Majority Requirement: Legislature
The majority requirement, with variations, was applied to the election of town representatives until 1939. The majority requirement does not appear to have been applied to the senate. Town representation was replaced by population-based representation (districts rather than towns) in 1965 but election by plurality was retained. In the event of a tie vote a second, recessed election would be held.
The earliest law governing the election of town representative is silent on whether a majority is required for election (An Act Regulating the choice of town officers and petit jurymen, passed 18 February 1779).
The majority requirement is implied in a 1787 act (An Act for Regulating the Election of Governor, Lieutenant Governor, Council, Treasurer and Representative, passed 8 March 1787). Voters had a two-hour opportunity to cast a ballot for town representative. At the end of that time the ballots were counted and if no choice was made the town constable "shall be at Liberty to count the votes afterwards brought in." The law does not state when these additional ballots would be counted, though presumably it would be no later than the completion of the subsequent votes for state officers.
By 1797 (Revised Laws of 1797, p. 546) the law read that "if no person shall have a majority of all the votes, the presiding officer of the meeting shall notify the same; and call on the freemen as aforesaid, giving a reasonable time only for receiving such votes, till an election shall be made."
The law was amended in 1838 (Act 15) allowing five hours, rather than two, for voting for town representative but the majority remained the same as in 1797.
In 1913 (Act 11) the law was amended to allow plurality election if no majority winner emerged after three ballotings: "... if no person has a majority of the votes given, the presiding officer shall so inform the freemen and another balloting shall be had, a reasonable time only being given for receiving and counting the votes; and ballotings shall be continued, until an election is made, provided that after the third ballot the person first receiving the largest number of votes shall be declared elected." This language was retained in a 1915 amendment to the election law (Act 5).
Act 8 of 1935 allowed election by plurality, starting with the second balloting. Blank or defective ballots were not counted.
In 1939 (Act 8) the majority provision was eliminated and election was by plurality. In the event of a tie the presiding officer would call for a second balloting, "a reasonable time only being given for receiving and counting the votes", until an election was made.