Condorcet is a confusing and inexpressive voting system

Posted: November 9, 2015 in democracy, New Zealand
Tags: , ,

Fairfax has an interesting article up by Eric Crampton, in which he laments that the referendum might not pick a Condorcet winner. He actually understands voting systems, I would say, but he’s not exactly picked a great one to advocate. I agree with him to the extent that I think releasing anonymized voting data so people can run it through other electoral systems seems like a legitimate use of the OIA to me, and shouldn’t compromise secrecy. (I have fired off an enquiry to the Electoral Commission checking on this info, and asking them to identify any legislation that would prevent disclosure of the number of each unique preference order chosen in the first referendum)

Update: I did get my OIA back, but it refused to release the information on the same grounds, and I really didn’t think it was worth taking to the Ombudsman.

But determining if there even is a Condorcet winner requires voters to rank every option, an exercise that often fatigues voters who only want to vote for options they’re enthusiastic about. Requiring people to rank minnow options is a recipe for suppressing voter turnout. (They had to make voting compulsory in Australia to combat the fact that people don’t want to rank every option, which their at-large STV system requires for no sensible reason) Many people legitimately do not care which of several options they get if their actual preferred options are knocked out of the race.

There are two other problems with a Condorcet race. The first is that in insisting that head-to-head (or pairwise) competitions are the best measure of success, it actually robs the race of wider context. Sure A beats B, and B beats C, and A beats C, but you can only ever tell how any option fared relative to a single other option. You can’t see that actually A is the second or third choice of many voters, and that in a more expressive race B might actually be the best candidate.

I have said before that the way the referendum works is the best way it could work, if we vote using an election system we’ve already trialed in New Zealand.

The last problem with a Condorcet race is that it often doesn’t produce a winner. Using flags as an example, what if Koru beats Red Peak, Red Peak beats the Red White and Blue silver fern, but that silver fern beats Koru, and they all beat the remaining two options? Then there is no Condorcet winner. Election systems based on this idea of head-to-head contests then apply mathematical rules, often about how decisively each option has beaten each other option, to decide a winner, when this information should be supplied by voters. STV does a crude version of this by asking voters to rank every option they want to win. (Our version in New Zealand allows them to omit options they don’t care about, and treats them all as last-equal, never assigning your vote to them)

STV is not a perfect voting system. It’s not even the best voting system we know about. It fails the “favourite betrayal” criteria under certain circumstances, meaning you can cause your favourite to win by ranking them lower than your actual preference, and cause them to lose by ranking them first. But it is a more expressive and generally superior voting system to Condorcet systems, and it generally produces a good result compared with FPP “tick only one box” systems.

If Eric wants a more representative vote, I suggest he advocate Range Voting for future referenda. Here’s what it might look like for the first referendum: (You could even sneak the current flag onto the ballot and eliminate the need for two referenda in this system, as unlike STV, it wouldn’t cause any issues adding the current flag into the ballot)

flag referendum range vote

Basically, you rate as many flags as you like from 1-9. The voting form could be exactly as simple as the STV one, or you could include check boxes like above for people with difficulty writing clearly distinct numbers.  On the form above, we would count the vote as 9 for Black and White silver fern, 8 for Red Peak, 5 for Black Blue and Red silver fern, no preference for Koru, and 1 for Red White and Blue silver fern.

That would mean that this voter would feel that Black and White silver fern is the best possible option, and Red White and Blue silver fern is the worst possible option. They think Red Peak is very good, and that the Black Blue and Red fern is average. The scores for each option are then averaged in each counting station, and weighted by the number of people who recorded a preference for each option. (The number that didn’t vote for each option is also recorded) These totals can be passed to a central office, where some simple multiplication and addition can determine national-level winners easily. (The winner is the option with the highest average score that reaches a minimum threshold of people choosing to vote for that option. If say, less than 10% of voters expressed a preference for an option, it would be discarded regardless of it’s rating as being too obscure, to protect from obscure options winning with a relatively small number of votes, especially in elections with a large number of available options to rate)

The advantages of this system are numerous. First, it implies a preference order. Secondly, it allows people to express the size of the gaps in their preference order- this voter not only thinks that the Red White and Blue fern is the worst option, they think that even their second-to-last preference is average, while that option is terrible. It allows voters to express how bad they feel the options they don’t prefer are. Voters can even deliberately rank their most-preferred option lower than 9, or their least-preferred option higher than 1, if that’s how they honestly feel. (although that’s a less strategic way of voting- it’s a form of deliberate favourite betrayal, described above)

It has all the advantage of determining a “beat path” (from Condorcet) or a “preference order” (from STV) with the added bonus that it puts these things in context of how much each option beats or loses to each other option, and doesn’t require complicated totalling, instant runoffs, (which can introduce accidental favourite betrayal) or mathematical resolution when no condorcet winner is found. (For range voting to result in a draw, the electorate actually has to exactly prefer the candidates by the same amount)

This is the perfect system to use for a referendum when there are multiple options to choose from. It lets you independently express opinions for multiple options without one option affecting another, it can eliminate multiple-stage or multiple-question referenda like the flag referendum or the MMP referendum. And it’s just a more expressive way of voting.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s