Mayoral elections at Michel Delving
 

We know that the Mayor of the Shire was elected every 7 years at Michel Delving. But we also know that many Shirefolk didn't travel much out of their own immediate locality. For example, if a hobbit lived in Stock, Rushey or Sarn Ford, these were considerable distances from Michel Delving. And surely it would have been impossible for every hobbit of voting age to travel to Michel Delving anyway?

So did the Shire have a postal voting system? Or was the Mayor a job concentrating on the West Farthing, with the Thain having authority in the middle of the Shire and the Master of Buckland controlling the east?

From what was described in the appendices and in the Scouring of the Shire, the Mayor was a somewhat casual, yet prestigious position. I think everyone would just choose who they thought was most suited for the job, and they'd be made mayor.

I think it was mentioned that the Mayor was elected at the Free Fair, so I would imagine that it would be the attendees who would cast their votes.

As Tar-Jêx said, Mayor was largely a ceremonial position anyway, so I don't think their was much concern among hobbits who didn't make it to the Fair.

Even though it's basically just a title, it would still be comforting with someone like Samwise as the mayor. That really is the entire point, just to be able to say you have a wonderful person, and a hero, as the mayor.

Probably. An appreciation of food beyond that of ordinary Hobbits seems to be an office requirement too, since old Will Whitfoot apparently needed to regain some weight after being a prisoner of Sharkey's men. Sam Gamgee had the necessary qualification. ;)