Why did Shlomo say "this one says the live baby is mine, and the dead baby is yours, and this one says no, rather, the dead baby is yours, and the live baby is mine"?
Radak citing Yerushalmi Sanhedrin 3:8: This teaches that the judge must repeat 1 the claims of the litigants, so they will know that the judge understood their claims and will judge according to them.
Abarvenel: The claimant said many matters (she took my baby?) Shlomo said, since there are no witnesses, your words do not help. We are left only with your claims - this one says, the live baby is mine?
Malbim: The women repeated this. Granted, perhaps the first time, she said first her primary proof. However, after this, she says what she wants to obtain via the judgment. The one who said first "the dead baby is yours", this was her objective; she did not really want the live baby, for it was not hers.
Kli Yakar: In Shochar Tov, it says 'Lishkol Ta'anosiehm Binfei Sheneihem.' I.e. even if the judge senses who is correct based on their claims, he must make it seem to them that their claims are equal, lest afterwards the 'loser' think that his opponent flattered the judge, and from the beginning he favored him. (Our text of Shochar Tov 72:2 and Devarim Rabah 5:6 is like the Yerushalmi; the text of Yalkut Shimoni 175 is like Kli Yakar says. -PF)
