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There is a history of political consultants leaving Washington after a tour of duty and heading west, to try their hand at California politics or even Hollywood screenwriting. Two prominent examples of this diaspora are Mike Murphy, a Republican, whose clients included the late Senator John S. McCain of Arizona, and Bob Shrum, a Democrat, a longtime speechwriter for the late Senator Edward M. Kennedy of Massachusetts.

Mr. Shrum and Mr. Murphy, who both live in Los Angeles, are joining forces to create the Center for the Political Future at the Dornsife College at the University of Southern California, where Mr. Shrum teaches. It joins a roster of university-affiliated organizations — the Institute of Politics at Harvard University and the Institute of Politics at the University of Chicago, run by David Axelrod, who was President Barack Obama’s chief strategist — devoted to the study of contemporary politics. The center will recruit players from campaigns and government as fellows, to work with students, and will sponsor conferences devoted to examining American political life.

“Mike and I are doing this together because we are both concerned about the state of our politics,” Mr. Shrum said. “We have been rivals and opponents, but we’ve also been friends. That’s not required of everybody in order to have a healthy democracy, but there at least has to be mutual respect and a commitment to deal with actual realities.”

The center has chosen three inaugural fellows: Dan Schwerin, the director of speechwriting for Hillary Rodham Clinton in 2016; Gentry Collins, former national political director of the Republican National Committee; and Symone Sanders, who served as press secretary for the presidential campaign of Bernie Sanders. Mr. Shrum said he hoped to expand the number of fellows as the center grows.