The referendum to decide on New Zealand’s next flag has been advertised as “your chance to decide”, but how much decision making power do we really have? The public were able to submit entries and will get to vote on which flag will be the final choice to challenge our existing flag. However, the flags in the shortlist have introduced a flaw that will skew the outcome of the referendum and weaken our ability to choose.
The referendum to choose the challenger flag will use the PV (Preferential Voting) format. This means that you will rank the flags in your preferred order by marking them with the numbers 1 - 4. Votes are then calculated in rounds. After each round the flag with the lowest votes will be eliminated and its votes will be re-allocated to the next preferred flag. Flags keep getting eliminated until 1 flag has more than half the votes and is declared the winner.
If a referendum is fair, each candidate should have an equal chance to succeed. You should be able to simulate thousands of test referenda with thousands of random votes each and end up with an even number of wins for each candidate.
| Flag A | Flag B | Flag C | Flag D |
|---|---|---|---|
| 25.00% | 25.00% | 25.00% | 25.00% |
However, if two candidates are almost identical, such as Flag A and Flag B, we can expect that a voter’s preference for each flag will be similar. A voter will still prefer one flag to the other, but will like/dislike them a similar amount compared to the other two flags. Flag A and Flag B are likely to be paired together as favourites, as least favourites, or right in the middle. This behaviour skews the outcome in favour of Flag C and Flag D.
| Flag A | Flag B | Flag C | Flag D |
|---|---|---|---|
| 16.67% | 16.67% | 33.33% | 33.33% |
When two flags are almost identical, they have a lower chance of being successful than the remaining two flags. This is because when voters pair the flags together, the flags are either put into 1 of 2 arrangements of advantage or 1 of 4 arrangements of disadvantage. This shows that a referendum containing two almost identical flag options is flawed from the start.
There has been a lot of controversy over the lack of variation in the flags that make up our referendum options. The shortlist contains two almost identical silver fern & Southern Cross flags (with colour variations), another silver fern flag, and a koru (a curled silver fern) flag.
It seems clear that either the panel didn’t take into consideration how their selection would be affected by the PV format, or that they intentionally introduced a selection that would have a weighted outcome under PV. Personally, I’m inclined to believe the former.
Regardless of how we’ve reached this point, the government should not proceed with the flag referendum until one of the identical silver fern designs is replaced by an alternate and drastically different design. This will make for a better process and a fair outcome for all.
Update
I’ve received feedback on Twitter that this logic should be followed through to the next level. That if Flag A and Flag B are essentially the same, they should be treated as a single candidate which shares the probabilities of both.
| Flag A + Flag B | Flag C | Flag D |
|---|---|---|
| 33.33% | 33.33% | 33.33% |
You can certainly run with this line of thinking and argue that this brings us back to a point where all options are equal. And you’d be right. However, as you may have already guessed, it introduces a whole new problem: We now only have three candidates.
John Key has argued that the law was written for the referendum to include 4 flag candidates and that the law will not be changed. This brings a conclusion that we really only have 3 flag candidates and one of the identical silver fern designs must still be replaced with a true 4th candidate.