Hundreds and perhaps thousands of non-citizens are illegally registered to vote in Kansas, a state that is at ground-zero in the conservative effort to police voter rolls and the liberal campaign to protect them.

The numbers are contained in a new study by Old Dominion University political science professor Jesse T. Richman. He gained fame as the researcher who put a national estimate on the number of non-citizens who register and vote. His contention that there are tens of thousands of illegal Democratic voters angered the liberal media and academia. Some professors signed an open letter blackballing him.

Mr. Richman did the Kansas study as an expert witness for Secretary of State Kris Kobach, the country’s leading elected official in the anti-voter fraud movement.

On Monday, the Republican lost his court case against the ACLU. A U.S. District Court judged ruled that his required proof-of-citizenship to register to vote was unconstitutional. He said he will appeal.

Mr. Kobach suffered another defeat in January. President Trump abolished his White House voter fraud commission co-chaired by Mr. Kobach. The aim was to try to capture an accurate illegal voting number by comparing registration lists with other data points, such as U.S. government rosters of permanent resident Green Card holders and visas.

But Democratic-run states refused to provide voter rolls, information that can be obtained by political parties for get-out-the-vote operations.

Mr. Richman’s Kansas analysis begins with the assumption that 115,550 adult non-citizens live in the state, based U.S. Census figures. From there, he relied on a number of different data sources to extrapolate numbers. Most important is the Cooperative Congressional Election Study (CCES) compiled by a consortium of universities and YouGov pollsters.

Based on actual names on registration lists, he estimates the number of noncitizen registered voters is between 1,202 and 3,813 based on the CCES from 2008 to 2016.

The numbers are much larger when the Richman study relied on surveyed noncitizens who said they were registered to vote.

Using the CCES from 2006 to 2016, the number is 18,488, about 15 percent of Kansas’ non-citizen population.

Mr. Richman told The Washington Times he is now working on new national numbers based on the 2016 CCES and its other surveys.

Mr. Richman’s previous work estimated that from 38,000 to 2.8 million non-citizens voted in the 2008 election won by Barack Obama.

The CCES authors dismissed Mr. Richman’s numbers, saying their analysis showed “zero” noncitizens voted.

There are national polls that tend to support Mr. Richman.

A 2013 National Hispanic Survey found that 13 percent of noncitizen Hispanics said they were registered to vote. That percentage could mean that 800,000 to 2.2 million noncitizen Hispanics are registered, based on U.S. Census Bureau statistics for that demographic, a nonprofit research group told The Times.

There are also examples of non-citizens voting. Anti-fraud groups have obtained voting lists and compared them to other data, such as jury pools where people were excused because they were not U.S. citizens.

The Public Interest Legal Foundation discovered that 1,000 noncitizens registered to vote in six countries and two cities in Virginia. Of them, 200 voted.

“Ultimately, I believe that the debate over fraudulent voting can best advance through a thoughtful exchange of views rather than an attempt to discourage citation or consideration of any study,” Mr. Richman said in a blog responding to his academic critics.

In the proof-of-citizenship case, Judge Julie Robinson rebuked Mr. Kobach, who acted as trial attorney, for not following federal rules of evidence. She ordered him to undergo six additional hours of legal training this year and next.

“It is not clear to the Court whether Defendant repeatedly failed to meet his disclosure obligations intentionally or due to his unfamiliarity with the federal rules,” said Ms. Robinson, an appointee of George W. Bush.

Mr. Trump disbanded his fraud commission last January.

The White House said, “Despite substantial evidence of voter fraud, many states have refused to provide the Presidential Advisory Commission on Election Integrity with basic information relevant to its inquiry.

Rather than engaging in endless legal battles at taxpayer expense, today President Donald J. Trump signed an executive order to dissolve the Commission, and he has asked the Department of Homeland Security to review its initial findings and determine next courses of action.”

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