Sen. Bernard Sanders had the worst bipartisan record of any senator over the last two years, according to a new study released Tuesday that said Republicans are more eager to work across the aisle, even as Democrats become more reluctant.

Meanwhile Sen. Susan Collins, a Maine Republican up for re-election next year, had the best score, for the third Congress in a row, according to the Lugar Center and the McCourt School of Public Policy at Georgetown University.

And despite three government shutdowns, a completely partisan tax cut and a failed GOP effort to repeal Obamacare, and historic levels of obstruction of presidential nominees, the last Congress was actually more bipartisan, the study concluded.

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Scholars said Republicans, particularly in the Senate, rushed to work with Democrats in writing legislation, in what the academics dubbed a “Trump effect.”

They speculated that while senators were pressured to vote for Mr. Trump’s agenda, they are searching out Democrats to work with on their own priorities.

“Most Congressional Republicans are accepting the president’s major agenda items and declining to criticize him publicly. This helps avoid a primary collision with the Trump base,” wrote Jamie Spitz and Jay Branegan at the Lugar Center. “But simultaneously, the Bipartisan Index shows that Republicans are quietly signing on to bipartisan legislation at a very high rate compared to what parties in the majority normally do.”

The Bipartisan Index eschews voting patterns and instead looks at willingness to co-sponsor legislation with someone from the other party.

The thinking, says former Sen. Richard, is that while party leaders control the issues that reach the floor, and thus can shape voting patterns, working on legislation across the aisle amount to “very carefully considered declarations” of where a lawmaker stands.

“Even as the rhetoric and overall atmosphere in Washington remains partisan, there is an appetite among many lawmakers for bipartisan problem solving,” said Mr. Lugar, who served six terms as a Republican from Indiana before losing in a GOP primary in 2012.

He called Ms. Collins “the gold standard for bipartisanship,” and she touted the study’s conclusions.

“I have long held the belief that Congress produces the best legislation when it listens to a variety of viewpoints and receives input from both Republicans and Democrats,” Ms. Collins said in a statement.

Of 14 bills she sponsored last year, she had at least one Democrat co-sponsor every single one. On six of those bills, she partnered with only one other Democrat. None of them became law.

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Of the 82 bills Ms. Collins signed onto as co-sponsors, nearly 50 were written by Democrats, and five more by Sen. Angus King, her fellow Maine senator, who while an independent caucuses and votes with Democrats.

Ms. Collins was given a bipartisan score of 3.16636 in the index, 19 percent better than runner-up Sen. Rob Portman.

Meanwhile, Mr. Sanders brought up the rear, with a bipartisan score of -2.03193. That was 27 percent worse than the next runner-up, former Sen. Luther Strange.

Also scoring high were GOP Sens. Shelley Moore Capito of West Virginia, Cory Gardner of Colorado and Lindsey Graham of South Carolina. The top-scoring Democrat was former Sen. Joe Donnelly of Indiana, who lost his re-election bid last year.

Of Democrats running for president, Mr. Sanders was the most partisan, but four other senators also had negative partisanship scores. Only Sen. Amy Klobuchar notched a positive score, meaning she was more bipartisan than the average.

In the House, all three Democrats running for president had bipartisan scores.