Benham's method

Benham's method is a variation of instant-runoff voting independently invented by Chris Benham, David Hill, and Robert Loring. The method calls for tabulating the first-choice of all voters on all ballots (as done with instant-runoff), but before each elimination check if there is an un-eliminated candidate who pairwise beats all other un-eliminated candidates, and elect them if they exist.

Between two candidates X and Y, X pairwise beats Y if more ballots rank X over Y than rank Y over X.

An alternative way of describing it is: "Elect the Condorcet winner (if there is one), otherwise eliminate the candidate ranked the highest by the fewest voters, and repeat". This can be further rephrased to also work as a variant of STV, in the following way: "Eliminate the candidate ranked the highest by the fewest voters unless that candidate is the Condorcet winner, in which case eliminate the candidate ranked highest by the second fewest voters".

When voters are allowed to equally rank candidates, Benham's method can either be implemented by equally splitting each voter's vote between each candidate they equally ranked highest, or giving each equally-highest-ranked candidate one vote. See the Equal-ranking methods in IRV page for more information.

Example
(This doesn't feature the actual ballot s, but shows the IRV round-by-round breakdown and the pairwise table; for each IRV round, a column next to it is created to show how many votes all candidates from the bottom going up have combined; this allows you to see how candidates were batch eliminated. The winner is the candidate who pairwise beats all other candidates remaining in the round): Note that in regular IRV, it's possible C could've lost because he had the fewest 1st choices, which would've resulted in A and B continuing to the next round and one of them winning.