If at least twenty percent of the qualified electors of a county, as determined by the number of votes cast for the office of governor at the preceding general election, shall petition the board of county commissioners for:

1. The increase of the number of county commissioners from three to five if the county, at the time of the filing of the petition, has three commissioners; or

2. The decrease of the number of county commissioners from five to three if the county, at the time of the filing of the petition, has five commissioners, the board of county commissioners shall submit the question presented by the petition to the qualified electors of the county at a special election to be held in connection with the next statewide primary or general election, whichever is specified in the petition.