partial orders and arenas

 When I first learned about partial orders I was confused and did not see where this would be useful. It was introduced in the realm of numbers. Many years later, I love the idea. Arenas are everywhere. A user sees 20 items. He selects one. Again and again. A partial order emerges. 

Note: This assumes that humans are perfectly rational, which is wrong, the intuition still holds and we can use proper methods in practices.