Legal Beagle by Graeme Edgeler

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Legal Beagle: Voting in an STV election

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  • Brent Jackson, in reply to Michael Homer,

    You planning to use your program for anything ?

    If you have access to any old STV election data, it'd be interesting to pump it through your program, and compare the results to see if they ever differ. I'm guessing that it is unlikely to ever make a difference in a real world election.

    Auckland • Since Nov 2006 • 620 posts Report

  • izogi, in reply to Brent Jackson,

    It'd probably have to be tested on data taken from somewhere other than a real local election in New Zealand. Section 89 of the Local Electoral Act appears to say that all voting documents must be destroyed after 21 days of secure storage, or as long as it takes for any required recount. Presumably this includes electronic records of voting documents.

    Wellington • Since Jan 2007 • 1142 posts Report

  • Michael Homer, in reply to Brent Jackson,

    I'm not planning to use it for anything, no, it just seemed interesting to write. It's not complicated and there are better implementations around.

    If the ballot records were available I might've given it a go, but they're not.

    Wellington • Since Nov 2006 • 85 posts Report

  • Steve Todd, in reply to Michael Homer,

    I've read the Wikipedia article again, this time more carefully, and I see that the Schulze method does indeed provide for equality of preference. (My apologies, Tim.)

    I note your comment about it being less intuitive, and that it would be "fairly inefficient at run time with a large number of candidates."

    Getting public servants and legislators to accept it, and provide for it for public elections, for what would be little or no demonstrable gain (especially giving away later-no-harm, which I believe is necessary for public confidence in preferential voting systems), would be very difficult, I think.

    Wellington • Since Jul 2013 • 125 posts Report

  • Michael Homer, in reply to Steve Todd,

    I note your comment [...] that it would be "fairly inefficient at run time with a large number of candidates."

    I was mostly talking about my own implementation there - I built it directly off the definitions, rather than efficiently. For a proper implementation computation cost wouldn't be an issue other than in really extreme cases.

    Wellington • Since Nov 2006 • 85 posts Report

  • Tim McKenzie, in reply to Rich of Observationz,

    For the rest of us, can you produce a real life instance where an STV election in NZ has produced an outcome you regard as unfair because of the counting system?

    In New Zealand? Probably not. As izogi pointed out, the vote data just isn't available. A little effort was made to have more vote data revealed for the first flag referendum, but the Electoral Commission believed it would have been illegal for them to reveal more data. (See .)

    That's not to say that there aren't perverse STV results in New Zealand; just that it's difficult to identify them, and even if you have your suspicions about a particular result, it would still be very difficult to prove its perverseness beyond doubt, without more data.

    However, Burlington in Vermont briefly used to elect its mayors using what they called Instant-runoff voting (IRV, which is basically single-winner STV, like we use for electing Wellington's mayor, for example); they released more complete vote data, so that, in 2009, although the result was "fair" in the sense that the rules announced before the election were, presumably, followed correctly, it was a somewhat perverse result in this way:

    The three main candidates were Bob Kiss, Andy Montroll, and Kurt Wright. Of those three, Andy Montroll was the first to be eliminated by IRV; then Bob Kiss beat Kurt Wright and won the election. But according to the preferences they revealed, 4067 voters would have been happier if Andy Montroll had won, compared to only 3477 who would have been less happy with that result; what's more, Andy Montroll would have won a similar preference comparison against Kurt Wright, and against all of the more minor candidates.

    Ironically, according to Wikipedia, more of a fuss about this result was made by Kurt Wright's supporters than by Andy Montroll's; apparently they felt that with 33% of first preferences (more than any other candidate) their candidate had been robbed of his legitimate victory, or something, even though, according to the preferences the voters expressed, he would have lost a two-way election against either of his main rivals.

    So instead of changing to a system that would have avoided the perverse result, Burlington reverted to a two-round sort of non-instant-runoff system that would have (if voters had expressed the same preferences) delivered exactly the same result, had it been used in 2009, only it would have taken longer, being a two-round system. (However, voter incentives may have been altered if the two-round system had been used.)

    Lower Hutt • Since Apr 2007 • 126 posts Report

  • Steve Todd,

    Again, this (the 2009 Burlington mayoral election) is a so-called monotonicity violation, detected after the fact. The first-preference votes given for the three main candidates were: Wright (Republican) 2,951; Kiss (Vermont Progressive Party) 2,585; and Montroll (Democratic) 2,063.

    According to Donald Marron, here: if about 750 of Wright’s supporters had [suddenly and unaccountably] decided to vote for the incumbent mayor, Kiss, instead, they could have engineered a better outcome for themselves by enabling Montroll (who, it turned out, was the Condorcet candidate), to win. (At the Second Round, Wright, with 3,294 votes, had 740 votes more than Montroll, who had 2,554 votes.)

    Readers already know what I think about all this. It flies in the face of commonsense. It’s like Act voters suddenly deciding to vote for the Greens candidate. And, had pre-election polling indicated Republican voters could successfully do this, wouldn’t Kiss’s supporters have switched their vote to Wright, to counteract the Republican strategy?

    To Rich, I draw your attention to this pro-IRV (single-seat STV) analysis of the result, from . Among other things, it points out that there was, in fact, no monotonicity failure in this election – “non-monotonicity *could* have affected the election [by Kiss’s votes being raised, so that Wright is eliminated and Kiss loses to Montroll in the final runoff], but did not[.]”

    The last few paragraphs about Condorcet voting methods are also interesting. It is pointed out that they "discount the relative importance of first choices", and how "that might affect candidate policy discussion".

    The simple fact is, not enough people, giving their true preferences for the candidates, voted for Montroll, for him to win. When he was eliminated, the contingency choices of the voters on his ballot papers were activated, resulting in his votes transferring 2 to 1 to Kiss, to elect that candidate.

    And let us not forget, any system that elected Montroll would have had to violate later-no-harm – and would almost certainly have been immediately discarded, also.

    In my view, it is quite wrong to describe the outcome of this election as “perverse”.

    Wellington • Since Jul 2013 • 125 posts Report

  • Rich of Observationz, in reply to Steve Todd,

    So, avoiding technicalities:
    - Burlington has a substantial natural majority for the liberal-left.
    - there was a right-wing candidate and two left wing candidates.
    - because of this, the Republican candidate led the first round. The Democrat was eliminated.
    - Both the Republican and the Progressive’s second preferences were of no consequence. The Progressive candidate won on the Democrat’s 2nd preferences, I presume.

    Apart from not winning, (as they would in a split vote under FPP), the Republican voters might have been peeved that the most left-wing candidate was elected when they preferred the Democrat.

    As you say, the Republicans could have achieved their preferred outcome by giving their first round vote tactically to the Democrat.

    Are there any voting systems that would avoid that and consider the Republican’s preferences?

    (I’d note that an indirect election would be fairer here in a couple of ways:
    - a council would be elected with members split maybe 39/34/27 R/VPP/D
    - the council would probably elect a mayor from the left of centre with broad support
    - the Republicans could influence that process
    - the Republicans would also be able to work with one of the left of centre parties on particular issues
    => hence, each party would have influence commensurate with their vote)

    Back in Wellington • Since Nov 2006 • 5550 posts Report

  • Rich of Observationz,

    Incidentally, it would be interesting how NZ would elect an executive president (or directly elected PM, put another way) using STV.

    In current conditions, I'd think that NZ First would be the first major party eliminated. Should National lack an overall majority (with ACT and Dunne preferences, and assuming all Green prefs went to Labour), the NZF preferences would determine the result: if National has 45% of the vote and NZF 10%, they would need half the NZF preferences to win.

    (Compared with MMP on the same numbers, where they could win with 40% and the support of Winston Peters).

    Back in Wellington • Since Nov 2006 • 5550 posts Report

  • Steve Todd, in reply to Rich of Observationz,

    Your summation is pretty much spot-on. The only correction I would make being that the Republicans could have achieved a *better* outcome for themselves if 750 of them had given their first round support to the Progressive candidate, not to the Democrat. That way, the Republican candidate would have been eliminated at Round 3 instead of the Democrat, and the 75% of Republican voters who ranked the Democrat second, would have enabled the Democrat to beat Kiss (the Progressive).

    (To be clear here, there is no electoral system that I know of (except for plurality / FPP) that would have elected the Republican candidate in this particular election (especially given that 85% of Progressive voters also ranked the Democrat second).)

    Are there any voting systems that would avoid that and consider the Republican’s preferences?

    Yes. Three that immediately spring to mind are: Condorcet pairwise counting, Nicolaus Tideman’s CPO-STV (Comparison of Pairs of Outcomes), and Schulze STV. And, of course, in the election under discussion, voters could have ensured the Republican preferences were considered by bringing about the property known as non-monotonicity – that is, that increased support, for a candidate who would otherwise have been elected [Kiss], can prevent that candidate from being elected.

    All three of these alternative methods violate later-no-harm – that is, that adding a later preference to a ballot should not harm any candidate already listed. As I’ve pointed out before, once voters know that later preferences can be used to defeat their earlier-preferred candidate(s), they, in all likelihood, will not express them, and then we’re back to FPP (single-seat elections), or to the Limited Vote (multi-seat elections).

    Following the 2009 Burlington mayoral election, it would seem that IRV fell victim to the toxic, two-party, FPP, electoral environment that, over many decades, has greatly contributed to the current parlous state of democracy in the United States.

    Wellington • Since Jul 2013 • 125 posts Report

  • Steve Todd, in reply to Rich of Observationz,

    (I’d note that an indirect election would be fairer here in a couple of ways:- a council would be elected with members split maybe 39/34/27 R/VPP/D


    Yes, what you say here could work in theory, but, unfortunately, at the time, the 14-seat Burlington City Council was elected by single-seat plurality in seven wards, with each councillor being elected for two years; there being an election in each ward every year. From my quick research, it seems to me that, in most elections, the incumbent is re-elected unopposed (except for write-ins). That’s FPP in America for you.

    I still think mayors should be directly elected, but the election should be as I described in a reply to you about a year ago, here : The position of mayor is a very important civic post that I think should be filled in accordance with the wishes of the people.

    Wellington • Since Jul 2013 • 125 posts Report

  • Steve Todd, in reply to Rich of Observationz,

    Wellington • Since Jul 2013 • 125 posts Report

  • Rich of Observationz,

    Without going down the rabbit hole, do you believe that we should then adopt the American/French system where the head of government (an even more important post) is also elected directly by the 'people'.

    Back in Wellington • Since Nov 2006 • 5550 posts Report

  • Steve Todd, in reply to Rich of Observationz,

    Heh, heh, it’s the garden path that’s beginning to worry me, Rich, not the rabbit hole.

    First, I’ll say that, in our Westminster system, the office of prime minister should never be directly-elected. The experience of Israel turns me right off that notion (not that I ever had it).

    If New Zealand were one day to become a republic, I would like the (non-executive) president of be directly elected by M-PV / IRV / AV, single-seat STV, whatever, as is the President of Ireland.

    I don’t like the French two-round system, because too many people have to “hold their noses” should a second round be required (Chirac-Le Pen 2002 being the classic example). Far better to get it all over and done with in one preferential vote election, with people having no incentive other than to express their true preferences for the candidates (as previously discussed).

    Wellington • Since Jul 2013 • 125 posts Report

  • Rich of Observationz, in reply to Steve Todd,

    Ok, so Auckland council, 1.4mln people, must have a directly elected leader.
    NZ in total, 4.5mln people, must *not* have a directly elected leader.


    Back in Wellington • Since Nov 2006 • 5550 posts Report

  • Steve Todd, in reply to Rich of Observationz,

    I was waiting for this, although I assumed you would refer to Wellington, rather than Auckland.

    I'll just say this: local government is different to national government. If you want to discuss governance, this is the wrong posting / thread. Besides, you're questioning me, rather than engaging in a discussion by offering us your views on the subject.

    Wellington • Since Jul 2013 • 125 posts Report

  • Rich of Observationz,

    But we *love* digression?

    Since I don't know what your argument is for direct election of mayors (beyond 'local government is different') then I can't really come up with an alternative view. Indirectly electing council leaders does work reasonably well (for most councils in the UK) and used to work for the ones that have gone to direct election (bringing Boris Johnson and dodgy corrupt cop Ray Mallon into mayoralties).

    Back in Wellington • Since Nov 2006 • 5550 posts Report

  • Nicci Coffey,

    You said: "For example, if the quota was calculated as being 100 votes, and on the first round, one of the candidates got 125 votes, then those excess 25 votes are distributed according to second preferences. To make it fair, the second preferences of all that candidate’s voters are used (not just the last 25!); this would mean that an extra 0.2 votes would be added to the second choice of each of the voters that had chosen the winning candidate as their first preference."

    I'm a bit lost on the second sentence. Can I clarify it's not only the last 25 votes, but also not any combination of 25 specific votes?

    I understands that you are saying all the second preferences are tallied. Are they then divided proportionately into the equivalent of 25 votes, and that proportion is what is re-distributed?

    So, 2000 votes are cast. 1334 are needed to win. One candidate gets 1500. All the second preference votes are calculated and pro-rata shared into 166 votes (ie. 1500-1334) and then that amount of votes gets allocated for the next count.

    This came up at a public meeting tonight, and a few people took the view it was 25 specific votes, leading to comments that it seemed the election result would change if a different 25 votes were used. I'd be keen to share the correct answer if you have time to comment. Thank you.

    Island Bay • Since Sep 2016 • 1 posts Report

  • Graeme Edgeler, in reply to Nicci Coffey,

    So, 2000 votes are cast. 1334 are needed to win. One candidate gets 1500. All the second preference votes are calculated and pro-rata shared into 166 votes (ie. 1500-1334) and then that amount of votes gets allocated for the next count.


    Candidate one keeps 1334 of their votes. Which is made up on 1500 votes worth 0.889333... votes each (this is called the "keep value"). And 1500 votes worth 0.11666... votes get added to the second preference choices of each of the 1500 votes .

    Before computers some elections have used the last 134 votes, or the a random 134 votes, but we don't. I think there was once a recount in an Australian election where the vote changed because different votes were counted last. But it cannot happen here.

    Wellington, New Zealand • Since Nov 2006 • 3215 posts Report

  • Steve Todd, in reply to Nicci Coffey,


    While your understanding of how surpluses are distributed, and Graeme’s confirmation of it, are correct, your example of 2,000 votes cast and 1,334 being needed to win, could not actually happen. If two candidates are being elected, the initial quota would be 666.6666… (2000 / 3).

    To give you a brief, but slightly more detailed explanation of how surpluses are transferred, I’ll use the 2013 Southern Ward election (see the Calculator Commentary and Iteration Report at , then scroll down to the bottom of page 9, of 12).

    There were six candidates vying for two seats, and 7590 votes were cast. That means the initial quota was 2530.000000001 votes (7590 / 3, plus a billionth of a vote). Only two candidates could attain that many votes, there being at most only 2529.999999998 votes left for anyone else to attain.

    Paul Eagle received 3626 first-preference votes, giving him a surplus of 1095.999999999 votes, which had to be distributed before the lowest candidate was excluded from the count (there being only 170 votes separating the lowest two candidates).

    He kept 0.697738555 of each of his 3626 votes (being the quota of 2530.000000001 / 3626), giving him a new total of 2530.000000430 votes – fractionally above the quota. The remaining 0.302261445 of each of his 3626 votes were distributed to the other candidates in accordance with the voters’ second-preference choices.

    At the second iteration, David Lee received 386.290126710 votes (1580.290126710 less his total at the first iteration of 1194 votes). That means he was the second-preference choice of 1278 of the 3626 people who voted for Eagle (1278 × 0.302261445 = 386.290126710).

    Ginette McDonald was the second-preference choice of 797 people, Bryan Pepperell of 486 people, Will Moore of 260 people, Brent Pierson of 313 people, and Don McDonald of 75 people. That means 417 people voted only for Eagle (i.e., they gave him their unique first preference), the remaining value of their votes (that Eagle did not need, to stay above the quota) becoming non-transferable – a total of 126.043022565 votes.

    At the commencement of the third iteration, the lowest candidate, McDonald, was excluded from the count and his keep value was permanently re-set at 0.0; a new, lower, quota was calculated, to take account of those 126.04… votes that had dropped out of the election; Eagle’s keep value was re-calculated (because the new, lower, quota gave him a new surplus – of about 42 votes, not enough to save McDonald, who was now about 252 votes behind Pierson); and all 7590 votes were recounted, using Eagle’s new keep value. And so on.

    While the process is extremely tedious (which is why a computer is needed to produce the result), mathematically, it’s quite straightforward.

    Wellington • Since Jul 2013 • 125 posts Report

  • Sacha, in reply to Steve Todd,

    Ginette McDonald was the second-preference choice of 797 people

    surely Tawa is north of the Southern Ward? :)

    Ak • Since May 2008 • 19745 posts Report

  • Rich of Observationz,

    Carpetbaggers from Porirua regularly seek office in our city - I favour building a wall.

    Back in Wellington • Since Nov 2006 • 5550 posts Report

  • Steve Todd,

    I was casually playing around on the Internet the other day, and stumbled across the Otago University Magazine, Issue 19, February 2008, in which there was an article titled “Voting with your feet”, by Nicola Mutch. In this article, a Dr Chris Rudd (who had claimed to originally be a proponent of the single transferable vote (STV) system for local body elections, but had since changed his mind) was quoted as saying—

    “I thought it [STV] would be fairer and more accurate. But, in every single case we’ve studied, the person who won the first-choice race won the election. Ranking your candidates hasn’t changed any results, but it has added a layer of complication to the whole system.”

    I have seen several examples of candidates coming from behind to win / take a seat. It happened in Kapiti Coast District (at-large) in 2007 (Wooding overtaking Mansell, which Rudd and his fellow researchers must surely have been aware of); Celia Wade-Brown overtaking Kerry Prendergast in 2010; and Mark Peck overtaking Prendergast’s husband, Rex Nicholls (at the second iteration), to take the third seat in the 3-seat Lambton Ward in 2013, to name three.

    In addition, although the researchers wouldn’t have known this in 2008, we must never overlook the impressive performance of Jinty MacTavish in Dunedin’s Central Ward in 2010, who was 11th on the count of first preferences, was elected 4th (out of 10), and who finished with the third-lowest final keep value – a very clear example of the power of second and subsequent preferences.

    What people like Rudd would appear not to realise, is that when people vote in STV / PV (single-seat STV) elections, they rank the candidates in their true order of preference, because they know their later preferences cannot harm their earlier preferences. (Readers who have followed this thread will know that this particular property of STV is one that I consider to be extremely important – in fact, vital.)

    That being the case, it stands to reason that the leading candidates at the first iteration will almost always be the most-preferred candidates in the election (sometimes with exceptions that become apparent as any particular count unfolds).

    Consequently, those who argue that repeated counts and transfers are therefore unnecessary, overlook the fact that the purpose of second and later preferences is to correct the distortions that arise from allowing only first preferences to be cast (particularly in *single-seat* FPP elections), and that, as I say, the system allows voters to list their true preferences without fear of wasting their votes, thereby ensuring the correct candidate, or candidates (in the collective opinion of those voting), is / are chosen.

    And, let’s not forget, under PV (in particular), the split vote, whereby, in FPP elections, electoral support for candidates A1 and A2 is divided, allowing candidate B to win (as will happen in Auckland this coming weekend), is completely eliminated.

    Interestingly (at least to me), on 15 September [2016], a Kapiti Coast resident, in a letter to the editor of the Dominion Post, argued the opposite of Rudd. The writer warned voters not to rank-order too many candidates, because “If you choose to number your preferences then your one vote can be split, supporting all of your numbered preferences depending on how the vote counting proceeds, including those that you don’t want.” (He said this had happened in Kapiti Coast – 2007?) Putting that the other way around, he was saying that lower rankings could be used to defeat candidates you like! Apart from the fact that he was quite wrong, overlooking STV’s later-no-harm property, he actually didn’t know what he was talking about.

    A candidate who comes from behind to win a seat does so because the voters, collectively, preferred that candidate to the one who was pipped at the post. In such a situation, the surplus votes of already-elected candidates, that are transferred to, say, candidate X, to help X overtake and defeat candidate Y, will, in every case, show a lower preference ranking (or no preference ranking at all) for the now-defeated Y, compared to the now-elected X, on the relevant voting documents.

    Therefore, contrary to the assertion of the writer referred to, above, Y was not a candidate that X’s supporters liked and inadvertently helped defeat. Under STV / PV, that simply cannot happen.

    Wellington • Since Jul 2013 • 125 posts Report

  • Sacha,

    Placed my votes today for Auckland DHB (region's only STV election) and ranked all 28 candidates just to suppress the last few. Took a bit of reading in between, mind.

    Ak • Since May 2008 • 19745 posts Report

  • Steve Todd, in reply to Sacha,

    Wow! Not bad. I managed 13 of 20 candidates for the C&C DHB. I didn't have sufficiently adverse opinions of the remaining seven, to "suppress" a most-disliked candidate.

    I suppose you could say the moral of my story, above, was, rank-order as many or as few of the candidates as you see fit. Whatever we all do, it's all good. In all STV elections, there's enough proportionality to satisfy pretty much everyone, particularly for those voting in the DHB elections, and especially for those lucky people who are voting in the Dunedin City and Palmerston North City elections (14, and 15, citywide, respectively).

    Wellington • Since Jul 2013 • 125 posts Report

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