The character trait that Penelope demonstrated when she calls for the suitors to hold a contest is her demonstrating cleverness, like Odysseus does when he tricks and overcomes his foes.
The other character that has a similar trait with Penelope is Odysseus.
In the epic, Oysseus's intelligence or cleveness is highly valued. The goddess, Athena, favors Odysseus because of his intelligence. Penelope demonstrates this trait when she first tells the suitors that she will choose a husband after she has woven a tapestry. She unravels it at night so it is never complete. When they discover her trickery, they demand she choose a husband. To keep them at bay longer, she devises the contest. It is an incredibly difficult feat to shoot an arrow through the ax handles, but it is an acceptable contest because it has been previously completed, by Odysseus.
