Throughout the series we see different people get executed via different means. For example:
Lord Ned Stark gets decapitated by Ser Illyn Payne on orders for King Joffrey Baratheon.
Mance Rayder and Shireen Baratheon get burnt at the stake.
Alliser Thorne and Co. get hanged till death.
The question is, how is execution method determined? I know that GRRM is a fan of medieval times and in those times Lords were often decapitated while peasants were hanged.
Are there different execution methods for different crimes? What does Westerosi custom dictate regarding executions of a commoner vs a highborn?