Amidon is a city in, and the county seat of Slope County, North Dakota, United States.Amidon was the smallest incorporated county seat in the 2000 census. When the 2010 census reported its population as 20 it became the second-smallest incorporated county seat after Brewster, Nebraska, with a population of 17. Brewster is the county seat of Blaine County, Nebraska. In 2000 Amidon had 26 people to Brewster's 29.There are two other unincorporated county seats that are smaller: Mentone, Texas, the county seat of Loving County, and Gann Valley, South Dakota, the county seat of Buffalo County, South Dakota.Located on US 85 about 31 miles north of Bowman, North Dakota, it is the closest city to White Butte.