WASHINGTON – In an ad that appeared on New Hampshire television two weeks ago, an elderly man dumps an armful of pill bottles on the checkout stand of a pharmacy.

He says he’s stocking up before Republican Sen. Kelly Ayotte privatizes Medicare. She wants to turn it into a voucher program that will “cost families big time,” he explains.

Who’s behind the ad? Like more than a third of all ads running in U.S. Senate races this year, it’s impossible to tell.

A study by the campaign finance watchdog Center for Responsive Politics and Wesleyan University’s Media Project finds that a type of political group that does not have to disclose its donors is responsible for $80 million in ads nationally.

That’s 35.8 percent of all advertising in Senate races, according to the study out this week.

Without knowing who is paying for the ads, voters are robbed of “an important clue” that allows them “to take a claim made in an ad with a grain of salt,” said Travis Ridout, a Washington State University political science professor who works with the Wesleyan University project that analyzes campaign donations.

Robert Maguire, a Center for Responsive Politics investigator, said voters should know the identities of those supporting their elected representatives.

“If you, as a voter, are watching an ad about a certain candidate’s stance on environmental regulations, it makes a difference if that ad is funded by a true grassroots organization or if it’s bankrolled by an energy company that has a financial incentive in certain policy outcomes,” Maguire said.

“And once that candidate is in office, constituents have the right to know if their representative is swayed by the funders who helped him or her get there,” he said.

In 2012, candidates paid for two-thirds of the ads in their Senate races. This year, candidates are behind only one-third of the advertising, as voters see more messages from outside groups, the study found.

A Bloomberg poll last year found 78 percent of those surveyed — including large majorities of Democrats and Republicans — favor repealing a 2000 Supreme Court decision that gave rise to unlimited spending by outside groups, including those not required to disclose their donors.

Benefactors of dark-money ads — including Ayotte, her Democratic opponent Gov. Maggie Hassan, and Democratic Pennsylvania Senate candidate Katie McGinty — have condemned the growing influence of money from political groups.

Yet, none this week would condemn the dark-money ads doing their work for them by attacking their opponents.

The $2.4 million anti-Ayotte Medicare ad was funded by a liberal political group, Majority Forward, according to the Center for Responsive Politics. As a registered non-profit, the group does not have to say where it raises its money, as long as its ads do not expressly say whom to vote for, or whom not to vote for.

The anti-Ayotte ad — and a nearly identical ad the group ran about Senate Majority Leader Mitch McConnell, R-Kentucky — only tell viewers to let the senators know “not to privatize Medicare” and to “stand up for seniors.”

But, rather than simply being concerned about that issue, Majority Forward says on its website that it is affiliated with the Senate Majority PAC “to elect candidates whose policies represent the goals of the majority of Americans who want to move our country forward.”

The Senate Majority PAC’s website says it is working to take back the Democratic majority in the Senate.

Ayotte, according to a running tally by the campaign watchdog, also benefits from groups that do not disclose their donors, including $1.5 million spent by the U.S. Chamber of Commerce against Hassan.

In all, outside groups — including those that do and do not disclose donors — have spent $20 million to help Ayotte, and $13 million to help Hassan, according to the Center for Responsive Politics.

Dark-money ads are playing a role in the closely watched Pennsylvania Senate race, as well.

Americans for Prosperity, which does not identify its donors, has spent $1.1 million against McGinty, according to the watchdog group.

It ran a television ad last week criticizing her for giving grants and tax breaks to renewable energy companies while serving as the state’s environmental secretary. Some of the companies closed without providing the jobs they promised.

McGinty, meanwhile, has benefited from $2.5 million worth of ads placed by Majority Forward that target her opponent, incumbent Republican Sen. Pat Toomey. The group has run ads about Toomey’s “love affair with Wall Street” and his anti-abortion positions.

All told, outside groups – including those that do not disclose donors and the political committees that do – have spent $27 million on behalf of Toomey and about $20 million to support McGinty, according to the Center for Responsive Politics.

McGinty has criticized the Supreme Court’s Citizens United decision allowing corporations and unions to spend unlimited amounts of money advocating for the election or defeat of a candidate.

McGinty’s campaign spokesman, Josh Levitt, did not respond when asked about the ads that Majority Forward is running against her opponent. He said only, “Katie supports overturning the Supreme Court’s Citizens United ruling that allows this out-of-control spending to happen, and she supports ending the ability of special interests to spend unlimited and undisclosed funds in elections.”

Toomey’s spokesman, Steve Kelly, did not respond when asked about anti-McGinty ads placed by groups that do not disclose donors. He pointed to a Philadelphia Inquirer story saying Toomey has opposed limits on campaign donations as restrictions on free speech, but he favors more disclosure of donors.

In New Hampshire, Ayotte and Hassan have proposed different versions of a pledge to limit outside money in their Senate race. Each has attacked the other for not signing the pledge.

“Corporate special interests have spent more than $40 million dollars to support Kelly Ayotte’s campaign because she votes for their agenda in Washington,” said Hassan’s spokeswoman, Meira Bernstein. She said Ayotte has refused to sign Hassan’s proposal.

Asked about the ads being run on Ayotte’s behalf, the senator’s campaign spokeswoman, Liz Johnson, also pointed fingers.

“Gov. Hassan could have kept third-party special interests out of New Hampshire” by signing the pledge,” she said. “But she refused, and now her Washington allies have now spent more than $20 million on her behalf just this year … Hassan wanted these negative ads and millions in third party special interest money to flood New Hampshire.”

Kery Murakami is the Washington, D.C. reporter for CNHI’s newspapers and websites. Reach him at kmurakami@cnhi.com.