Monday, 9 November 2015

Condorcet Conundrums

The elimination ballot New Zealand will use for its coming flag referendum isn't a bad one, but it is a shame that they won't be releasing the data that could tell us whether we've failed to choose a Condorcet Winner.

Here's me at the Dom:
Instead of asking the Electoral Commission to check first for a Condorcet Winner, Parliament told the Commission to follow a simple elimination procedure. It works as follows. If any flag is the first choice of a majority of voters in the first round, things are simple: that flag would by definition be the champion of all. But things get trickier if there is no first-round winner. In that case, the option that was the first choice of the fewest voters is dropped.

Let's take a simple example. Suppose that a million people vote in the flag referendum. 350,000 voters prefer the Black, White and Blue silver fern design but rank the Koru as second and all other options below that. 340,000 prefer Red Peak, rank the Koru as second, and all other options rank below that.

Finally, 310,000 prefer Koru as their first choice, rank the Black, White and Blue silver fern second, and all other options lower. Under the elimination procedure, the Koru is eliminated first because it is the first choice of the fewest voters.

A majority then prefers the Silver Fern to Red Peak. But, had Silver Fern faced Koru head-to-head, the Koru would have won – and it also would have beaten Red Peak in a head-to-head race.

Whenever a flag is the second choice of many voters but the first choice of few, the elimination procedure that the Electoral Commission will use risks choosing a flag that would have been beaten in a head-to-head race by another option. It might not matter, as there are only some configurations of voter preferences that would yield that kind of result. But it is disappointing that the New Zealand Flag Referendum Act did not ask the Electoral Commission to check.

Even worse, the Electoral Commission is forbidden from publishing the data that might let us know whether the voting procedure has resulted in the wrong flag being chosen. I asked the Electoral Commission whether they could provide the data that would let other researchers test which flag might have been chosen under different voting rules. Their Senior Legal Advisor replied that Section 50 of the New Zealand Flag Referendums Act 2015 prohibits them from disclosing that information and that they would decline any Official Information Act request on that basis.

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