Talk:Counting single transferable votes

Changes

I re-jigged the changes to establish the difference between Hare and Cincinnati - they both use random redistribution of votes, but Hare's are from a randomly determined surplus, whereas cincinnati is drawn at regular intervals from the whole set, to ensure a fair spread. Also emmphasised that the transfers from Hare can be from first preferences as well as from later transfers.

This is not the essential difference. The method of randomisation is a separate issue from the set from which the surplus is selected. The term "Cincinnati method" does not encompass every aspect of the process used in Cambridge. I have created a separate heading for randomisation. I also added a new grouping to emphasise the difference between surplus for previously-unelected candidate, and transfers to already-elected candidate. Joestynes 03:22, 27 May 2005 (UTC)

Right, that looks fair enough, though I still think that the example isn't entirely up to snuff, since the surplus is transfered with Hare whether it's a surplus from transfers or a simple first preference - i.e. the last 20 of 220 1st preferences would likewise be transfered...--Red Deathy 07:02, 2005 May 27 (UTC)

That's true (except saying the "last" 20 votes presupposes some ordering, whereas votes are usually randomised). I've just added the statement that, where the surplus arises from first preferences, the Hare System and the Cincinnati System are equivalent. The example is designed to highlight the difference between them, which occurs when the surplus arises from transfers. Joestynes 07:29, 27 May 2005 (UTC)

I reformatted the page so that it would be a lot easier to read. Basically, just changed indents and such so that each of the different methods could be distinguished as a separate topic and bumped the Example to its own major heading. --Leep4life 20:37, 14 December 2005 (UTC)

I could not locate any sources for the term "Cincinnati method" having anything to do with consequential surpluses. Indeed, the method used in Cambridge (the "Cincinnati method") does not allow consequential surpluses to arise. I have accordingly removed any references to the "Cincinnati method" as distinct from Hare. I would be very keen to be proven wrong if anyone has sources for the position previously expressed in the article. RunasSudo (talk) 08:31, 27 September 2021 (UTC)

Warren?

There is another technique, which also requires computer counting, called "Warren" - I assume, like "Meek" it's named for it's inventor. Can anyone explain the differences between the Meek and Warren methods? I think it's described in the Tidemann paper that introduced CPO-STV, but I can't find a copy of that any more - the link in CPO-STV is broken--Po8crg 02:03, 8 February 2006 (UTC)

Senatorial/Gregory

Do these methods really transfer fractional surpluses from all votes, or just those which arrived in the counting round which put the candidate over quota? I.e. are they a fraction version of Hare or of Cincinnati. The article currently suggests of Cincinnati (while saying Clarke) but I have seen a fractional version of Hare used. And the link [1] has a commentary for Dromore in 21 May 1997 saying "Of the 602 votes transferred to Gribben, 327 transferred further" suggesting that this is more Hare-like than Cincinnati-like. Similarly, is Clarke Hare-like or Cincinnati-like? --Henrygb 00:55, 22 April 2006 (UTC)

I believe the description of the Gregory method here is incorrect. My understanding is that the ERS97 rules and N. Ireland rules are examples of the Gregory method, and in these methods transfers of surplus votes are based on the last batch and not on all of the votes. What is described here sounds more like the weighted inclusive Gregory method. jeff (talk) 17:09, 21 July 2008 (UTC)

Correct it is the weighted inclusive Gregory method.

${\rm {{Surplus\ Transfer\ Value}=\left({{\rm {{Total\ value\ of\ Candidate's\ votes}-{\rm {Quota}}}} \over {\rm {Total\ value\ of\ Candidate's\ votes}}}\right)\times {\rm {Value\ of\ each\ vote}}}}$

Both are similar in implemenation with the difference being which votes the formula below is applied. The last bundle is a system designed to facilate a manual count where the weighted inclusive Gregory method can be applaied to all votes. Prsa (talk) 10:56, 14 August 2008 (UTC)

The last bundle fails to fulfill the 2 principles outlined by B.Meek. Namely

• Principle 1. If a candidate is excluded, all ballots are treated as if that candidate had never stood.

• Principle 2. If a candidate has achieved the quota, he retains a fixed proportion of every vote received, and transfers the surplus remainder to the next non-excluded continuing candidate, the retained total equalling the quota

Elimination

Of course it's an extremely unlikely scenario, but what happens if too many candidates have the same number of votes after, say, a few counts? What is the mechanism for deciding whom to eliminate? When using examples to explain the system it's naturally easier to take round numbers, and now my example has come to a standstill after two elections and one elimination. --Dub8lad1 20:42, 17 May 2007 (UTC)

It depends, all could be eliminated at once, or, if I recall correctly, they can toss a coin to see who goes out first.--Red Deathy 07:56, 18 May 2007 (UTC)

With any voting system, one can construct a hypothetical election where each candidate receives identical votes; some random lottery will be needed in such cases. That aside, there are some points in McDougall Trust articles [I've added a link to the index on the article page]:

From Random tie-breaking in STV:

Ties can arise in any STV election during exclusion. With some methods ties can arise at other stages as well; Jeffrey O’Neill [2] lists the cases. O’Neill also lists four tie-breaking methods. Two methods use the first or last difference in prior rounds to break a tie, and two methods use later preferences — Borda scores or most (fewest) last place preferences. Brian Wichmann [3] proposes to examine all possible outcomes.

From A new way to break STV ties in a special case:

• The ERS rules [6] and the Church of England rules use the first-difference method in an attempt to break a tie.
• The Meek algorithm [7] uses a deterministic algorithm based upon a random number generator to break a tie. No manual intervention is used. The New Zealand variant uses a similar method.
• When the Church of England rules are applied using a computer, then the software must break the ties without manual intervention in a manner which is not defined (by the rules).
• For Ireland, the manual rules are being computerized and have been used for three trial constituencies in 2002. Here, tie-breaking invokes a manual procedure, ie, the computer software does not break the tie.

  A curiosity is that in the Irish rules if when allocating surplus remainders there is a tie of the fractional part, the surplus vote is given to the candidate with the largest total number of papers from that surplus; if that is also tied then first difference is used.

• It seems that a Condorcet comparison has been used to resolve a strong tie between A and B (i.e. tie can’t be broken by first/last difference) in very small manual counts i.e. examine the papers to see how many times A is ahead of B compared to vice versa.

jnestorius^(talk) 22:19, 20 May 2007 (UTC)

Terminology: Various discussion have been had about the use of the word elimination during the count process. In the end is was considered more appropriate to use the word exclusion as the candidate is not eliminated but excluded from the count. Six to one half a dozen to the other. The other definition that under discussion was the words hopeful as opposed to "continuing candidate" Hope may or may not be applicable. If a candidate is in a un-winnable "hopeless" position are they really hopeful? Prsa (talk) 16:42, 9 August 2008 (UTC)

Some systems look back in the count and exclude the candidate that had the lowest prior value if a tie still exists then the decision is made by drawing lots (be it by a computer generated algorithm or manual selection (Draw out of a hat). Of course with the introduction of computer technology to assist in the count there is no need to remove the remainder values from the value of the vote. This limits the chances of a tie even more. Prsa (talk) 11:04, 14 August 2008 (UTC)

Meek's method?

On the subject of this pages meek's method section. Does anybody follow it? The paper referenced at the bottom gives a perfectly understandable explanation for anybody with the skills to reproduce it here.

Where does the formula 1-(quota/candidatesVotes) come from for the weighting of an elected candidate. If you read the paper everybody starts out with a hopeful weighting. When he becomes elected we use the equation w1j=w0j*q/vj, where in this case w0j=1. We then iterate this formula repeatedly till vj=q.

see section 2.9 in the paper for details.

Zfishwiki (talk) 16:07, 7 May 2008 (UTC)

Okay, I've corrected the formula for the weightings, but there is still a lot of room for improvement in the section.

Zfishwiki (talk) 18:00, 9 May 2008 (UTC)

Meek's method really needs more prominence. To my mind it is pure STV. It is based on simple principles and its basic algorithm is simple and elegant. Its Achilles heel, of course, is that it includes an "infinite" recursion (in practice usually of the order of 10 iterations give more than sufficient accuracy) and therefore requires a computer. That's why it only came along in 1971, but conceptually it allows us to throw out all the approximations that were necessary before we had computers (and several more that have been invented since).

It also makes it possible to allow voters to express equal preference.

Dmollison (talk) 13:06, 13 February 2016 (UTC)

This is still not good enough. The formula:

1 -\text{nth Weighting}

which is redered as "1-nth Weighting" needs 'n' to be defined, at least!

Nick Barnett (talk) 08:04, 9 February 2020 (UTC)

The numerator terms in the formula after 'The quota is found by' need clarification: (Votes - Excess / Seats + 1): Are these Votes total votes? What is the excess in excess of? Briancady413 (talk) 17:58, 16 October 2020 (UTC)

No objection here to giving prominence to Meek's method. But it is an exaggeration to say that it makes it possible to "throw out all the [other methods]". Meek's method is not a good one when paper ballots must be counted by hand. — Preceding unsigned comment added by C.M.Sperberg-McQueen (talk • contribs) 13:59, 6 October 2021 (UTC)

Wright System

Hi, I'm the author of the OpenSTV software. There are two problems with the references to Wright STV on this page. First, it is given undue attention as it is not well known and not used by anyone AFAIK. There are some vocal proponents of Wright STV but a few people being vocal should not justify it being included here. Second, it is misleading to say "The UK's Electoral Reform Society recommends essentially this method" as this is not true and the purported reference does not support the assertion (I know what the reference is although the link is broken). The quote to a statement by the PRSA seems inappropriate as this is not a page for advocacy. I suggest removing all references to Wright STV. For the record, I think Wright STV is a good system but there are many good STV systems that are not discussed here. Perhaps there should be a page that exhaustively lists STV systems. jeff (talk) 19:12, 23 November 2011 (UTC)

• 
  The Wright System Flow Chart

Update: I think I have worked it out. Thanks Prsa (talk) 16:45, 9 August 2008 (UTC)

Hi I am new to wikipedia and am not sure how to list references. I have added a reference to the Wright System which is a submission made to the Australian Parliament to change the way the Australian Senate and Victorian Upper-house count is done. It's aim is to introduce a weighted Surplus Transfer Value calculation and an alternative to the current segmentation distribution of excluded candidates. The Wright System , named after Jack Wright author of "A mirror of a Nation's Mind". It uses a reiterative count process as a preferred alternative to the current segmented distribution. One single transaction per candidate. Distribution of a candidates surplus is the same as in the WA legislation. This proposal differs from the meek's system.

The submission has been received favourably by the Victorian and Australian Parliaments' Electoral Committees

The Wright system fulfills the 2 principles outlined by B.Meek. Namely

• Principle 1. If a candidate is excluded, all ballots are treated as if that candidate had never stood.

• Principle 2. If a candidate has achieved the quota, he retains a fixed proportion of every vote received, and transfers the surplus remainder to the next non-excluded continuing candidate, the retained total equalling the quota

Prsa (talk) 11:06, 14 August 2008 (UTC)

I agree that the Wright system was being given too much prominence, especially as it has its own wikipedia page. I have also corrected the claim that it fulfils both of Meek's two principles. If it did, it would be Meek's method, I think! It deviates from Meek in not transferring to already-elected candidates. The justification for this is practical, as it makes hand-counting feasible.

Dmollison (talk) 12:58, 13 February 2016 (UTC)

Segmentation

In the section on the Wright System I don't really understand what is meant by "segmentation". Could anyone explain this? Martinwilke1980 (talk) 22:52, 1 October 2008 (UTC)

The terminology "segmentation" refers to the grouping and segmentation of votes in the process of distributing preferences. Under the Hare-Clark last bundle system votes are segmented into parcels or bundles based on the order in which they are received. Under the Australian Senatorial rules votes are aggregated and segmented based on the value of each vote. Segmentation came about as a way of breaking down the counting process in order to provide shortcuts to facilitate a manual count. In the process it created distortions and inequality in the count. Ideally there should be no segmentation and all votes should be transferred in one single transaction and not broken down into segmented sections. I hope this answers your question. The Meek method along with the Wright system was designed to avoid the need to segment the counting process. Meek being the most accurate and the Wright system being a refinement of the Australian Senate rule. It uses a reiterative counting process where the vote is rest and restarted on every exclusion. Where every vote is transferred in a single transaction without segmentation. One transaction per candidate (Distribution of surplus or redistribution on a candidates exclusion. 123.200.221.128 (talk) 23:35, 15 November 2009 (UTC)

"Surpus reallocation" section contains sub-par material

"The Duggan-Schwartz theorem proves that every choice voting system [...] is subject to gaming the system"

This "Duggan-Schwartz theorem" isn't elucidated or linked, so it's impossible to tell. But I can say for sure that by definition, no theorem proves anything. —Preceding unsigned comment added by Handelaar (talk • contribs) 17:24, 28 November 2008 (UTC)

Surplus re-allocation

This section needs substantial revision because it contains no information about the Inclusive Gregory Method (used for Federal Senate STV elections in Australia) or the Weighted Inclusive Gregory Method (used for local government STV elections in Scotland). —Preceding unsigned comment added by 83.67.85.174 (talk) 17:51, 6 February 2009 (UTC)

The weighted Gregory transfer system is also used in Western Australia, Tasmania and the Australian Capital Territory. It is extensively covered in the article. Counting_Single_Transferable_Votes#Gregory_method 123.200.221.128 (talk) 23:41, 15 November 2009 (UTC)

Equal rankings?

The article makes no mention of how to handle multiple candidates at the same rank. I know that some suggestions for this have been thrown around on the election-methods list, but have any been used in a real election? DanBishop (talk) 02:39, 11 May 2009 (UTC)

The established process is that if more than one candidate has an equal value then looking back in the count the candidate that had the lowest score is excluded first. If no candidate has a lower rating then the tie is broken by drawing lots. By retaining the remainder of any division with the value of the vote reduces the likely hood of a draw situation. The other option that needs to be considered is the question of bulk exclusion in which case the order of exclusion does not matter or effect the outcome of the election 123.200.221.128 (talk) 23:48, 15 November 2009 (UTC)

Copy-edit

Reduced the word count by 40% or so, and standardized much of the wording. I left several comments and questions in line because the original text was so broken. Looking at related articles, this one seems incomplete and still confusing. Cheers!

Lfstevens (talk) 03:44, 23 November 2011 (UTC)

Naming of article subsections?

I got to this page via a link to Gregory method, i.e. http://en.wiki.x.io/wiki/Gregory_method, which then redirected to http://en.wiki.x.io/wiki/Gregory_method#Gregory_method - but, there's no Gregory_method anchor on the page, only a Gregory anchor.

I presume this is true for other available redirects, but I'm relatively unfamiliar with this level of detail of how wikipedia functions.

So, I thought of changing the section name from "Gregory" to "Gregory method", but I'm not sure if that's the correct way to go about solving the problem that the redirect doesn't actually get me to the point in the page that it's trying to get me to.

If someone who knows the system better could either comment on what's a good methodology or just change it, that'd be lovely.

Lindes (talk) 14:30, 8 November 2012 (UTC)

Bias

This sentence seems quite biased

"The system minimizes "wasted" votes, provides approximately proportional representation, and enables votes to be explicitly cast for individual candidates rather than for closed party lists"

This ignores open list voting, which does allow voters to explicitly vote for individual candidates. It implies that SVT is the only proportional voting system that allows voters to vote for individuals. It can't be allowed to stand as is, as far as i am concerned, and will rephrase or simply remove the last part of the sentence. — Preceding unsigned comment added by 2.104.112.41 (talk) 15:46, 13 January 2015 (UTC)

Full ballots and how many winners meet the quota

The section on the Droop quota says in part:

Droop produces a lower quota than Hare. If each ballot has a full list of preferences, Droop guarantees that every winner meets the quota rather than being elected as the last remaining candidate after lower candidates are eliminated.

Neither of these two claims appears to be true as stated. To take a simple case, imagine an electorate of ten filling four seats. Unless I am mistaken, the Hare quota is 10 / 4 = 2.5 (which has the same effect as being 3) and the Droop quota is 1 + floor(10 / 5) = 3. The Droop quota will often be lower than the Hare quota, but not always. And even if all ten electors fill out a full list of preferences, there are not enough votes to elect four people each with a quota of three. Similarly, if 1001 electors are filling 999 seats, filling all 999 seats with the Droop quota of 2 would require 1998 votes.

There may be thresholds such that when the number of electors, or the number of seats, or their ratio, exceed or are less than the threshold, the second property claimed would be guaranteed to hold. A little algebra makes me believe, for example, that the second property is guaranteed to hold when (1 + floor(votes / (seats + 1)) is less than or equal to (votes / seats), i.e. when the Droop quota is in fact less than or equal to the Hare quota. But as formulated, the sentences quoted appear to be simply false.

It would perhaps be better if the paragraph read

Droop usually produces a lower quota than Hare. When this is the case, then if each ballot has a full list of preferences, Droop guarantees that every winner meets the quota rather than being elected as the last remaining candidate after lower candidates are eliminated.

[Addendum: when the number of voters is greater than or equal to the square of the number of seats being filled, the Droop quota will not exceed the Hare quota; when the number of voters is greater than or equal to the number of seats but less than the square of the number of seats, the Droop quota will exceed the Hare quota half the time. In those cases, Droop cannot guarantee that every winner receives a full quota of votes.]

C.M.Sperberg-McQueen (talk) 01:04, 5 October 2021 (UTC)

Droop always produces a smaller quota; the issue is this article uses an incorrect definition of Droop. Rounding up is not necessary. (If you did want to round up, you'd have to round both Hare and Droop.) –Sincerely, A Lime 03:09, 17 May 2024 (UTC)

Hare Quota

Article currently says:

The Hare quota's large size means that elected members have fewer surplus votes and thus other candidates do not get benefit from vote transfers that they would in other systems. Some candidates may be eliminated in the process who may not have been eliminated under systems that transfer more surplus votes. Their elimination may cause a degree of dis-proportionality that would be less likely with a lower quota, such as the Droop quota."

This is not a true statement. Evaluating simple examples of STV with the Sainte-Lague index of disproportionality suggests that Hare is fairer to small parties. A great deal of disproportionality is introduced by a small party failing to win a seat with less than quota if that seat instead goes to a party that already has a seat. The advantage of Droop is that is makes it impossible for a majority of the vote to win a minority of the seats. But this outcome is rare, and in parliamentary systems with many STV constituencies the aggregate outcome is likely to be fair.2A02:C7C:8A4A:BF00:491B:4117:D14:FA64 (talk) 22:09, 23 April 2024 (UTC)

with the Sainte-Lague index of disproportionality

Well, it's worth noting every quota will do better by some metric of disproportionality—Droop will look better if you compare apportionments using the Jefferson index (i.e. most overrepresented party). This outcome is also exceedingly common even in STV apportionments done by Droop quota; Malta has had 3 separate majority-preservation failures since 1981.

However, you're completely correct about Hare being, on average, the unbiased quota (see Electoral quota). STV is just bad at being proportional in general. –Sincerely, A Lime 03:02, 17 May 2024 (UTC)