This is an electoral system in which voters rank candidates. In a race between N candidates, each candidate may be ranked in any of the N positions. By ranking all the candidates, a voter indicates which candidate would get their vote in a race between any two candidates. I would call this a "virtual two-way race". A Condorcet winner is a candidate who wins all virtual two-way races. Sometimes there is no Condorcet Winner, a fact "discovered" at least three times, by an ancient whose identity I cannot determine, by Condorcet, and by Kenneth J. Arrow . The voter is therefore asked for the "Lowest approved rank" in order to facilitate a solution to a cyclic preference in the electorate.

If more than one candidate is ranked in a particular position on a particular ballot, that ballot is not used in the calculation of the virtual race between candidates in that rank. Condorcet Voting explains how such virtual races are used to determine whether or not there is a Condorcet Winner who would otherwise be the winner of the election. If a ballot does not indicate which is the "lowest approved rank," then the default "lowest approved rank" is used, and that rank is 1. Candidates for whom no rank is selected on a particular ballot are given the lowest rank. In other words, the rank of an unmarked "Lowest approved rank" is 1, but the rank of an unmarked candidate is last.

When there is no Condrcet Winner, an approval count is generated for all candidates in the cyclic preference. A ballot on which the candidate is ranked at or above the "Lowest approved rank" adds one to that candidate's approval count. The candidate with the highest approval count wins the election.