In book 12 of The Odyssey, Odysseus is forced to make a decision between passing by Scylla, a horrible six-headed sea-monster, or Charybdis, a giant whirlpool. Circe, the witch, tells him privately that
No mariners yet can boast they’ve raced their ship
past Scylla’s lair without some mortal blow —
with each of her six heads she snatches up
a man from the dark-prowed craft and whisks him off.
However, she nonetheless advises him to steer nearer to Scylla's cave, risking the deaths of six of his men, rather than to move too close to Charybdis and risk his "'entire crew.'" Odysseus still hopes that he can fight Scylla and prevent his men's deaths, but Circe assures him that Scylla is "no mortal," and there is "no fighting her, no defense— / just flee the creature, that's the only way.'' Then, once the ship has passed Scylla, Odysseus and his men must not harm the cattle belonging to the sun god on the island of Thrinacia. If the men "harm them in any way," their ship and lives will all be destroyed. Odysseus tells his men about the danger presented by the sirens as well as the danger presented by Helios's cattle, but he makes
No mention of Scylla—how to fight that nightmare?—
for fear the men would panic, desert their oars
and huddle down and stow themselves away.
Scylla does, indeed, eat six of Odysseus's "toughest, strongest hands" on deck. In short, Odysseus decides the fate of six of his men by not deciding much of anything (other than to draw nearer to Scylla than Charybdis; to risk some and not all). The lots of all his crewmen, himself included, are cast together, but Odysseus withholds life-and-death information from them in order to maintain his leadership of them.
The "semi-barbaric king" in "The Lady or the Tiger?" also leaves a certain amount of decision-making up to fate and withholds life-and-death information from those accused law-breakers he subjects to treatment in his arena. The narrator describes it:
This vast amphitheater, with its encircling galleries, its mysterious vaults, and its unseen passages, was an agent of poetic justice, in which crime was punished, or virtue rewarded, by the decrees of an impartial and incorruptible chance.
Once the accused person enters the arena, he must choose between two identical doors. He must open one, whichever one he prefers, and "he was subject to no guidance or influence but that of the aforementioned impartial and incorruptible chance." Behind one door waits a hungry and vicious tiger; behind the other waits a perfect bride, chosen specifically for the accused person. His punishment or reward, then, depends on his choice, and his choice depends upon chance. Likewise, Odysseus did not seek to protect certain men from Scylla; they all were subject to the same risk, the same chance that Scylla would gobble them up. Obviously, information about which door hides the bride and which door hides the tiger is withheld from the prisoner, and the king manages to maintain a tenuous "innocence" because the prisoner has the "whole matter in his own hands." This king maintains his leadership, then, by withholding crucial information from his subjects and then leaving their fates up to chance; Odysseus, similarly, maintains his leadership by withholding crucial information from his crew and leaving their fates up to chance.