In favour of Re-weighted Range Voting

Posted: November 20, 2016 in democracy, New Zealand
Tags: , , , , ,

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)

Pre-footnote notes:

RRV, like any election system, has advantages and disadvantages. It’s mathematically impossible for an election system to be perfect, (there’s a strict proof looking at a subset of desirable election system criteria called Arrow’s Impossibility Theorem that shows that set is mutually exclusive, but more criteria have been specified since then and some of them are a little more specialized or even close to a “marketing technique” for specific voting systems, such as Later-no-harm is for the STV/IRV system, the only system that passes that criterion) so it’s more a matter of making sure the advantages suit what you’re voting on and what values the voters hold about their decision-making process.

For local elections, this is often a tradeoff between fairness and how easy it is to vote, as you can potentially be electing between four and twenty candidates on a single ballot, depending on varying vacancy sizes and how many local bodies you qualify to vote for. I personally get a mayoral election, a ward election, a regional election, and a DHB election, which this year added up to electing 13 people between them. At-large contests using fair voting methods, like STV and RRV, are generally good compromises at the local level, so long as ward sizes remain relatively large. (smaller wards are less proportional, and therefore I would consider three-winner wards an absolute minimum, and seven-winner wards an absolutely maximum. My ward in Wellington is a two-winner ward, which is a very bad idea IMO, and probably inherited from the previous ward structure. Given we also elect DHBs at the same time as councils, it makes sense to keep wards relatively small, so 3-5 winners is probably ideal, especially if the DHB elections can be kept to a similar number. Asking people to elect more than 11 people on one ballot is demanding a lot of attention from voters, which will depress turnout.)

By “fair,” I mean meeting a few reasonable mathematical criteria like:

  • Being immune to cloning of either the harmful or beneficial type,
  • Minimising the opportunity for near-ties6 to reduce contention about close results,
  • Discouraging “favourite betrayal” where the optimal strategy is frequently to vote highest a candidate you do not prefer the most,
  • Producing results which are reasonably proportional,
  • And meeting the monotonicity criteria, which basically means you can’t cause someone to win by voting against them in some way. (in STV/IRV terms, that would mean that ranking someone lower on your list or leaving them off your list can never cause them to win a race they’d otherwise lose. In FPP  terms, it would mean not ticking someone can’t cause them to win a race they’d otherwise lose.)

By all these measures, RRV is a “fairer” system than STV5.

By “proportional,” I basically mean that in a contest where all candidates are members of parties and all voters align with a single party, we should expect the proportion of seats owned by each party to roughly resemble the proportion of voters supporting that party, allowing for reasonable rounding errors, and other noise from the fact that people and parties in reality do not align quite so perfectly, with people having varying degrees of sympathy to multiple parties in reality. So in a three-winner ward that is 60% Labour supporters, 25% Green, 10% National, and 5% ACT, you could call the result semi-proportional if it elected 2 Labour Councillors and one Green, with the National and ACT voters disenfranchised due to the ward being too small to represent them, and the Labour and Green supporters being slightly overrepresented as a result. In a ward with four winners that’s 50% National voters, 25% Labour and 25% Green, you would expect 2 National Councillors and one each for Labour and the Greens, which would be perfect proportionality. Disproportionality is results like where you have 51% Labour voters, but National controls Parliament with a majority of 52% of MPs. (this sort of result used to happen relatively often under FPP thanks safe urban seats eating up a lot of extra Labour votes, and the fact that we used to allow rural seats to have far less people in them rather than keeping electorates roughly equally-sized) It’s okay to get things a little out of whack, but once you’re reliably picking the actual loser more than about 5% of the time, it starts getting unbearable. Below that, and it’s okay so long as they’re comparatively small in a way that scales to the importance of the contest. By the time we get to the national level, we should be aiming for 0-2% disproportionality, which is why I usually make a point of complaining whenever a party polling above 2% fails to hit our absurdly high Party Vote threshold. Even Open List systems, my dream national-level system which mathematically doesn’t necessitate any disproportionality, can still end up with some degree in practice because you typically have at least a “win one seat outright” threshold in such a system, meaning that as much as 4% of the vote goes to waste as “Others,” in a typical election, including such venerable names as the Civilian Party, or United Future.

(Note that such a “low” threshold would still serve as a reasonable barrier, keeping out every joke party ever, but allowing ACT in without an electorate win for much of their political career, (although requiring parties to win a list seat outright would have seen ACT die off by 2014) and disqualify United Future after it died instead of keeping it around as an electorate zombie party. We would also have had some more representation for the far-right over various New Zealand elections, including both Christian Heritage (in the first MMP election) and the Conservative Parties, (in the last couple of elections, but likely not in 2017 from current polling) both of which would likely still have managed to die off eventually, but deserved their time in Parliament to show off their actual ideas beforehand, so that they could be judged appropriately by the people, and there would be room for the MANA party in Parliament, too, or the Alliance if you want to go back in time a bit for counterfactuals, like I did with Christian Heritage.)

1By STV, I mean the system used to elect DHBs, where you provide a continuous ranked list and multiple candidates can win. Our legislation on how STV works in New Zealand is actually very smart, and allows for people to rank or not rank any number of candidates they want, so long as they don’t miss any numbers. If they do, every ranking before the missed number still counts, so any vote that at least writes “1” next to a candidate is at least partially valid.4

2I’m arguably being a little mean in describing RRV and STV as semi-proportional, but there is a big difference in proportionality between these systems and list-based ones which average only 1-2% deviation from proportionality like MMP, or variations on the Open and Closed List systems that are strictly proportional. This is probably because I value proportionality very highly in election systems, being someone who has large critiques of most mainstream political movements (ie. a third-party voter) I don’t really get to vote for someone I like unless the election provides a high degree of proportionality.

3Confusingly, we know IRV as STV in New Zealand as well. In Wellington we use this system to pick our mayor. It’s just STV with a single winner.

4Deliberately writing only “1” next to a single candidate is actually a variety of strategic voting called “bullet voting,” which ironically is a critique levelled by STV supporters against Range Voting, because you can vote FPP-style by rating a single candidate maximum, and either blanking or rating all others at the minimum score. Actual elections which made anonymized ballot information available suggest that bullet-voting is a more common strategy in IRV and STV elections than in RV elections. The reason for this is that RV and RRV are both a lot more expressive than IRV and STV, allowing for equalities (eg. rating two candidates you consider average as ’50’) and expressing the depth of support (eg. rating one candidate ’51’ but another ’99,’ which under IRV/STV would be ‘2’ and ‘1’). Allowing people to independently evaluate each candidate gives them a lot more room to be honest if they wish to, and with instructions on how to vote provided, it’s usually quite clear that the best way to vote honestly is to rate at least one candidate each at the maximum and minimum possible scores.

RRV is still new enough that there is no robust public information available, so we’d be pioneering if we adopted it anywhere in New Zealand, but it seems reasonable at this stage to assume that strategic voting patterns would be relatively similar to Range Voting, allowing for differences based on the reweighting mechanism as I outlined above when considering what re-weighting rules would be best.

5Getting into specifics, IRV and STV function in a very weird way, known as an Instant Runoff, where the last-place candidate in each round is eliminated until the vacancy can be filled with a clear winner. This simulates an actual runoff, where you hold multiple FPP-style votes, eliminating low-ranking candidates according to a set of rules, until a candidate wins an absolutely majority of votes, but does so using vote-reallocation according to lists instead of actual voter psychology, making it a bit harder to predict the winner, and requiring some pretty complicated maths to do so. In terms of ties, because of this runoff, IRV is susceptible to as many as c-1 near-ties in a c-candidate election. In practice for prestigious offices like mayor of a major city, elections can easily have seven or more candidates, and each near-tie can influence the result of subsequent runoff rounds. I expect this is why some authorities resist releasing anonymized data for STV elections in New Zealand, which for wonks like me makes it difficult to show counterfactuals of who could have won various contests if we change the rules, which is a useful thing to study.

IRV and STV both fail monotonicity, which is the closest thing to must-pass criterion that exists, an it effectively requires that voting someone lower on a list cannot make them win. This is due to their odd quirk of instant runoffs where it can be beneficial to give your first preference to a less-preferred candidate in order to knock another candidate out of the race, making your most-preferred candidate the eventual winner on later-preferences. They do this to pass the aforementioned Later-no-harm criteria, which I can see being desirable for people who believe in majoritarian decision-making, as it effectively does the reverse of monotonicity- it guarantees that ranking a choice second can’t cause your first-ranked choice to perform any worse than not ranking anything in that place, and so on down your ranked-list. I haven’t seen a mathematical proof that monotonicity and Later-no-harm are mutually exclusive, but I’d be very surprised to learn that they aren’t.

The Later-no-harm criterion seems intuitively beneficial until you realise that this means that effectively as long as your first choice is in the race in a ‘Later-no-harm system’, your second choice doesn’t get any benefit from your vote. There is an argument to be made that this makes sense in an STV system where often the first round results in some of the vacancies being filled outright and their leftover votes being redistributed for round 2, but in IRV it’s essentially a recipe for polarisation and doesn’t allow for compromise or unity candidates, which should be a legitimate way to win. (and I say this as someone who has been known to criticise compromising from time to time, so I’m not exactly an outspoken fan of moderate politics)

STV also has a disadvantage in how its spillover votes work: you’re incentivized to try and rank more than the number of winners in your vote, as that way every time someone on your list ends up a winner, a fraction of your vote still transfers down to the next person. This brings people who want to vote effectively dangerously close to the Australia-style “you must rank every single candidate” style of voting, which is exhausting when the list of candidates starts getting too long. In contrast, there is neither an advantage nor a disadvantage to leaving a candidate blank in a range vote, it literally just means a candidate is too obscure for you to confidently judge them, and if enough other people feel the same way, that candidate is auto-disqualified so that, say, five people can’t elect them by being the only ones who know enough or care enough to vote for the obscure option with perfect scores.

RV and even RRV are also comparatively easy to tally compared with STV. RRV can be tallied easily in a spreadsheet, but votes can only be “compressed” by counting the number of times each unique rating combination occurs. (STV has the same problem with being unable to compress votes, but to a lesser degree as ranked order ballots have less combinations of unique votes) RV is incredibly easy to total and can even display partial counts and interim results, as each polling station can simply go through counting the rating for each candidate one at a time, and then phone in or submit via internet an average approval rating and a “weight” for that candidate, ie. the number of valid nonblank votes, with the only additional information needed being the total number of valid votes counted. (this only is needed if your quota for eliminating obscure candidates is a certain percentage of valid voters expressing a rating for them, rather than an absolute number)

Both STV and RRV require electronic tallying for results to be turned around within an acceptable timeframe, however each can be tallied using mechanisms no more complicated than a spreadsheet. Of the two systems, RRV is probably easier to intuitively comprehend the mathematics behind it, and thus slightly easier to construct a tallying system for. Unlike with RRV, there’s no guarantee that you’d be able to call any of the vacancies before tallying started using STV. However, in very clear races, STV can often call multiple vacancies purely from first preferences, as it depends on quotas to elect candidates. RRV in contrast has to apply a re-weighting to determine the subsequent candidates. With RRV, it’s relatively easy to call the winner of the first vacancy based on interim or final results, with STV you have no idea until someone hits the actual quota to be elected on first preferences. The quota to win an STV vacancy outright is generally Votes/v+1, where v is the number of total vacancies. Because STV redistributes votes until every elected candidate meets this quota and redistributes all votes exceeding the quota, it’s difficult to compare how convincingly each winner performed unless multiple winners meet quota in the same round. RRV is relatively unambiguous because you can compare raw approval ratings, making landslides more callable and allowing reporters to discuss the degree of mandate a candidate possesses for their policies.

This isn’t to say that IRV and STV aren’t okay systems with advantages. They have significantly improved local body elections over the FPP and block-voting systems they have replaced in New Zealand, but they should be viewed as stepping stones when we suspect better options might be available, and we shouldn’t be afraid to try out new voting systems that have had good results at an organisational level if we have evidence to suggest they might be an improvement. And we can always return back to them if we try something else that doesn’t work for us. Local elections should to some degree be laboratories for democracy.

6Exact ties are vanishingly rare in elections, but even coming too close to a tie results in calls for recounts and possibly court cases over how the election was conducted to try and overturn the original winner. If you believe that part of the point of an election system is to avoid this kind of controversy, then it’s a good thing for an election system to minimise the chances of a near-tie. RRV can only tie or near-tie once for every winner in the worst case scenario, wheras STV can potentially tie once for every round of counting, and there can be as many rounds as c-1 in an c-candidate election. There are all sorts of definitions for what counts as a near-tie, so it’s difficult to exactly model how likely they are rather than simply looking at the worst case scenarios, because it depends on the context of how large the voter pool is, whether there’s a history of election tampering, and how litigious the society is.


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