If at any election any candidate receives a majority of all of the valid votes cast for a particular office and term, he or she shall be deemed elected. If no candidate receives a majority, there shall be a run-off election, except that, if before the time for holding such run-off election, all or all but one of the candidates entitled to have their names printed on the ballots at such run-off election have died, become disqualified, or given written notice of their withdrawal to the clerk in whose office the election was held, there shall be no run-off, but there shall be a special election for the office and term in question.