Posts Tagged ‘local elections’

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)