This is not so much a political map as much as it is a cultural and religious one. Notice the ones that both allow and like to practice Corporeal Punishment are the old Southern States. The ones that allow it, but don't practice it so much are the cowboy states. The culture in both values toughness and self sufficiency. More than that there is a belief that physical discipline is the only way to get through to a misbehaving kid. The Republican Party nowdays can count on the votes from these places because they have been espousing their cultural values.