Deliberately overlook, ignore, as in
She decided to turn a blind eye to her roommate's goings-on. This expression is believed to come from the siege of Copenhagen (1801), in which Lord Horatio Nelson, second in command of the English fleet, was ordered to withdraw but pretended not to see the flagship's signals to do so by putting his glass to the eye that had been blinded in an earlier battle. His attack led to a major victory. Also see
turn a deaf ear.