While the Mayor of Michel Delving may have been the only elected official in the Shire, the Thainship was a hereditary position borne by the chief Took. Originally appointed by the Hobbits as an authority figure to take the place of the King after the destruction of the North Kingdom. As such, the Thain was “the master of the Shire-moot, and the captain of the Shire-muster and the Hobbitry-in-arms.”
As these were rarely needed in the Shire the Thain, like the Mayor, was for the most part little more than a ceremonial position. Indeed, the Hobbit best known for skill in battle prior to the War of the Ring, Bandobras (Bullroarer) Took, was never Thain, with the position passing to his older brother Ferumbras II instead (although his father Isumbras III would have been Thain at the time of said battle, the Battle of Greenfields). The Thain was also referred to as “The Took,” as the head of the Took family. As was common with Kings, the Thain would add a number to the end of his name if necessary; i.e. Paladin II (who was Thain at the time of the Lord of the Rings).
In LotRO, Thain Paladin Took II plays only a minor role as part of a quest chain, where he decides what is to be done about fireworks that were stolen by brigands.
During the War of the Ring, the Thain was one of the Hobbits who refused to put up with Sharkey’s Ruffians. Under his orders, the Tooks shot three Ruffians and managed to hold the Great Smials. Upon the return of Frodo & Co., the Thain led a company of Tooks to chase one band of Ruffians away and hold off another, in addition to sending a hundred Tooks with Pippin (who happened to be his son) to support the uprising at Bywater. The Thain, along with Merry and Pippin, was later put in charge of rounding up the last remnants of the Ruffians. As the only male child of Paladin II, Pippin became Thain Peregrin I, and the title was then passed down through his line. He, along with the Master of Buckland (Meriadoc the Magnificent) and the Mayor of Michel Delving (Master Samwise) would later be named Counsellors of the North-kingdom by King Elessar.