Why NOT…. the STV voting system

The following was posted as a comment on the Hope you’re right, Professor Hayward thread. However, WordPress autoformatting interfered with the original formatting of Calvin and Jeremy’s submission. Their paper is included here as a PDF file, showing the tables and formulas.

Calvin says:

In case anyone is remotely interested in the outcome of the forthcoming election, I felt it timely to revisit mine and Jeremy Belcher’s submission to the Electoral Commission after the 2004 event. It was an attempt to highlight the flaws in the ‘Meeks NZ STV’ system as adopted. In the event it failed. Now that we are faced with an eleven candidate outcome, I am convinced that any result relative to the wish of the people will be purely coincidental. However, if, as Mike Stk has said, I am on the wrong track then so be it.

Submission to the Electoral Review Committee (PDF)
STV: Meeks (NZ) – A Flawed Method For Use In Democratic Elections
By JM Belcher & CR Oaten
20 February 2005

Post by Elizabeth Kerr

41 Comments

Filed under People, Politics, Project management

41 responses to “Why NOT…. the STV voting system

  1. Russell Garbutt

    Given that we are stuck with this type of STV voting system here in Dunedin for this election at least, then is there a voting strategy that will ensure that candidates that voters DO NOT WANT in Council will not be elected?

    As far as I can see, it is to make sure that any such candidate is not ranked at all by the voter. That way the counters cannot transfer any votes to anyone that is not wanted.

    Hence my original little slogan, “Don’t rank the rank”. I see that it has been slightly augmented by someone else to improve it to “Don’t rank the rank – leave them blank”.

    As far as I can see this is a strategy that will work if understood or appreciated and will at least prevent those that voters think unworthy getting in through the back door.

  2. James

    Hi Calvin,

    This is an extremely interesting submission, and has given me great pause for thought. However, after looking over the results for Cargill ’04 & ’07, and Hills ’07, I’m not convinced.

    1. In your hypothetical example, you have a strong ‘sleeper’ vote for Paul McMullan in second and third preferences, where he has around 1700% more in his second and third preferences than his first preference vote. Looking at vote redistributions, it is possible to calculate actual examples of sleeper votes in later preferences. The highest in the 3 elections I considered was 90% (Nicola Holman ’07). The next was 45%. I appreciate that exaggerated examples can get a point across, but 1700% is orders of improbable.

    2. You make much of Paul McMullan’s second preferences going to Teresa Stevenson, based on perceived similarities. However, she was also the strongest candidate overall on first preferences in ’04 (and elected at iteration 2, which is in itself unusually early). In ’07, she was not elected until iteration 4, and in every case where later preferences were redistributed, she polled highly. Therefore, her election is not based on some fringe element at work, rather, genuine popularity. Even if it were a ‘fringe’ at work, the actual number of fringe votes redistibuted is (by definition) low, so has little impact.

    3a. The proposed Belcher/Oaten method is not without problem. For example, it gives equal ranking to preferences 1-3. It could be assumed that voters will be most careful with their initial rankings, and that these are the most meaningful. The existing system gives strong weight to this element.

    3b. The lack of ranking for the number of candidates to be elected in the Belcher/Oaten method may bias those candidates with name recognition. A voter might genuinely favour several candidates as the first few choices and then ‘fill’ by those names they recognise. The latter would be given equal weight to the former. This will be especially problematic in the new 11 seat super ward. In fact, I am of the suspicion that that Belcher/Oaten system would heavily favour the well known existing councillors.

    _________________

    Relatedly, it is interesting to see in STV that there are still hangovers of pre-computer days. This is prevalent in quite a lot of statistical analysis. The idea of taking the lowest ranking voter and re-allocating is clearly a counting-by-hand driven step. With modern computational power, there is no reason that previously eliminated candidates could not be re-considered for inclusion based on later preference votes.
    Having said that, one of the reasons why processes haven’t changes is that based on re-analysis of existing data, a lot of the old shortcuts do usually produce the optimal (or as close as makes no difference) solution. In fact, looking at the first preferences (which I accept are not quite like FPP where you had 3 votes), STV and that approximation of FPP would have produced the same results in Hills and Cargill in those 3 elections, except Chris Staynes replaced Lee Vandervis (Staynes had a big ‘sleeper’ vote, doing the same or better in every iteration, whereas Vandervis did not fare well in lower preferences).

  3. James

    As far as I can see this is a strategy that will work if understood or appreciated and will at least prevent those that voters think unworthy getting in through the back door.

    There might be something to this. I note that when Nicola Holman was removed at iteration 7 in 2004, her re-allocations were highest for Michael Guest. These are more likely to be preferences 7 or higher, and may not be what her supporters intended.

  4. Stu

    I am astounded that anyone would consider marking all council candidates in order of preference as a good idea. The question posed at the ballot box effectively is: “Do you (the voter) want THESE people to serve on Council?” Doesn’t matter what the underlying system is: if you make a mark by a person’s name, then you are saying you find them fit to serve.

    My voting process runs along the lines of: do I know this candidate? do I know what they stand for? can I research this candidate and find out if they have the skills and experience that I see as necessary to serve effectively? If none of the above – if you have not engaged with me in any way as a candidate – you do not get my vote.

    Am I missing something here?

  5. James

    I am astounded that anyone would consider marking all council candidates in order of preference as a good idea.

    It does break one of the fundamental rules around measurement, in that ranking neccessarily makes the interval between each rank equal. While looking over this, I did consider rating each candidate 1-5 (1=hell no, 5=hell yes) plus a “don’t know” box would work better. However, I could also see problems with this. Then I remembered that democracy is the worst form of government, save all others that have been tried.

  6. Calvin Oaten

    Thanks guys: But none of it explains away the fact that all of the secondary preferences marked on the top polling candidates papers are set aside and never taken into account. Only those on the lesser, until quotas are met. Bummer that.

    • Elizabeth

      ODT sets out what it plans to do between now and September 17, when the delivery of postal voting papers begins, in order to help readers make informed choices:

      ### ODT Online Sat, 21 Aug 2010
      Much at stake in local body elections
      There is much at stake in this year’s local body elections. Today, we publish Southern nominations for the 2010 local body elections. It is every adult’s democratic right in this country to vote (just as it is their democratic privilege not to). We urge you to exercise this important right. Public participation in the democratic process is the very cornerstone of our nation.

      * Local body elections candidates 2010

      Read more

  7. James

    They are taken into account, just not very strongly. I believe it’s the bit that your submission refers to as arcane. If the quota is 1200, and an elected candidate has 1300 votes, then their second preferences are allocated to the value of the surplus (ie, 100 votes). So if 20% of their second votes are for candidate B, then candidate B gets 20 extra votes.

    It would be nice if these were kept as a separate iteration rather than merged for transparency’s sake, but there are a few that can be directly observed.
    Cargill 2004 – Iteration 10, Hudson’s and Stevenson’s later preferences are proportionally allocated to Guest and Hall
    Cargill 2007 – Iteration 7, Hudson’s and Stevenson’s later preference’s allocated to Guest and Holman
    Hills 2007 – Walls at Iteration 9, and then Staynes at Iteration 16.
    Interestingly, in all of those elections, the last candidate to be elected has been elected on the basis of the second (and later) preferences of the top polling candidates.

  8. Russell Garbutt

    James, having read the full findings of the Tribunal in the case of Guest, I can’t believe for a moment that anyone would want their vote to go to that guy. Unbelievable that he has the gall and effrontery to stand, but interesting to note that Mr Acklin seems to be his strongest supporter.

    But to return to the STV issue, it seems that the Dunedin method of STV whereby voters do not have to rank all candidates in order of preference is one of the least adopted of this system of voting. Nonetheless, this is what we’ve got, so what people have to understand quite clearly is how to vote strategically.

    If, purely as an example, you don’t want any of the strong pro-stadium, “put it on the plastic for the next generation”, “forget about the core, non-exciting things like water, sewage, transport, roading, parking – just give me a new rugby stadium” candidates, then don’t rank them at all.

    Wasn’t this what the learned Professor was saying the other day?

  9. James

    … then don’t rank them at all.
    The danger I see in this, say there are 3 councillors a voter despises so deeply that they want none of them equally, then by all means don’t rank them. However, if there are other councillors who you despise, but despise 20% less, such that you would marginally prefer them, then giving them a bottom ranking is important. Otherwise you are effectively abstaining, and apparently, according to the sage analysis of another recent vote, abstention is the same as support. This is particularly the case in the central ward. With 39 candidates for 11 places, conceivably you could have most of your first 20 preferences eliminated, and if you don’t discriminate among your ‘rank’, then you might give advantage to those with name recognition.

    I guess to go back to my first statement, you should only rank those who you absolutely (and equally) do not wish to have as councillors.

  10. James

    On the super ward…

    In trawling through the sums, I see both positives and negatives about the superward. The negative is the possibility that in the end, your first 20 choices could be eliminated, at which point I suspect the last 19 are not going to be terribly meaningful.

    On the plus side, a candidate with a smaller but sound following on a certain issue that cuts across the city might be more empowered by the super-ward. Say someone who is a staunch heritage advocate (or the environment or whatever) who has a good profile. Not enough support to make it in a single ward, but perhaps enough in a super ward.

  11. Calvin Oaten

    Thanks for all the comment. But when you weigh it all up, isn’t FPP by far and away the simplest and fairest multi candidate outcome solution? Everybody picks as many as they want-up to 11- equally weighted, counted and the greatest numbers win. Seems simple to me.

  12. James

    For the superward, I suspect it may not make a great deal of difference*, but I am very relieved that we have STV for mayor. If hypothetically there were two strong challengers to an unpopular incumbent, the chances of the incumbent being re-elected because of the opposition vote being split amongst the two challengers is much reduced with STV.

    *In principle, I think STV is fairer, certainly in smaller wards, but I do have some concern about the impact of having to potentially rank 39 candidates.

    • Elizabeth

      I sort of rely on a Mayor not to be let loose on the city because s/he has or should have the councillors as her/his mandate before action. I’m an old FPP supporter from way back. Any high tech explanation of the STV process clouds my brain cells and I can’t breathe.

      It is when the Mayor, like now, has bandits outside council running the ship that I do nil by mouth.

    • Elizabeth

      ### ODT Online Mon, 23 Aug 2010
      Local body candidates meeting shy of questioners
      By Eileen Goodwin
      The phrase desperate and dateless had a new twist on Saturday when Dunedin City Council candidates narrowly outnumbered “speed dating”-style voters at an event devised to put voters face-to-face with those who seek to represent them.
      Read more

  13. Anonymous

    With the possible exception of Teresa, I wouldn’t date any of them.

  14. Russell Garbutt

    “date” meaning what?

    {When ODT says “desperate and dateless” it means what it says. -Eds}

    • Elizabeth

      I think I’d rather not know :D

      • Elizabeth

        Haha. Didn’t take long. Tired.

        Trev (DCC candidate) at the Wall, Facebook The DCC has lost the plot.

        Trevor Turner Hi everyone, I have about exausted myself with discussions about the stadium. I would like some questions on other stuff. Please see the discussion marked ‘Trevor Turner, Candidate for Dunedin Central’. Or go directly to my facebook page

  15. Phil

    Hard to be sympathetic towards Trevor. He opened the door, thinking it would be a sure fire vote winner. Every second sentence had the word “rugby” in it. About 30 years too late for the “real bloke” persona to draw support. And too late to re-invent himself now. A valuable lesson in learning about your market before launching forth.

  16. Russell

    “James, having read the full findings of the Tribunal in the case of Guest, I can’t believe for a moment that anyone would want their vote to go to that guy.”

    It’s very simple if you don’t like the guy, don’t put a number beside the name. So if you don’t want to vote for Guest don’t, the electoral system we have in place doesn’t FORCE anyone to vote for everyone. Indeed you still have the democratic right to walk into a voting booth and put a number 1 next to the person you want in power and walk out, or spoil the vote.

  17. Russell Garbutt

    Paul, correct. Don’t rank the rank, leave them blank is perhaps a glib way of putting it, but it remains perfectly valid. While it is true also that everyone has the right to spoil their vote, it seems that this is a pointless and fruitless exercise if the action is supposed to be a gesture of not wanting to support the status quo.

    What I was pointing out was that after reading the findings on Guest the full document opened my eyes to some more of what he had been up to at the time, and more importantly how he persists in somehow dismissing or minimising what he has done. Whether voters accept that will be up to them.

    Allied to this is the fact that most people in our City have not read that full document. Our news in the mass media is controlled by selection. Whether we call it censorship, or whether we call it journalistic realism, my position is that people who may have felt inclined to sort of believe Guest by reading the ODT selection of what was important, perhaps would not feel the same after reading the full document.

    More importantly, if correctly reported, Chin and Acklin’s comments in particular take on special significance knowing that they have read the full document. Their reported statements seem to me to indicate that they condone a range of actions that Guest has been found guilty of, that society finds repugnant and unacceptable.

  18. Fliss

    thanks ejk and plc for getting all that done and dusted with proper advice from James who knows heaps about stv.

    And also to Trevor for finally outing himself as a candidate for DCC. Good on you for putting head above parapet. We know who you are now and why you have been saying what you have been saying for last few years and that is awesome.

  19. Steve

    Hello, James—

    In your post of 22 August (10.27 a.m.), above, responding to Calvin’s submission, you said—

    “Relatedly, it is interesting to see in STV that there are still hangovers of pre-computer days. This is prevalent in quite a lot of statistical analysis. The idea of taking the lowest ranking voter and re-allocating is clearly a counting-by-hand driven step. With modern computational power, there is no reason that previously eliminated candidates could not be re-considered for inclusion based on later preference votes.”

    It is a truism that, just as the candidate who is “first past the post” is not necessarily the correct winner, the candidate who is “last past the post” is not necessarily the correct candidate to exclude. This is an inevitable consequence of the guarantee in STV elections that later preferences cannot upset earlier preferences (rather than being “clearly a counting-by-hand driven step”). It is this guarantee that gives voters the confidence to rank-order candidates in their own true order of preference and not have to worry about what other voters might be doing. (Under STV, there is nothing to be gained by voting tactically. Indeed, it could well backfire on voters in that the candidate(s) they really want could be excluded through lack of support.)

    At least three systems that I know of have been devised that keep candidates in the running, who would otherwise be excluded early, so that they might benefit from later preferences. They are all what you might call “experimental” and have not been used in real elections.

    The authors of one such system (called ‘Sequential STV’) have this to say, as to whether or not their system should be “recommended for practical use”—

    “Should it be used?

    With this new version, should it be recommended for practical use? That depends upon whether the user is willing to abandon the principle that it should be impossible for a voter to upset earlier preferences by using later preferences. Many people regard that principle as very important, but reducing the frequency of premature exclusions is important too. We know that it is impossible to devise a perfect scheme, and it is all a question of which faults are the most important to avoid.

    In considering this, we need to take into account, among other things, that the true aim of an election should not be solely to match seats as well as possible to votes, but to match seats to the voters’ wishes. Since we do not know the wishes we must use the votes as a substitute, but that makes it essential that the votes should match the wishes as far as possible. That, in turn, makes it desirable that the voters should not be tempted to vote tactically.

    They would not be so tempted if they felt confident that later preferences were as likely to help earlier ones as to harm them, and if they could not predict the effect one way or the other. At present, we see no reason to doubt that these requirements are met.

    All things considered, we believe that Sequential STV is worthy of serious consideration.”

    Should STV be modified to reduce “the frequency of premature exclusions”, the later preferences of some voters would help earlier preferences, the later preferences of other voters would harm earlier preferences, and the later preferences of other voters still, would both help earlier preferences for some candidates and harm earlier preferences for other candidates. Such consequences of modifying STV would *very* likely occur in an 11-seat electoral area (such as the Central Ward) where, this year, there are 39 candidates and some 30,000 voters.

    Simple electoral systems are prone to giving unfair outcomes. To achieve fair outcomes (based on the votes cast) you have to complicate them a little. But, to paraphrase one US academic in this field, there is a trade-off between “refinements” in STV (improved treatment of surpluses, as with NZ STV; improved process of exclusion) and the cost in manageability – for example, very complicated election rules, computer programming, and reporting of results (that really *would* be opaque, as Calvin already complains of).

    We must keep in mind that we are dealing with public elections, not private elections. Therefore, bearing in mind that STV is still very new to New Zealanders, I think we should continue to allow the public to get used to what we have (over many more election cycles) before even thinking of making further refinements.

  20. James

    Hi Steve,

    Thanks for the response to this point. I’ve been enlightened by your explanations, particularly with reference to the potential influence of ‘party’ factions on multiple FPP results. It’s worth noting that Dunedin has no CitRats or Labour candidates, and that broadly speaking, apart from some success by ‘Greater Dunedin’ at the last election, no platforms have gained any traction in Dunedin (yet). In that circumstance, where a person might vote for top candidates based on multiple criteria, the same distortion wouldn’t occur; so there could be some merit in giving import to the top few votes.

    On the computing issue, some procedures (for example, linear regression) use inclusion/exclusion rules dating from a time when they were either run by hand, or on far less powerful resources. So, for example, it might be possible to run many millions of possible varying strategies on multiple election datasets, without the device sweating too much. Relatedly, some software I use defaults to terminating after 100 iterations (which takes under 1 second). When it fails to do so, I often bump it up to 10,000, and it usually mows through that pretty quickly, so again, I suspect the limit of 100 dates back to a time when computers were much, much slower.

    However, with elections, the number of possibilities gets large very fast. I believe Calvin orginally wanted data on which he could test his new system. In the Cargill Ward in 2004, with 8 candidates, there were 40,320 different permutations of ranking the 8 candidates (far exceeding the number of voters). Thus, to be able to calculate the votes themselves could entail a very great volume of data (for you would need to know how many voters picked each permutation, which could be anywhere from 100 to the number of voters).

  21. Steve

    Hello, Stu—

    In your post of August 22, at 10.39 a.m., above, on the subject of a voting strategy to ensure that candidates not wanted by voters do not get elected, you stated that you do not consider rank-ordering all the candidates is a good idea, and concluded by asking “Am I missing something here?” Given that voting documents start arriving in people’s letter-boxes today, I thought I would respond to your question.

    The process you intend going through in deciding who to rank-order is perfectly legitimate. At some point, you will say to yourself that the remaining candidates whom you have not so far marked have not engaged with you “in any way as a candidate”, and your rank-orderings will conclude at that point. If it turns out that you have not marked (say) 27 of the 39 candidates, that is absolutely fine.

    Having said that, however, the question being posed at the “ballot-box” (or, as I would say, at the kitchen table), rather than being “Do I want THESE people to serve on council?”, is really “If my first-choice candidate is excluded from the count (or does not need all of my vote to be elected), whom do I want my vote (or the surplus portion of my vote, as the case may be) to be transferred to, to help elect that candidate?” The candidate you choose gets your second preference. Then the question is, “If my second-choice candidate is excluded from the count, etc.” The candidate you choose gets your third preference, and so on, until you are unable to rank-order any of the remaining candidates whom you have not so far marked.

    What voters need to keep in mind when voting is that, regardless of the number of candidates they personally think are worthy of being on council, all 11 of those seats ARE going to be filled, and that it is quite likely that some of them will be filled by candidates they considered UNworthy of being on council (because 8.33% of the voters, in each case, DID consider them worthy). That being the case, and bearing in mind that later preferences can never harm earlier preferences, voters should rank-order as many candidates as they can, in order to have their say as to the filling of as many seats as possible.

    For example, the Central Ward count will eventually come down to two candidates, X and Y, contesting the 11th seat (all other candidates being either elected, or excluded). Although a particular voter might consider both candidates to be unworthy of election, the fact remains one of them is going to be, so he or she might as well have his or her say as to who that candidate is. The particular voter would have his or her say by giving a higher preference to the candidate who is the lesser of the two evils (or by rank-ordering one candidate but not the other). Candidate X might have received his or her 18th preference and candidate Y might have received his or her 23rd preference (or no preference at all). The remaining fraction of his or her vote that went to candidate X might well be, in a very close contest, the difference between candidate X filling the last seat and not candidate Y.

    By rank-ordering as many candidates as possible, that particular voter will have exercised as much influence on the make-up of the next council as possible. He or she might not truly consider candidate X “fit to serve”, but the point is, by helping to elect candidate X over the lesser-preferred candidate Y, that particular voter will have done as much as possible, with his or her single vote, to bring about the best possible overall outcome from his or her point of view.

    So, yes, Stu, in my view, you WERE missing something, but I hasten to repeat there is nothing wrong with the strategy you intend to adopt.

  22. Peter

    Just vote for people you know enough about – and can trust – is my motto. I’m not going to strategically vote for someone who is…….OK… because I don’t want X, Y or Z.

  23. Steve

    And fair enough, too, Peter. I have no argument with that. However, rank-ordering as many candidates as one reasonably can, is not strategic voting; it is simply ensuring you have as much influence on the result of the election as possible.

    • Elizabeth

      ### ODT Online Sat, 18 Sep 2010
      People not voting for many reasons
      By David Loughrey
      At the last local government election, in Dunedin and across most of New Zealand, voter figures dropped below 50% for the first time since the re-organisation of local government in 1989. Dunedin City Council reporter David Loughrey asks why the public is turning away from the action at the very heart of our system of government, what is behind the problem, and how it can be fixed.
      Read more

  24. Calvin Oaten

    Steve; isn’t ‘ensuring you have as much influence on the result of the election as possible’ the name of the game? The concept of ‘strategic voting’ seems to me akin to pinning the tail on the donkey in competition with you and all the other voters blindfolded.

  25. Steve

    *I* certainly would have thought so, Calvin. Nowadays, with candidate profile statements, candidate websites, much improved coverage of local elections both by newspapers and the electronic media, together with public meetings, it shouldn’t be too difficult for voters to rank-order as many candidates as they *reasonably* can.

    Yes, given that, under STV, votes (or the remaining parts of votes) are not transferred to a lower-preference candidate until the fate of the candidate with the immediately higher-preference has been determined, as either elected or excluded, the FPP concept of ‘strategic’ or ‘tactical’ voting is not actually possible; it doesn’t apply. That is one of the good things about STV. Voters have no incentive whatsoever other than to vote their true preferences. By not voting their true preferences, voters would simply be putting at risk the chances of election of the candidate(s) they most prefer.

    Your analogy of strategic voting is spot on. Very well put.

  26. Elizabeth

    The trouble is, perhaps, the lack of viable candidates presenting for election to Dunedin City Council. Just about everyone I know is saying this.

    No real campaigning is happening – not even a good old rally at the Town Hall or similar. Many of us can’t get Channel 9, although that forum is extremely limited anyway. Not one flyer in the the mail. The computer is something to hide behind too, most of the newbie candidates have no presence whatsoever.

    Instead, we have a Mayoral Forum at a small venue (Otago Museum) with attendance by ballot!

    Maybe it’s better in the outer districts and suburbs…

  27. ro

    I have a question for you Steve… what happens to my voting paper if my 1st choice (say) wins a seat on the first iteration of the vote? Are my other 13 (say) acceptable candidates discarded? Or are my votes for those other 13 not discarded until 11 candidates have received enough votes on subsequent iterations to gain seats?

    I ask because I have been hearing conflicting answers. And I am confused because it seems possible that we have more than 1 whole vote for one mayoral position but may have only one vote for 11 councillors.

  28. Steve

    Hello, ro—

    If your first-choice candidate attains the quota at the first iteration, that candidate’s keep value (currently 1.0) will be recalculated, and the surplus portion will be transferred to your second-choice candidate when the votes are re-counted (at the second iteration). For example, if the initial quota is 2400 votes and your first-choice candidate receives 2500 votes, his or her keep value will be 0.960 (2400/2500 = 0.96). At the second iteration, your first-choice candidate will keep 96% of his or her 2500 votes (2400), to stay at, or just above, the quota, and the remaining 100 votes (4% of 2500) will be transferred to your second-choice candidate. Those 100 votes (across 2500 voting documents), will stay with your second-choice candidate until he or she is either elected, or excluded from the count.

    So, your remaining 12 preferences (preferences 3 to 14, inclusive) just sit there on your voting document until the fate of your second-choice candidate has been determined. Should your second-choice candidate be excluded from the count, the surplus votes of your first-choice candidate will be transferred on to your third-choice candidate. The remaining 11 preferences (preferences 4 to 14, inclusive) still just sit there until the fate of your third-choice candidate has been determined, as either elected or excluded. And so on.

    Whether voting in the mayoral / WC-C Ward elections, or in the multi-seat Central Ward / M-T Ward elections, the value of your vote is always 1 (and only 1). In, say, the mayoral election, if your first three most-preferred candidates are excluded from the count, one at a time, your single vote will be transferred to your second-, then to your third-, then to your fourth-preferred candidate. At the conclusion of the count all the voters remaining in the election will be lined up behind the two most favoured candidates, one of whom will have more votes than the other (barring a tie, of course). This is what happened in 2004, but in 2007, Mayor Chin received an absolute majority of votes at the first iteration, so the count concluded immediately.

    It occurs to me that you are not aware of my explanatory papers, posted elsewhere at this site. You can find them at the “In defence of STV” post (put up on August 26), immediately following the main article.

  29. ro

    Thank-you for this explanation. I had seen your earlier accounts but then, reading others on other sites, I became confused. And in my head I can’t quite get round the inverse of my example above: what situation would obtain for my 13th-ranked candidate to have my endorsement distributed to her? What must have happened for this vote of mine to be awarded?

  30. Steve

    Hi, ro—

    I could have added another sentence to my second paragraph, after “And so on.” That sentence would be, “Under this scenario, should your third-choice candidate be the 11th and last candidate to attain the quota (i.e. be elected to fill the 11th seat), or ends up being the runner-up candidate, your preferences 4 to 14 would remain unused – not discarded – just unused, because, in either case, the final keep value for that candidate would still be 1.0.”

    Under STV, voters each have a single vote, which is transferable, if necessary. They use their vote by giving their first preference to the candidate for whom they vote. Later preferences, after the first preference, are not votes, they are merely contingency choices only, whereby voters are indicating what they want to have happen to their vote (or the surplus part of it, as the case may be) should their first-preference candidate be excluded from the count through lack of support, or does not need all of their vote to be elected.

    Now, keeping in mind that a later preference does not come into play until the fate of the candidate with the immediately higher preference has been determined, as either elected or excluded, there are two ways your 13th-ranked candidate can benefit from your vote. First, if the first 12 candidates you have ranked are all excluded from the count through lack of support, then, following the exclusion of the 12th-preference candidate, she will receive your entire vote, at value 1, the value of unity. (This could well happen in the Central Ward, given that there are 39 candidates standing for election.) Your entire vote will then stay with her until her fate is determined. (Were this to happen, then, at this point in the count she has, in effect, become your first-preference candidate, because, upon answering the question “Of the candidates now available, whom do you support?”, your answer was your 13th-ranked candidate.)

    Second, and far more likely, is the situation whereby some of the candidates you have ranked in the first 12 are elected, and the remainder are excluded. The fraction of your vote that finally gets to your 13th-ranked candidate (to help elect *her*) will be dependent on the keep values of the elected candidates whom you have ranked in your top 12. This is best explained in the “How was my vote used?” section of the paper that describes the New Zealand method of counting single transferable votes – the third paper down, page 3. If, after reading that section, you need further clarification, I would be happy to provide it.

  31. Steve

    Hello, ro—

    I have constructed an extended example of how a vote might be used, down to the 13th preference, for your information. Please see the link, below.

    Candidates B, D, E, H, J and K are elected, with varying final keep values. The candidates in between have been excluded (and therefore they each have a final keep value of 0.0). The first-preference candidate, A (the candidate for whom this voter voted), was excluded, so the vote transferred to B, to help elect him or her. B is an elected candidate who ended up needing only 47.72% of this vote (to stay at, or just above, the final quota), so the remaining value of 52.28% went to D. However, D is also an elected candidate, with a final keep value of 70.26%. Therefore, D kept 70.26% of the remaining value of 52.28%, being 36.73%, leaving a new remaining value of 15.55%. And so on, down the preferences until we come to candidate M (who is still hopeful). By this time, only 0.01% of the value of the vote remains, which is transferred to M. (M, with a final keep value of 1.0, is either the last candidate to be elected, or is the runner-up candidate.) The 14th-preference candidate, N, is also an elected candidate, but this vote did not help to elect him or her.

    It can be seen that while this voter was not able to help elect his or her first-preference candidate, he or she has the satisfaction of knowing that this vote contributed significantly to the election of his or her second-, fourth- and fifth-preference candidates (candidates B, D and E), to the extent that those candidates received 47.72% of it, 36.73% of it, and 13.42% of it, respectively (see column 5). In addition, it contributed, in a minor way, to the election of three more candidates, being H (1.29%), J (0.67%) and K (0.16%), and possibly to the election of M (0.01%). Not a bad outcome.

    Finally, if you add up the percentages in column 5, you will see they sum to 1.0000. (In reality, the STV Calculator calculates keep values to 9 decimal places after the point, adding a billionth of a vote if the result is not exact, ensuring precise accuracy.)

    https://dunedinstadium.files.wordpress.com/2010/09/vote_example.pdf

  32. Peter

    Steve. I know I am not mathematical, but this does my head in. Does it really matter? Vote only for people you consider good candidates in order of preference. Simple.

  33. Steve

    Yes, I agree with you Peter. If you don’t like some candidates, or are indifferent to many of them, don’t rank them. But, for those who find they can rank-order a few more, having studied the candidate profile statements, etc., they should do so, so as to have as much influence on the result as possible.

    Many people *do* wonder how their vote was used. All I have done is show those who are (or may later be) interested, how they can work it out. I laid it out in some detail this morning, because ro specifically wanted to know the circumstances in which his or her vote could benefit his or her 13th-ranked candidate.

  34. ro

    Steve, you couldn’t have answered my questions better. Thank-you.

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