Now new research illuminates a key source of partisan animosity: Our internal pictures of the opposite party are terribly inaccurate. When asked about the groups historically associated with each party, we think these groups make up a vastly larger fraction of each party than they really do. In other words, we think each party is essentially a huge bundle of stereotypes — and this tendency is particularly pronounced when we’re characterizing the opposite party.

The research, by political scientists Doug Ahler and Gaurav Sood, can be tidily summarized in this graph. It shows people’s average guesses for what percentage of each party is in each group, as well as the true percentage.

On average, Americans thought that 32 percent of Democrats are gay, lesbian or bisexual. The correct answer is 6 percent. And they thought that 38 percent of Republicans made more than $250,000 a year. The correct answer is 2 percent.

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It goes on from there. Americans overestimate the percentage of Democrats who are black, union members or atheists. They overestimate the percentage of Republicans who are seniors, evangelicals or Southerners.

These misperceptions are even worse when people are evaluating the opposite party. Democrats overestimate the fraction of Democrats who are union members by 25 points. Republicans overestimate it by 34 points. Republicans overestimate the fraction of Republicans who are wealthy by about 30 points. Democrats overestimate it by about 40 points.

Depressed yet? It gets worse:

You might think that these misperceptions are concentrated among people who generally ignore politics. It’s the opposite: People who pay attention to political news have worse misperceptions in almost every case.

Giving people money if they got the answer correct didn’t make estimates any more accurate.

Telling people the overall percentage of Americans in each of these groups — which you might think would help people figure out the percentage of Democrats and Republicans in these groups — actually made misperceptions worse.

Moreover, these misperceptions matter. Ahler and Sood conducted experiments in which some people’s misperceptions were explicitly corrected. After being given correct information, people had more favorable views of the other party and were less likely to see it as ideologically extreme.

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This study tells us something crucial about what partisanship means and has always meant. When we hear “Democrat” or “Republican,” we often think about who that party is. That is, we associate certain racial, religious and social groups with each party — often the same ones that we have for decades. Knowing which of those groups we like in turn helps us choose a party.