People cheer as Sen. Ted Cruz (R-Tex.) is declared the winner at the caucus-night gathering at the Iowa State Fairgrounds on Monday in Des Moines.  (Christopher Furlong/Getty Images)

Allegations of dirty political tricks in Iowa are flying.  Donald Trump is tweeting about little else.

The Washington Post’s Philip Bump summarized the dust-up: “Trump referred to Cruz’s campaign having emailed voters during the caucuses implying that Ben Carson was dropping out of the race. That email was excoriated by Carson in his statement on Monday night, and Cruz’s team copped to it on Tuesday.”

So Trump and Carson are suggesting that misinformation about Carson’s withdrawal may have caused some Carson supporters in Iowa to vote for Cruz instead.

Here’s the question that political observers are pondering: Could this episode hurt Cruz or even benefit Trump? Our new research can shed some light.

In a perfect world, voters would disapprove of dirty tricks on the campaign trail. Trump’s behavior implies this view. He seems to think that the more he talks about Cruz’s email, the worse Cruz will do going forward.

However, a great deal of research points in a different direction. This research demonstrates that, unsurprisingly, voters often process information in a biased way. We interpret new information in a way that allows us to maintain the opinions we already have.

If this is true, then Cruz supporters will likely shrug off the incident as untrue or as justifiable hardball. People who don’t support Cruz would tend to be more offended.

Another scenario is really the worst case — one in which Cruz’s dubious email makes Carson supporters feel so alienated from politics and its dirty tricks that they disengage entirely.  This would amount to a perverse reward for cheating. In short, the misdeed demobilizes your opponent’s supporters.

We investigated these scenarios in a forthcoming article in the journal Political Behavior. In our study, survey respondents were exposed to a news story about a dirty campaign trick — either stealing yard signs or making phone calls that contained misleading information about when the polls were open. The party of the perpetrator was varied at random.

When asked their opinions of the dirty trick, voters were pretty biased. If it was your party that perpetrated a dirty trick, you were far less offended than if the opposing party had done it. This implies that Cruz supporters and supporters of other candidates, such as Carson or Trump, will react very differently to the allegations.

But the silver lining in our research is that people’s overall trust in government didn’t change even when they read about dirty tricks. In other words, we find no perverse public-opinion reward for dirty tricks.

So Cruz supporters will probably shrug it off, no matter how much Mr. Trump tweets about dirty tricks. Meanwhile, the irritation Carson supporters experience probably will not alienate them from the political system.

On the whole, the lack of a public-opinion penalty for perpetrators of dirty tricks is probably bad news for those that hope for cleaner politics. It’s also a good explanation for why dirty tricks persist.

Ryan L. Claassen is associate professor of political science at Kent State University and the author of Godless Democrats and Pious Republicans? Michael J. Ensley is associate professor of political science at Kent State University.