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Mr. Gallegly, 67, in a prepared statement issued by his office last week, didn’t mention redistricting as a reason for stepping down, instead saying he and his wife decided “now was the right time to begin the next chapter in our lives.”

“There’s a lot of uncertainty and potential expense involved, and my guess is that several of these people in their 50s or 60s took a look at that and said, ‘I don’t need that trouble,’ ” Mr. Cain said.