Both men believe that their sons should be held accountable for their behavior.
Willie admits to Mister Edward that Mitchell is responsible when he says, "what he done" referring to Mitchell. The consequence for Mitchell is a strapping with a whip. Mister Edward also believes that Paul must be held accountable. In his dialogue, it's clear that he believes Paul deserves a punishment. However, he chooses not to whip Paul. Instead he revokes all of Paul's horse-riding privileges. He says, "you'll never get to ride Ghost Wind again...You won't ride any of the other horses either." Mister Edward believes that keeping Paul from riding the horses will keep him from doing something like this again since he'll remember the consequence and his actions better than if he had been whipped.
I believe the term for this is "peripheral vision."
