@Inkan1969  
Theory: Equestria’s system of government is a kind of Federated Monarchy. Towns and cities are governed at the regional level by elected officials, who serve as advisors to the monarchs, who exercise ultimate power over decisionmaking for the country in general. Each elected official serves as a representative for their respective township in the royal court, which has at least some say over the way things are run, similar to how a senate functions.
 
Or if you want to be cynical, elected officials don’t actually do anything in Equestia, and are simply there to placate anypony who doesn’t feel represented and act as scapegoats when the princesses screw the pooch.

The elected official can’t do a thing without help from royalty.

@Artie downer  
We hardly see the mayor at all.

Huh, we don’t see these two together that often

MAYOR SCRUNCHYMARE :D

Whenever the Mayor makes an appearance, I smile.