of results and administration of oath -- Determination by house of General Assembly. A successful candidate in a special election held for the purpose of filling a vacancy in any elective office shall take office immediately upon certification of the election results by the State Board of Elections or the county board of elections in which the special election was held, administration of the oath of office, and if the successful candidate was a candidate for the General Assembly, upon being determined to be a member by the house in which membership is sought.