The county canvassing board must be composed of the county recorder, county auditor, chairman of the board of county commissioners, and a representative of each of the two political parties that received the highest number of votes cast for governor at the most recent general election at which a governor was elected. An individual who served on an election board during the election may not serve as a political party representative on the canvassing board for that same election. The district chairmen of the political parties from each legislative district within the county shall appoint the respective political party representative. The county canvassing board must be comprised of at least five members, and both political parties must be represented. Each political party from each legislative district within a county may request representation on the canvassing board if there is equal representation from each of the political parties. For any special county election when the election does not involve any legislative or statewide office, the county canvassing board must be composed of the county recorder, county auditor, and chairman of the board of county commissioners.