This is sometimes called splitting the baby. A less lurid, but more accurate, synonym is split the difference. The original story was about an ostensible compromise so horrible that it was really a ploy to test who cared the most, but the meaning has changed over time—and not everyone accepts the newer usage.
The story from the Hebrew Bible (1 Kings 3) goes that two prostitutes both claimed to be the mother of the same baby boy, and King Solomon was called to judge the case. He ordered that the baby be chopped in two, and each woman get half. The legend says that one woman begged that he let her baby live, even if she couldn’t keep him, but the other then told Solomon she’d rather he killed the baby than let the other woman have him. Solomon then declared that the woman who tried to save the baby must be the real mother.
In the slang of American lawyers, though, it’s come to mean something different: if a negotiation is stalled, and the two parties cannot agree on a fair amount of money, but they both agree that it’s somewhere within a certain range and want to come to an agreement quickly, a “split-the-baby” negotiation is one where they meet exactly in the middle, whether that makes any sense or not.
A minority opinion is that “split the baby” should only be used like in the original story, as an alternative that’s so bad for both parties that it forces them to negotiate a better compromise. To those people, if the mother of the bride wanted to invite a hundred people and the groom’s family only wanted to invite fifty, inviting seventy-five would be “splitting the difference” but they would not call it “splitting the baby.” Proposing to make both families travel to Kansas because the bride and groom can’t decide between New York and California might be “splitting the baby” even to them, but only if it’s such a bad alternative that it’s supposed to motivate them to back down, and then they don’t.