Now the company has agreed, on behalf of Ailes, to settle Carlson’s suit for a stunning $20 million, according to three people familiar with the settlement. To reinforce their seriousness about creating a new culture in a post-Ailes world, the company is expected to offer Carlson a public apology as part of the settlement. (The company, according to two people familiar with the discussions, has also reached settlement agreements with two other women.)