Simpson is a city in Cloud and Mitchell counties in Kansas, United States. As of the 2020 census, the population of the city was 82. Simpson w…Simpson is a city in Cloud and Mitchell counties in Kansas, United States. As of the 2020 census, the population of the city was 82. Simpson was originally called Brittsville, and under the latter name had its start in 1871 when a saw mill opened at the site. The present name was adopted in 1882 in honor of Alfred Simpson, an original landowner.