This is the procedure Vermont law required for state and federal legislative races until at least 1916. Both our U.S. and Vermont State Representatives used to need a majority rather than a mere plurality to win election. A modern two-round runoff election, rather than just being a new election, eliminates candidates who are deemed to have little chance of winning. With the more common method, all but the top two candidates are eliminated. This expediency assures that the runoff will end with a majority winner on the next ballot.
Runoffs are common in southern states but are rare in Vermont.
It is used in some municipal elections, such as in Burlington. However, the Burlington City Charter is even more expedient. This batch elimination runoff is also specified in the Vermont General Assembly's joint rule 10 when electing members to such boards as UVM or state college boards of trustees. The third method involves dropping the bottom candidates one at a time in a series of runoffs. If after two ballots no candidate has a majority, the bottom vote-getter is eliminated and balloting is repeated.