In the unlikely event of a tie (where no candidate wins all their matches) the tied candidate with the fewest votes against them wins.
I think calling this situation a "tie" only generates confusion and makes the method seem weak. Just saying "In the unlikely event where no candidate wins all their matches..." seems fine.
Instant Matchup Voting
The formal procedure for IMV has five standard phases, plus three tiebreaking phases:
In keeping with my suggestion to avoid referring to cyclic ambiguities as ties... "five standard phases, and three more phases in certain rare cases"
3. Pairwise Matrix
The results from all the ballots is summed up in what is called a 'pairwise matrix', where the rows indicate votes -for- a candidate, and the columns indicate votes -against- a candidate.
I think the pairwise matrix step you show should be moved entirely to the "notes" section. In the step before, you showed how to break a vote down into its matchups. In the step after, you show what to do with the vote totals. All that the pairwise matrix is, is a way to display results. It confuses the casual viewer and takes them away from the general flow of how Condorcet works (which you did a great job describing up to that part, by the way). If you leave this in the body, you'll lose a lot of people who were following you just fine up to there.
6. First-round ties
I'd call this, "procedure when no majority winner exists" or somesuch.
8. Second-round ties
If two or more candidates have the least number of people voting against them (within statistical uncertainties[6]), these then form a second-round tie. If there is no alternative mechanism available[7], the winner is picked at random from within the second-round tie.
I would just call this "ties" as oppose to second-round ties. This is (in the context of plain Condorcet) an actual tie, as oppose to what we were looking at before.
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