UPDATE: I propose another possibility. The sorting is based on the hats you have unlocked.
EDIT: Not all of the leader boards have the same ordering. But it is consistent for a particular leader board. There is an order.
Unsure of the reasoning behind the order but here is what I have figured out (may be some out of order near the top but I can't tell based on the leader board at the moment) from left to right on the leader board listing:
- I Do Say So
- Brundhilde
- Witticism
- Yakety Stacks
- Bushido
- Gotta Catch em All
- Moshi Moshi
- Yer a Wizard
- Shiver Me Timbers
- Spoiler Alert
- Bushido
- La Margritte
- Git R Done
- Jammin Out
- Soup de Jour
- Cat on the Hat
- Constantinopolitan
- My Dear Watson
- Cheddar Head
- Just Jesting
- Howdy Pardner
- Copacabana
- Where is He!?
- Cake is Not a Lie
- The Abby
- Gangnam Style
- A Need for Speed
- Guide my sleigh
- n00b hat
- I Feel Fine
- L'chaim