — its treasurer hasn’t returned repeated requests for comment — outspent the campaigns of both Sorrell and Donovan.

If the group’s advertising blitz yielded just enough votes for Sorrell to win, then his victory came at a cost of about $310 per vote.