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Female staffers adopted a meeting strategy they called “amplification”: When a woman made a key point, other women would repeat it, giving credit to its author. This forced the men in the room to recognize the contribution — and denied them the chance to claim the idea as their own.

“We just started doing it, and made a purpose of doing it. It was an everyday thing,” said one former Obama aide who requested anonymity to speak frankly. Obama noticed, she and others said, and began calling more often on women and junior aides.

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