When a senator or representative-elect shall die, remove from the state, refuse to serve, become insane, or be otherwise incapacitated, or when at an election for any senator or representative no person shall receive a plurality of the votes cast, a new election shall be held. A vacancy in the senate or house of representatives shall be filled at a new election. The general assembly shall provide by general law for the holding of such elections at such times as to insure that each town and city shall be fully represented in the general assembly during the whole of every session thereof so far as is practicable. Every person elected in accordance with this section shall hold office for the remainder of the term or for the full term, as the case may be, of the office which that person is elected to fill, and until a successor is elected and qualified.