Thursday, April 20, 2017

Wonk Central: Why We Don't Use The Hare Quota In Hare-Clark (Or The Senate)

For this exciting episode of Wonk Central I turn to the question of the Hare Quota, and why it is deservedly extinct in Single Transferable Vote multi-member electoral systems like the ACT and Tasmanian parliaments, and also the federal Senate and various state upper houses.  A warning that as usual for Wonk Central articles, this piece is especially mathsy.  A more important warning: I strongly advise readers with the slightest interest in the merits of different quotas for STV to stay well away from Wikipedia coverage of the matter.  It is so bad that I can't work out where to start in attempting to improve it.

The Hare Quota is best known to the psephosphere through the output of one Anthony van der Craats (aka MelbCity, democracyATwork etc) who continues to argue that the current Droop Quota disenfranchises voters and distorts outcomes in favour of the major parties.  An example is here (PDF); I am not sure if it is a representative example and I don't really care; any random one is enough to get the flavour of it.

Recently the Hare Quota made a surprise appearance in Bob Day's failed challenge against the new Senate laws (a challenge brought at a time when Day was not actually eligible to even be in the Senate, as it turns out).  Day asked the court to find in favour of the Hare Quota and against the Droop Quota for the Senate, but not much was seen of this claim in the actual arguments.  The court concluded that Day's argument against the Droop quota was "elusive", and that even had it been valid, there was no codified principle of proportional representation for a quota system to offend against anyway.

The Hare quota is sometimes used in multi-member elections that do not employ preferences.  While it can cause problems there too (such as encouraging parties to deliberately split into multiple tickets), this article is only concerned with its use in STV elections.

I hope that this piece will save people the effort of arguing with Hare-quota supporters who complain about the Droop quota.  While these people are extremely few in number they can be extremely persistent with their pet theory.  All you need to do if you see this nonsense is to thwack it with the link to this article.

The quotas

If a candidate gets a quota in one of these sorts of multi-member STV elections, they are elected.  If they have over a quota then spare votes are passed on to other candidates and the elected candidate is brought down to a quota in this process.  Whether these spare votes consist of all the candidate's votes at reduced value, some of them at reduced value, a selection at full or even increased value (etc) will vary by the system and the stage of the election at which the candidate has crossed the line.  The key question for this article is what that actual quota should be.

The Hare Quota is simply the number of formal votes divided by the number of seats.  If there are 42000 formal votes and 6 seats then the Hare Quota is 7000 votes.  The Hare Quota was used in some early implementations of STV but recent examples of its use in serious legislatures seem to not even exist.

The Droop Quota, now generally used instead, is:

(votes/(seats+1))+1  , rounded down.

So for 42000 voters and 6 seats, the Droop Quota is 6001 votes.

The argument for Droop Quota

The argument for the Droop Quota is that, for an election for n seats, the Droop Quota is the smallest number of votes that n candidates can reach, but more than n candidates cannot.  If the quota was 6000 votes, then in theory seven candidates could get exactly that many each, so there might be a need to break ties.  If the quota was higher than the Droop Quota, then not only might the count take longer than it needs to (an issue with hand-counting) but also votes could flow pointlessly as preferences to candidates who are already mathematically sure to win.

(In electoral systems that allow votes to exhaust, a common modification is to have a progressively reducing Droop quota rather than one fixed for the whole count.  Now that computers can easily handle this, it would be nice to see a lot more of this in Australian systems.)

Hare Quota: failed arguments and other problems

The wasted quota argument

The major argument made for the Hare Quota is that if there are n seats and Droop Quota is used, then around 1/n of the vote never elects anyone, but sits as an allegedly "wasted quota" of supposedly "disenfranchised" votes.  Quite often these votes pool with a candidate who is neither elected nor excluded - the candidate who comes seventh in an election for six seats, and loses because he/she is in last place, everyone has been excluded and there are no other votes left to distribute.

If we apply this to a single-seat preferential election, we should immediately notice how silly this is.  For a single-seat election, the Droop Quota is 50% of votes, plus one, rounded down, which is also known as an absolute majority.  Does this mean those whose votes finished with the losing candidate out of the final pair were "disenfranchised" and their votes were "wasted" just because they did not elect anybody?  No, it just means that when only one seat is elected it isn't possible that everyone preferences the winner.  Elections have winners and losers.

Also, when someone wins big in a single seat election, the supposedly wasted vote isn't 1/n - it's actually much smaller.

Both these points apply in multi-seat elections too.  Just as somebody has to come second in a single seat election, so also somebody has to come sixth in a race for five seats.  In the Hare-Clark or Senate systems using Droop quota this person is left without quota while the others are elected, but it happens in the Hare quota too.  For instance for a Hare Quota six-candidate election with five seats and 5000 voters, suppose the six candidates poll 1000, 900, 850, 800, 750 and 700 votes.  The candidate with 700 votes is excluded immediately and loses.  As all the other candidates will automatically win, and distributing the excluded candidate's preferences will not change the result of the election, so effectively 14% of the votes have been "wasted".  This isn't some scandal of disenfranchisement, it just means that six into five doesn't go.

And the number of votes left with the final failed candidate under Droop Quota is usually not that close to 1/n anyway, unless the outcome for the final seat is very close.  In Tasmanian House of Assembly elections, in theory the wasted quota is 16.67%, but in practice in 2014 the rump candidate finished with 11.1-13.7%.  Exhaust plays a role here, but even without it, margins of 2% or so for the final seat are not uncommon.  In theory one could keep distributing votes once the last candidate got a quota and thereby "fill up" the wasted quota, but why bother.  After all, the votes coming in have helped elect someone.

And indeed, it's often not understood that the votes that make up the "wasted quota" also include fractions of votes that have been used to elect successful candidates.  Even if there is a "wasted quota" of vote values, that doesn't mean there is a quota of voters who have not helped elect anybody.

Hidden Vote Wastage

What the Hare Quota devotees won't tell you when they talk about the "wasted quota" is that it is actually their system that wastes vote-values, only the vote-wasting is hidden through the count rather than sitting somewhere obvious.  Once a candidate has reached the Droop Quota, they are certain to be elected no matter what the quota is even if they don't get any more votes for the rest of the preference distribution.  So all the votes they get between the Droop Quota and the Hare Quota are unnecessary to them, and will just reduce the value of their surplus below what it would be under Droop.

This is most starkly seen if we look at the Hare-Clark system, in which only the last bundle of preferences that puts a candidate over the line are thrown again as a surplus, rather than all votes they have received being thrown again as in the Senate.  Suppose there are four seats and candidate A tops the poll and polls the Droop Quota (20%+1) on primaries. Candidate B polls last and polls 4%, all of whom put candidate A second. In a Droop quota election, candidate A is elected immediately.  Candidate B is excluded, and B's votes flow at full value to whover else is in the race.  In a Hare Quota election, Candidate B's votes flow to Candidate A even though Candidate A was already certain to be elected, and flow no further from this point.  Although they technically help elect someone, they really make no difference.  B's votes may as well have been thrown away after the primary count, so it is really the Hare quota system that is destroying voter intention.

Over the course of a Hare quota STV election, this hidden vote wastage can waste (n-1)/(n*(n+1)) of the value of all votes before the final seat gets decided - 15% for 4 seats, 13.3% for 5 seats, 11.9% for 6 seats and so on.  And this is genuine pointless vote value wastage, not the spurious conception of "waste" that comes from the fact that not everyone can always vote for a winner.  It's a point completely missed by those who think the use of the Droop quota is just a convenience for manual processing.

Minority Rules

A well-known paradox with the use of Hare quota for STV goes like this.  In a very polarised electorate six candidates for five seats run in two teams, A, B and C versus D, E and F.  The first team's voters all vote in the order A-B-C, meaning that A gets a primary vote of 52%.  The second team's voters split their votes, with D getting 17% of primaries, E 16% and F 15%.  A is elected with a surplus of 32% which flows to B.  B is elected with a surplus of 12% which flows to C.  Now C is last with 12% and loses.  As a result team A-B-C wins two seats with 52% of the vote, and team D-E-F wins three with 48%.

In contrast using the Droop system: the quota is now 16.67% so all of A, D, B and C are elected with quota, and the surpluses of D (0.33%) and C (2%) will then decide the last seat between E and F.  The more popular team wins three seats, as it should be.  Some might say parties should be encouraged to pick a range of candidates who can poll healthy primary votes in their own right, but it's not a party's fault if it happens to have a candidate who its voters all think is especially good.

This objection is in itself widely and rightly considered fatal to the use of the Hare quota in STV.


Supporters of the Hare Quota frequently argue that it is more proportional.  That it is more helpful for small parties generally compared to the Droop Quota is pretty obvious because the major parties cop hidden vote wastage every time a surplus is thrown.  The table below shows what share of seats a party would be guaranteed in a five-seat election, assuming a 100% down-the-ticket preference flow (but no preferences from any other party) for various sizes of primary vote under each system:

In the Hare quota system parties are only guaranteed a seat share exceeding their primary vote share if they poll above 90% (in this case they are certain to win the fifth seat without quota).  But in the Droop system there are bands where this occurs at as low as just over a sixth of a vote, and these become commoner as the vote increases.

However, it may well be that the Hare quota system would be too favourable for leading minor parties.  A good example is the 1998 Tasmanian state election, in which Labor (44.8%) won 14 seats, the Liberals (38.1%) won 10 seats, the Greens (10.2%) won 1 seat and Tasmania First (5.7%) won nothing.  The Greens were clearly diddled on a proportionality basis (more so than has been normal in the 25-seat House). Using the Hare quota, however, the seat result would have been 10-10-5, with Labor under-represented for their vote share and the Greens getting almost twice as high a share of seats than votes.  Indeed, the result of this 1998 election using the Hare quota would be exactly the same as for the 2010 election at which the Greens actually did break 20%!

In conclusion

The Hare quota is simply not a valid option for STV elections.  The system fails to prevent the so-called "wasted" vote issue in the Droop system, which actually isn't an issue at all, but in the process wastes votes itself (and lots of them.)  The system creates a risk of a minority beating a majority unfairly.  While it has been claimed that it results in greater proportionality, that claim has not been tested enough using real electoral data, and even if it were true, the other defects mean that the system is unusable anyway.

Note: Normally I reject posts that advocate the Hare Quota from this site but this thread is of course an exception.  If anyone wants a go at defending the indefensible, go right ahead.


  1. Well put, Kevin. One further related mark against the Hare Quota is that a candidate in any STV system is guaranteed to win the final (or sole) seat as soon as he or she has more than half of the votes remaining in the count. (Putting aside for the moment the issue of optional preferences exhausting, because that affects both the Hare and the Droop quotas). Under the Droop quota, in a race for five seats, with the quota being 16.6667%, all five candidates need a full quota to be elected. A candidate with "only" 16.6665% could still be defeated in a nail-biter. By contrast, under the Hare quota, in a race for five seats, with the quota being 20.0000% or (in some versions) 20.0001%, the first four candidates need a full 20% to be elected, but whichever candidate wins the fifth and last seat is home and hosed as soon as he or she passes 10.0001%. In other words, the final candidate - who is, all else being equal, likely to have lower first-preference support than the other four - needs only half as many votes to win a seat!
    Sure, you could keep eliminating the lowest and distributing their preferences until the fifth candidate does officially pass 20%, but (a) that's only a victory lap and (b) by exactly the same token, you could do the same under Droop Quota STV and increase the likelihood that all or most of the five with 16.6667% will edge up to, or over, 20%.
    Thomas Hare deserves accolades for coming up with the idea of a single transferable vote, but his version was a first draft that has been improved upon in the 150 years since. Like the Julian calendar, it's been superseded by a more finely-tuned Mark 2.0, and for good reason. (STV advocates have also dropped Thomas Hare's and JS Mill's model of a write-in ballot with 650 lines for names of candidates for all 650 Commons seats, elected at large.) Arguing that the Hare Quota gives better representation is the psephological equivalent of arguing that printing more dollar notes makes everyone wealthier: it has a certain intuitive appeal at first glance but doesn't hold up when you study it more closely.
    PS: Some Hare-quota advocates cheat by arguing that most party-list systems employ the Hare and not the Droop quota. This is true for the minority that use largest remainders, but for the majority that use D'Hondt highest averages (eg, the Hagenbach-Bischoff method used in Switzerland), it makes no difference to the ultimate allocation of seats which quota is used as an initial short-cut.

  2. Hi Kevin,

    Just trying to get my head around this concept of a Hare quota. I noticed that you have accidentally linked to a document on your C: drive.

    1. I thought I had fixed that link! It should be fixed now.

  3. Excellent walk through. I will definitely refer to this in future.

  4. Your comment in relation to single member electorate 50% rule is false and misleading. If you apply a fully proportional quota (x.y) this can and does still apply in a single member seat The quota being 100% Whilst at first this may seem illogical it never the less still applies as the 50% rule is the tipping point. Further calculations are not required.

    The Droop quota was introduce to mainly facilitate a manual counting system. the requirement to continue to count all votes to the end point was cumbersome and time consuming and in most cases 95% would produce the dame result. When I first became inclived in countings systems I also was of the view that the Droop quota made sense.


    With the adoption and use of a computer based counting system the need and justification for the Droop Quota no longer exists

    The current systems in use are outdated and flawed.

    If you subscribe to the principle that all votes should be counted equally then continued use of the Droop quota is brought into question. It should be discontinued. Computers can perform the calculations necessary with minimal delay.

    I suggest you undertake a number of re-counts of the senate vote and apply the principal and methods outlined in the Wright System documentation. QLD and Victoria Senate 2007 are worth looking at as is the WA Senate election in 2013, The Wright System aims to strip out all the adaptions and modifications that were applied to facilitate a manual count.

    1. Thought you'd find this eventually!

      Firstly you don't provide any evidence that my comments are "false and misleading". You are refuting some argument that I never made in this article and may never have made at all about applying Hare to a single-seat election.

      You present no evidence that "The Droop quota was introduce to mainly facilitate a manual counting system." This isn't the case - arguments for replacing the Hare quota with the Droop quota based on the Hare quota causing unfair wastage were already widespread in the late 19th century, eg Baily's "Proportional Representation in Large Constituencies" (1872).

      The comments about Wright are a red herring as Wright can be used with either quota and the arguments for its adoption go to different questions. One can have a computer-count system with Wright using the Droop quota and there might well be good arguments for doing that. But that's a different debate.

  5. PS. The tipping point in a pure proportional quota system (x/y) would be x/y/2.

    If w apply the reiterative model where the count is reset and restarted following every exclusion, this would faciliate optional preferential voting as the quota would be recalculated on each iteration/ Any votes that do not maintain a value or indicate a valid preference for a continuing candidate would be excluded from the count as they drop off. This would address a number of concerns that have arising following the Green/Liberal modifications to the Australian Senate voting system.

    Above the line voting

    A further refinement should be considered to Group Voting. Any vote 'above the line' should be distributed and allocated equally to all members of the group. The order of exclusion within the group being the reverse order of the group ticket. This would better reflect the voters intention and would limit the opportunity for others to game the voting system.

  6. A good example of the flaws of the Droop Quota is the City of Melbourne 2012 Council Election. Team dole received 38% of the vote and only elected three positions Whilst the Greens on 12% elected two.

    The other issue comes with using a count back system where only votes used to elected the vacating candidate are taken into account. Those votes left on the table are ignored. Under a full proportional quota the countback system would work as intended.

    1. I assume that Melbourne 2012 example cluttering up Wikipedia undeservedly is yours. If so the Greens are shown as having 15.6% (not 12%). In the Hare example the Greens with 15.6% get only one seat, but three little tickets with 6% each get one too (up from two in the Droop case). This could be argued to be unfair just as easily.

      Really the City of Melbourne case is not even worth talking about because it is contaminated by Group Ticket Voting. Under the Senate system using Droop, the fourth Doyle candidate would have been in seventh position after surpluses and would probably have won, while the Greens would have been in eleventh, in a four-way fight for two seats. However using Hare, the fourth Doyle candidate would have been 11th after surpluses, behind the Greens in 10th. So with a real preferential system, the Droop quota would have been better for the Doyle team compared to the Greens and the Hare quota worse.

  7. Quota reset is also a different issue. There is no reason why the current system could not use a progressively reducing quota (with no other changes) and in my opinion it should.

    Re your proposed change to Group Ticket, there are definitely tickets for which it would not "better reflect the voters intention". For instance Jacqui Lambie Network 1 above the line voters did not regard Lambie, Martin and Waterman as equals but rather, in general, knew that a 1 above the line was also a 1 Lambie. Indeed, if the system had distributed their votes equally that may well have forced those voters to vote BTL. Now that BTL voting is so easy hopefully over time voters outside Tasmania can be educated to use it if they disagree with their party order.

  8. In the City of Melbourne example had a full proportional quota been used 8 percent of the electorate would have had their vote counted as opposed dumped on the wasted quota pile. Te system used inflated the Green vote . Instead of the greens electing two candidates a independent community candidate would have been elected. Try counting the vote based on real data. To blame the ticket vote is also somewhat ingenious as in may cases before group voting was introduced voters followed the recommendations of the party ticket. The mathematics still remain the same. you are denying a full quota -1 rights of representation and in the process increasing the vote and representation of the minor parties

    There are three main issues that need to be resolved.

    1. The weighted Surplus transfer. (Which most pundants are in agreement nees to be changed (See WA Upper-house legislation).
    2, The distribution of excluded candidate preferences. Putting an end to the skipping and jumping. A reiterative count (where the count is rest and restarted following every exclusion) solves this issue and also facilitates optional preferential s the quota is reset and recalculated on every iteration. A second pr subsequent preference will be allocated to the continuing candidate(s) in order of the voters preferences.

    3, the method of determining the quota. Pure proportional means that all continuing votes are allocated and counted without distorting the outcome. The City of Melbourne count is a good example of that. These issues also manifest itself in non group ticket vote counts also.

    The other example worth looking at is the 2007 and 2010 Senate count and the WA Senate preliminary count before votes went missing.

    The method of calculating the quota needs to be considered and debated separately to the first two issues which stand alone.

    Changes to the Australian Senate voting ticket system introduced by the green/liberal alliance Exacerbate this distortion Pauline Hanson would not have elected two senators in the double dissolution.

    To initiate a full proportional reiterative count would have been prohibitive under a manual count. With the election of small voter elections) count. If you need the preference data files i can send you but they are published on the AEC web site.

    I suggest you go back to basics and consider the system a fresh opposed to blindly applying existing rules. Rules that were put in place to facilitate a manual count not to reflect the voters intentions. I sue to think as you did until I started looking at the real data and questioned the way elections were being counted.

    Again .. try counting the vote using real vote data. Look at Victoria 2010. Senat0r Feeny could have lost his seat had one nation placed the Liberals ahead of Labor.Not because of One Nations preference flow but because of the way the vote is counted. Some votes are worth more than others. In the 2016 Melbourne City Council vote the Greens vote is inflated by 8,000 votes disproportional to their support. Sorry The system as it stands can not be defended based on real data and pure mathematics.

    Adopt valid principles not perceived outcomes.

  9. I don't have a problem with One Nation winning two seats in Queensland. They polled more than a quota and their performance on preferences was sensational. It is not just about the primary vote. If they get one seat with their 9.2% and their excellent preference performance, and some micro (possibly two of them) with 2-3% and a miserable preference performance get the same, then I can't see why that would be any better. Except for people who are motivated by dislike of One Nation rather than a fair outcome. Likewise, why do you continually stress that the Greens could have been beaten by an "independent community candidate"? Surely the question is who is more deserving of the seat based on electoral merit, not what sort of candidate they are.

    Much of your post just repeats material my article already debunked, which is really just a waste of everyone's time. You don't engage with the point that there are always votes that don't elect someone. You don't engage with the point about Hare quota hidden wastage and you don't engage with the point about the potential for minority wins based on spreading of the vote within a ticket. You just keep repeating the same old claims.

    And again, surplus transfer and reiterative count are distractions to the debate about Hare quota vs Droop quota. They are independent issues.

  10. Yes but their representation was greater then their proportion of vote.

    Sorry you have not debunked anything just seeking to justify the unjustifiable. S

    urplus Transfer and method of distribution are the main problem with the Hare Clarke system (In Tasmania they use the flawed last bundle system - It had its place under a manual cont but its continued use can not be justified with the aid of computer technology)

    I have no problem with the principle of Single Transferable Votes.

    I do take issue with the way it is counted. Particularly when that system distorts the proportionality and voters inventions. Might as well adopt a Party List system.

    As to your assumption and statement as to 'who is more deserving'... Is this not the decision of the voters?

    If you count the 2012 City of Melbourne Election properly as outlined in the Wright System an independent Community Candidate would have been elected not a second Greens. The Greens vote was inflated by the system itself.

    1. There will always be some parties whose representation exceeds their proportion of the primary vote because it is not practical for all parties to be represented. That's simply a fact of life. Given that such parties must exist it is better that they be parties that have polled a substantial vote and also demonstrated a substantial voter-determined preference flow. You cannot talk about proportionality purely in terms of primary votes credibly here; this is Australia, not some primitive European system that doesn't have cross-party preferencing.

      You can say I haven't debunked anything but the fact is I've presented arguments that you've ignored. Anyone can see this so it is pointless denying and evading it. You should either address those arguments or admit you have no answer to them.

      "If you count the 2012 City of Melbourne Election properly as outlined in the Wright System an independent Community Candidate would have been elected not a second Greens" - Does this apply if the Wright System with the Droop Quota is used? If so then the issue isn't the quota. If not then there is a serious questionmark over whether we should even care. But in any case that election was hopelessly defaced by Group Ticket Voting which attacks proportionality by creating unnatural preference flows.

  11. The mathematics speaks or itself - The Senate voting system if flawed.

    The calculation of the Surplus Transfer value is seriously in need of review. (Not hard thing to fix. Needs to be based on the value of the vote not the number of ballot papers

    The method of distributing preferences is another no drainer. Votes should be redistributed according to the voters ecpress3d order of preferences.

    NO Full value vote should EVER skip a continuing candidate.

    If my candidate is excluded from the count then my vote should be redistributed according to my next available preference.

    The best way to achieve this is to adopt a reiterative counting process where the count is reset and restarted, The quota being recalculated on each iterations. This accommodates optional preferential voting where some vote no longer express a preference for a continuing candidate.

    As to the quota... the Droop Quota (x/(y+1)) ignores the votes of the so called Wasted QUOTA. All votes should be counted and considered in a full proportional system. (x/y) is the purest form of proportionality.

    You need to consider this question in conjunctions with the weighted Surplus and the reiterative count, which in the past has not been adopted as it was impractical to count it manually (Except in small electorates).

    The Write system strips back the modifications and removes patches and add-ons that were adopted to facilitates a manual count. No longer needed with the aid of computer technology.

    In the past they use to use a random distribution of preferences or as under the Tasmanian Hare Clark system they use the Last Distributed bundle.

    All votes to redistributed in a Surplus transfer should be transferred as a single transaction with the value of the vote being proportional to the transfer. (Not segmented)

    We need to start again, Look at the flow of data and remove those steps that do not meet the following principles.

    I have no problems with maintaining the Group voting. Very few people deviate from the direction of the group ticket. Those voters who do not support group voting can vote below the line.

    Happy with preferential voting above-the-line PROVIDED they fix the counting system.

    Group voting is not the issue the method of counting is.

    The system was made worst by the Green/Liberal alliance reforms in the lead-up to the 2016 Senate election.

    Again re-count the City of Melbourne 2012 Election. And then look at the 2016 Election where the Greens vote was inflated beyond there support.

    I have not fully canvassed the flaws in the Tasmanian Count Back system or the Hare Clark Last Bundle.

    The maths speak for themselves. If teh scale tips one way so be it,. But do mot remove or exclude votes to achieve your desired or preferred outcome. One vote one value. Single Transferable vote - The Wright system

    Principle 1. If a candidate is excluded from the count, all ballots should be treated as if that candidate had never stood.

    Principle 2. No full value vote should ever skip or jump past a continuing candidate

    Principle 3 Each vote MUST be treated and considered equally. One Vote one value. They should NEVER increase in value.

    There are two system that meets these requirements.

    The Wright System and Meek. ( I prefer the Wright system as it is less convoluted and easier to follow. The number of iterations nd transfers equal the number of candidates. The last iteration is the one that determines the outcome of the election

    Time to stop, rethink and start again.

    Pure Proportional Mathematically correct Same rules apply if there is one or multiple candidates,

    1. This isn't the place for discussion about a shopping list of irrelevant proposed reforms, this thread is about debating the use of the Hare quota in contrast to the Droop quota. If you submit any further comments to this thread that are mostly off the topic of the Hare quota, I may well not accept them. The invitation was to defend the indefensible, not to go on about irrelevant issues. Perhaps one day I'll post a thread here about Meek and Wright and so on, perhaps not.

      The article points out why the "wasted quota" argument against Droop is bunkum and you're still just sloganeering and not engaging with the points made. The idea that votes in the so-called "wasted quota" are not counted or considered is just obviously false. Of course they are counted and considered, they just don't happen to elect anybody - which also happens with votes under the Hare quota.

      I don't need to consider the question in conjunction with anything because the Hare quota has similar and fatal problems in all of these systems. It is true that the problems are more severe in, say, last-bundle Hare-Clark than when using Weighted Inclusive Gregory, for the reason I explained in the article. However, even when the Hare Quota hidden wastage is spread there is still as much of it in total.