Sherwood Boehlert isn’t subtle about his interests. Step into his office in the Rayburn House Office Building on Capitol Hill, and you see two white cabinet doors covered with signatures—one from astronauts who have flown in space and the other from major-league baseball players who have made it into the Hall of Fame.

When Boehlert announced last March that he was ending his 24-year career as the Republican congressman from the New York district that includes the National Baseball Hall of Fame in Cooperstown, political pundits wrote articles in which they worried about the loss of an increasingly rare “moderate” Republican and one of the last “down the middle” players in Washington. In announcing his retirement, Boehlert said he was proud of the moderate label because he believes “that the overwhelming majority of thinking people reject the extremes of the left and the right.”

Although Boehlert spent his career advocating...

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