Not later than the fourth Tuesday prior to an election on a statewide ballot measure, each chairman of a county campaign committee favoring a measure and each chairman of a county campaign committee opposing a measure shall file with the election authority a list of committee officers and a request to have the right to designate challengers and watchers under section 116.310. If only one committee favoring a particular measure and one committee opposing a particular measure file a list and a request, then each filing chairman shall have the right to designate challengers and watchers under section 116.310. If more than one committee favoring a particular measure or more than one committee opposing a particular measure files a list and request, then the election authority shall determine which chairman has the right to designate challengers and watchers. If the measure was submitted by initiative or referendum petition, the person designated under section 116.100 as the person to receive notice under sections 116.140 and 116.180 shall be entitled to designate the county campaign committee chairmen’s names to the proper election authorities by the fourth Tuesday prior to the election on that measure.