follow a middle course
To compromise between two extreme or polarizing alternatives; to find a solution, policy, or course of action that is acceptable or agreeable to two different or opposing sides. The small sovereign nation has gotten along for years by following a middle course between the two global superpowers on either sides of its border. The president's popularity among the more extreme members of his party was diminished by his attempts to follow a middle course with some bipartisan policies. Well, that's an unpopular view. If you want to win over independent voters, you really ought to follow a middle course.
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