It’s possible, in theory, that a preference ballot like that used in the NZ flag referendum could fail to select a Condorcet winner.
In that case, a flag that’s the strong second choice of many but the first choice of few is killed in the early rounds and so is not able to pick up the second-choice transfers as other options are eliminated.
But I doubt that’s happened this time around. Here’s the final tally, graphic courtesy of the NBR.
For a non-Lockwood (the top two) designs to have won, you’d need … well, there’s no path from here to there. There is no way that you can get to anything but a showdown between those two options since the total for each of them exceeds the total first-preferences of all of the three other options.
I’ve put in my OIA request for all the ballot preference data anyway, expecting it to be shot down, because I’m interested in whether the Electoral Commission actually has the law right on this one. They think it’s illegal to provide the number of ballots that conform to the different potential preference orderings; I’m interested in whether the Ombudsman will agree.
It’s also interesting that spoiled ballots beat Red Peak.
Update: Note too that iPredict has the current flag as 75% likely to win in the next referendum. How long those prices remain accurate will be interesting: they’re not accepting new deposits, so trading is limited to those currently with liquid accounts.