U.S. Republican presidential candidate Ted Cruz speaks with attendees at a campaign event in Hubbard, Iowa, January 30, 2016. REUTERS/Jim Young

WATERLOO, Iowa -- A decade ago ago, a trio of political scientists asked voters a powerful question: Why weren't they voting as much as their neighbors? Alan Gerber, Donald Green, and Christopher Larimer -- two professors from Yale and one from the University of Northern Iowa -- wanted to find out whether peer pressure and social norms could drive up voter turnout, so they mailed more than 180,000 Michigan households a letter telling them that they were part of a study, in which other people would find out if they stayed away from the ballot box.

"We're sending this mailing to you and your neighbors to publicize who does and does not vote," read one mailing, accompanied by a chart that noted whether or not their neighbors had cast a ballot.

The letter worked. Political consultants, like Democrat Hal Malchow, found that similar letters in real elections could boost turnout by up to 2.5 percent. In his best-selling book "The Victory Lab," reporter Sasha Issenberg pointed to the "social pressure" experiment as a daring, clever way to bring out a political base. In 2012, MoveOn used pressure-style mailers to turn out progressive votes for President Obama.

Yet today, a similar letter from Sen. Ted Cruz's (R-Tex.) to Iowa Republicans is becoming a mini-scandal. On Saturday morning, Republican strategist and writer Sarah Rumpf found a tweet (now deleted) from Iowa voter Tom Hinkelday, displaying a Cruz mailer meant to look like a "VOTER VIOLATION."

"CAUCUS ON MONDAY TO IMPROVE YOUR SCORE," read the mailer, patterned after a report card, "and please encourage your neighbors to caucus as well. A follow-up notice may be issued following Monday’s caucuses."

Cruz's campaign quickly confirmed the origins of the mailer, even as Cruz endorser and radio host Steve Deace pronounced it fake. And Iowa Secretary of State Paul Pate, a Republican, condemned it.

"Accusing citizens of Iowa of a 'voting violation' based on Iowa Caucus participation, or lack thereof, is false representation of an official act," he said in a statement. "There is no such thing as an election violation related to frequency of voting. Any insinuation or statement to the contrary is wrong and I believe it is not in keeping in the spirit of the Iowa Caucuses."

The mailer even alienated the sort of Iowan who might appreciate it: Christopher Larimer. In a series of tweets, he asked that reporters make it clear he had nothing to do with the Cruz literature.

And in an email, Larimer told the Washington Post that Cruz had taken a good idea and bent it.

"As a researcher who has done randomized field experiments with get out the vote mailings," Larimer wrote in an email, "what I can say is that mailings that call attention to an individual's vote history as well as that of their neighbors' have been shown to be effective in terms of significantly increasing voter turnout. We draw on norm compliance theory which suggests that publicizing behavior regarding a social norm increases the likelihood of norm compliance."

That was if the ad was crafted in a smart way. "The Cruz mailing is more negative than anything we have done and has the potential to elicit a negative response or what psychologists call 'reactance' or 'boomerang effect,'" warned Larimer. "The mailing also states that a 'follow up notice' will be sent following the caucuses on Monday. This is not possible as caucus turnout is private and maintained by the parties."

Cruz, however, had no regrets.

"I will apologize to nobody for using every tool we can to encourage Iowa voters to come out and vote," Cruz told reporters in Sioux City, Iowa. He pointed to a statement from one of his supporters here, former Iowa secretary of state Matt Schultz, who said the mailers are "common practice" and are modeled after 2014 mailers put out by the Iowa Republican Party.

Asked about the mailer at an event in Ames, Sen. Marco Rubio (R-Fla.) said he was puzzled by its intent.

"I had some voters mention to me they were upset about it, obviously," he said. "They had people's names and they gave them an F rating for how they voted. I think a lot of voters are disturbed by it. Again,  it's kind of an unusual way to end your campaign in the state."

Sean Sullivan, reporting from Ames, Iowa, and Katie Zezima, reporting from Sioux City, Iowa, contributed to this story. 

This post has been updated.