Solomoronic?

According to legend, when King Solomon was confronted by two women who both claimed to be the mother of an infant and begged Solomon to decide the matter, the king displayed his legendary wisdom by decreeing that, since it was impossible to determine the true mother's identity, the baby should be sliced in two and distributed equally between the plaintiffs.  The actual mother thereupon immediately renounced her claim, imploring Solomon simply to give the baby away rather than kill it.  The "Judgment of Solomon" has since become an exemplary tale of executive wisdom.

In Solomon's defense, there were no CSI-style DNA labs in ancient Israel, so a certain degree of improvisation was called for.  But this strategy has always struck me as somewhat questionable.  I mean, do you suppose the king was actually joking?  "Hey, guys, if you don't stop bickering, I'm just gonna chop the baby in half, OK?"  And while Solomon could certainly expect a mother to object to the violent slaughter of her own baby, what kind of uncivilized hellscape was he presiding over that he would expect the other woman to so casually accede to attempted infanticide?

If I were Solomon, I would be all like, "OK, not only do YOU (woman who protested) get the baby, but YOU (woman who was going to go along with it) need to check yourself into a mental hospital!"  Or, whatever passed for mental hospitals back in those days.  Cappadocia, maybe, I don't know.