Currently, there are no known politic system. We know Celestia is the ruler of Equestria, but even that is debatable as Celestia never once made any decision beside assigning Twilight Sparkle to live in Ponyville Library, and requests Rainbow Dash and Applejack to finish helping the leave fall.

Mayor in general seem to be the authortic figure in Ponyville. She is seem giving speeches, most are short. 

In our roleplay, Mayor Mare is responsbilte for all regulation and approval at a Town level. 

There is a election scheduled to come up soon, however the detail is not yet available.