Wrong: in medieval times, they “tried” witches by throwing them in a pond. If they floated, they were guilty and burned. If they sank and drowned, they were innocent. Either way you got rid of them!
Better try: no, it was the other way around. If they sank, they were guilty, and if they floated they were innocent.
Correct: in a cold-water ordeal (which in medieval times was rarely used on “witches”; more men were given it than women and it was used more to find facts in earthly crimes than supernatural ones), the verdict was indeed guilty if they floated and innocent if they sank. But they didn’t let them drown. They fished them back out and let them go.
Ninth-century theologian Hincmar of Rheims described the cold-water ordeal
as follows: “[H]e who is to be examined by this judgment is cast into the water
bound, and is drawn forth again bound.” If he is guilty and “seeks to hide the
truth by a lie, [he] cannot be submerged”: he will float (Howland 1901, p. 11).
If he is innocent, he can be submerged: he will sink.
Also, the linked paper presents a more speculative theory about how these kinds of ordeals (and it’s more plausible with the more common hot-water and hot-iron ordeals) could actually have been used to fairly reliably distinguish the guilty from the innocent. (Answer: by creating a “separating equilibrium”.)
I don’t see it – unless we’re positing that criminals believe this method works, and then admits to the crime to avoid being dunked?