Posts Tagged ‘range voting’

God that’s a technical name, right? Anyway, it’s time to discuss voting systems again. I’ve been looking around to see if anyone is advocating further electoral reform in New Zealand, and it looks like there’s no active organisations, which is a shame, as there’s some improvements we could do to our council elections at the very least. (I’m thinking maybe I need to help co-found one if anyone’s keen)

Re-weighted range voting is an interesting system that could suit our ward elections. (or even be used instead of FPP for the electorate vote in MMP, potentially) It’s a district-based system, but like STV1, it uses at-large districts and is semi-proportional. (that is, you have big wards which typically elect at least three winners, and it’s proportional for each district, but when all the districts are taken together as a larger whole, it generally works out less than ideal in terms of representing the entire city/country/etc… because of the limited amount of winners in each district amounting to “rounding errors” that multiply through the number of districts to a degree)

It is a multi-winner variant of Range Voting, which in my opinion is probably the ideal voting system to use when you have three or more candidates running for a single vacancy. Most Range Voting proponents don’t advocate it as a multi-winner system because in that environment it is beneficial to clones, (that is, normally the best strategy to win one of the additional vacancies is to imitate the best winner from last time, “cloning” them, and eventually leading to one-party rule in each district, similar to US “blue states” and “red states”) however the re-weighting part controls for this effect to make the system semi-proportional2.

From the voters’ perspectives, Range Voting and its Re-weighted cousin are exactly the same, they just elect different numbers of people. They get a list of all the candidates in the race, and each one either has a series of tick boxes next to them (indicating a range) or a space where a number can be written, say between 1-99. Votes under 50 indicate a bad candidate, and votes over 50 indicate a good candidate, with 99 being the best choice available, and 1 being the worst, and with most variants allowing for candidates left blank if a voter doesn’t know enough to consider them either good or bad. (generally there is a quota requiring a certain percentage of valid votes not to have left a candidate blank for them to be a winner)

In vanilla Range Voting, a simple average of all ratings for a candidate determines their result, exactly like an approval rating. Whoever has the highest approval rating wins. Strategic voting does happen in this system, but it’s not too harmful- it mostly revolves around making a call whether to exaggerate certain candidates up to 99 or down to 1 instead of being honest, in which case the election isn’t too different to just being able to tick as many people as you like on an FPP-style ballot.

In re-weighted range voting, once all the average scores are calculated and the highest score wins, they fill the first vacancy. In order to get a proportional vote, everyone who supported that candidate has the “weight” of their vote reduced for the purposes of subsequent vacancies, as they got a choice they like already, and you use an algorithm to determine whose ballots are weighted less, and by how much. (for practical purposes, this does mean that you would want to determine the winner using an electronic system, and would need to count each unique permutation of scores for an accurate result rather than simply tabulate averages, making variants with larger “ranges” difficult to count, and favouring single-digit variants where you rate candidates from say, 1-9) The system then shows you a new set of re-weighted approvals for round 2, and the second winner is the highest of these. Rinse and repeat for each additional vacancy.

Note that unlike STV or IRV3, your vote never “moves,” so at all times the full information you provided while voting is being considered. You moving a candidate from 50 to 75 can cause them to win even if you rated another candidate 99. In IRV, if you rank a candidate number 1 and they’re one of the top two candidates in the race, all your other preference information is irrelevant. Proponents of STV consider this a problem because they essentially consider that it’s a bad thing to be able to vote in such a way that you can compromise and “hurt” your first preference. In reality, isn’t it sometimes better that the winner be a compromise candidate that we all agree is above average?

The version of Re-weighted Range Voting I’ve seen advocated usually proposes that anyone who votes above the minimum for a candidate should have their ballot re-weighted as a fraction of the maximum score. The disadvantage of that algorithm is that it discourages people to vote honestly about candidates they think are below average, but not terrible, as their actually preferred candidates might not be elected due to the re-weighting if they vote honestly and a below-average candidate is selected in an early round. Let’s call this the distance-from-minimum model.

I briefly considered that perhaps the re-weighting should calculate a difference from the median possible score (ie. 50 in my example, which should intuitively mean that the voter believes the candidate is average) and use distance from that score that as a multiplier, so that people actively opposed to the winner of the first vacancy would have their chance of picking the next winner go up, while those who rated them average or didn’t rate them experience no chance, and those who like them have less influence on the second winner.

The really weird thing about that algorithm is that it could cause some perverse incentives for third-party voters, and actually does have some weird strategic voting implications. Say for instance there’s a strong Labour vote in your ward, so you’re sure they’ll win the first vacancy, and you support a Green winning the second vacancy. You know that your Green voters can’t bring the Labour candidate’s average down enough to cause them to lose altogether. In that case, you’re actually better off to rate the Labour candidate 1 (ie. the worst possible score) so that your Green candidate is more likely to get elected, even if you think the Labour candidate is well above average. If people misjudge the chances of who’s likely to get elected, that sort of strategic voting could muck up the winner pretty badly, or if voters’ inclination or ability to vote strategically this way is unbalanced, it could make the election very unfair, so that algorithm doesn’t make sense, either.

The best way to do the rating seems to me to be to weight down the scores of everyone who votes a winning candidate as above-average, that is, who rates them above the median possible score. This doesn’t introduce too perverse an incentive to highly strategic candidates, (at worse, strategic voters may reduce strong candidates that are their second-choice or less to the median possible score) it doesn’t punish people for honestly rating candidates they don’t like closer to the median possible score, and it still achieves proportionality by re-weighting the ballots of everyone who thought a winner was above-average, and in practice I would expect every vacancy winner to have an approval rating above the median possible score during the first-round tally anyway.

Re-weighted Range Voting has already successfully been used in organisational elections, such as winnowing the fields for certain oscar nominations, so I think it’s probably ready to be trialled in local elections and see how it works in practice. Bayesian statistical analysis suggests that in both strategic and non-strategic elections, the distance-from-minimum model performs very well, and I would expect the distance-above-median model to perform even better, however these are mathematical experiments and the real world sometimes differs from models in unexpected ways, so I certainly wouldn’t advocate RRV yet for national elections, even the relatively low-stakes electorate contests we have in MMP that normally don’t influence the makeup of Parliament by more than 1-5 seats in a 120 seat Parliament.

Variants of the single-winner system, Range Voting, are already used in all sorts of places. A version that discards extreme scores and doesn’t allow for blanks is used at the Olympics for judging performances, for instance, which is about as high-stakes as you can get for organisational voting, as the ballot isn’t actually secret so the judges can be criticised for getting it wrong. That would be an excellent system to use to determine who should be our mayors, and would make impossible some of the weird edge scenarios in IRV where an intuitively “wrong” winner is picked. (these usually involve some variation on a strong contender doing very well on second preferences, but being eliminated in an early round because of low first preferences. These scenarios have been observed in actual elections and aren’t exactly incredibly low probability given how often elections occur. In comparison, the nightmare scenarios applicable to Range Voting are much more unlikely in terms of actual observed voter behaviour, and are arguably desirable results)


So, I stumbled across a link to National Business Review talking about the Red Peak flag being added to the referendum today. (Briefly: I support it being added, I don’t think this is the Greens playing into National’s hands, and it’s exposed that Labour is being petty to try and upset the public about how badly National has dealt with this process. But I don’t think all of that is worth a blog)

Chris Keall from NBR claims that due to what he calls “preferential voting”, (generally known in New Zealand as Single Transferable Vote or STV) that Red Peak will be disadvantaged in the first stage of the referendum, due to the fact that the three fern designs are similar. (In evaluating electoral systems, we call similar choices “clones”. Some systems split the vote with clones, disadvantaging the clones. Others allow you to stack points for clones, making it easier for a choice to win when it has many clones to pad out its score) As someone who actually follows how voting systems works and advocates for reform of our voting system, (yeah, I’m not actually perfectly happy with MMP, but it’s better than any other systems New Zealand parties have proposed) let’s go to the classroom on why that’s not the case.

The problem with this argument is that STV is not vulnerable to this flaw. (every voting system has numerous flaws and advantages, the trick is picking one that’s suited to what you want to do) Similar options generally1 neither aid nor hurt each other in a single transferable vote, unlike the plurality system where you can check only one option. STV does an “instant runoff” if no choice achieves at least 50% of the votes when it’s used in a single-winner contest like the flag referendum. With five choices and no likelihood of a landslide, we’re definitely going to have a runoff in the election. Let me show you how this works. Let’s say the first preferences are as follows:

  • Silver Fern (Black and White): 6%
  • Silver Fern (Red White and Blue): 25%
  • Silver Fern (Black Blue and White): 35%
  • Red Peak: 30%
  • Koru (Hypnoflag): 4%

No design has more than 50% of the vote yet, so STV eliminates the option with the least votes in this round. That’s the Koru design. The algorithm tallying votes then looks at how the Koru’s second preferences were set, and reallocates all its votes according to that split. Let’s say 50% of Koru voters wanted Red Peak, 25% wanted the Black and White fern, and 25% only voted for Koru with no second preferences. Koru’s 4% is reallocated according to their second preference, and round two looks like this:

  • Silver Fern (Black and White): 7%
  • Silver Fern (Red White and Blue): 25%
  • Silver Fern (Black Blue and White): 35%
  • Red Peak: 32%
  • No votes/discarded options: 1%

We still need 50% for a winner, so we eliminate the least popular option again, this time the Black and White fern. Those votes are reallocated according to the second preferences of people who voted for the fern, and the third preferences of people who voted for the Koru but had their votes transferred to the fern. Let’s say half of them were Red Peak supporters, a quarter liked the Red White and Blue fern, and a quarter didn’t express any more preferences. We proceed to the third round.

  • Silver Fern (Red White and Blue): 26.75%
  • Silver Fern (Black Blue and White): 35%
  • Red Peak: 35.5%
  • No votes/discarded options: 2.75%

We still don’t have a clear winner, so we’ll have to eliminate the Red White and Blue fern, and proceed to the final round. If we say 10% of Red White and Blue voters didn’t express any further preferences, and 45% each supported the other two designs, Red Peak wins, despite the fact that first preferences for the Ferns added up to 66%. (If you do the maths, you’ll note that Red Peak doesn’t achieve 50% to win. This is because we actually ignore the no votes in determining 50%, but that’s difficult to show)

It doesn’t matter how many people vote for similar options in the first round, it only matters whether enough of the voters for those options rank them all in a block ahead of the other options. If Red peak had polled higher than any of the ferns in the first round, then in fact, the only other proposed system would have caused the ferns to lose, even though it’s likely fern voters will normally prefer other ferns over the two remaining designs.

The other system I mentioned is the one Labour proposed it its amendment bill that was shot down- using a Plurality Vote (the same as we do for electorates) to determine the winner, and rolling both referenda into one paper. If we had done that with the above example, the Black Blue and White fern would have won instead, because the less popular desgns split the votes away from Red Peak, even though Red Peak and the Black White and Blue fern designs were the most popular overall when people’s full preferences were accounted for.

This system is actually the best suited for the kind of referendum we’re holding in the first stage. It’s simple, (you rank as many preferences as you want, and all your consecutive preferences are counted. The only way to null vote is to not write a 1 anywhere) it doesn’t suffer from vote splitting, (that is, it doesn’t punish clones) and it allows you  to relatively1 safely vote your true preferences. Everyone’s vote is counted