Redirected from Talk:Droop quota
The quota you need to reach in Proportional Representation using the Single Transferable Vote to get elected.
Please stop changing this to lower case. It is a proper noun. It is the formal name of a formal electoral quota. It is not a generic term but a specific name of a specific item. FearÉIREANN 00:01 19 Jun 2003 (UTC)
except that PR.STV does not operate on the basis of such large constituencies. The largest in Ireland at present is 5 seats. I think the largest ever was 8 seats. I don't think Malta which also uses PR.STV has larger constituencies. For example, if you have 100,000 votes cast in a constituency that has 5 seats, that produces (100,000/6) + 1 = 16,667. So the quota each candidate needs to reach is 16,667. Using PR.STV, each candidate when elected has that proportion of votes they have over the quota redistributed through lower preferences. If no candidate is elected, the bottom candidates are eliminated. Eventually through the distribution of surpluses or eliminations, five candidates will reach the quota, with not enough votes left for any candidate to reach the quota a sixth time. (If they did that would cause a problem as there are only 5 seats. So the quota is constructed to ensure that it is mathematically impossible for anyone other than the five candidates elected to reach the quota. It works quite simply using PR.STV. FearÉIREANN 00:14 19 Jun 2003 (UTC)
It is a slight bit more complicated; eg how do they decide which votes are your surplus votes, do they always go for distributing a surplus or eliminating a low candidate, and also sometimes they eliminate a number en bloc. But it makes for riveting TV. Unfortunately Ireland is replacing manual counts which are slow and nail-biting (I covered the last Irish general election count in some Dublin constituencies for a Sunday newspaper until 2am!) with electronic voting, which can give counts in minutes. A lot of us election-anoraks will miss the fun, especially as there is a phenonemon known as a tallyman who is a professional vote watcher. They can watch ballot boxes being opened and incredibly predict how four of the five seats, sometimes five of the five, will go before the count even starts. So ireland would have three or four hours of tallymen's predictions from around the country, then 10-15 hours of nail-biting counts, often with demands of recounts and rechecks.
Here's an example of how it could work, using the above quota:
say I get 17,000 Number 1 votes. I would be declared elected. I would have a surplus of 333. Those 333 votes would be examined to see where there Number 2s went. If say 200 went to to Kingturtle, and you were previously at 16,660. In the second count, your total would increase by 200 to 16,860. You would be declared elected, having won the second seat. Your surplus (amount over the quota) would be 193. They would then be examined for Number 2s in the third count. If after their distribution no candidate was elected, the bottom candidate would have his/her total checked. Say mav had 500 votes. The returning officer would announce that no-one had been elected at the end of the third count, and he was now proceeding to the fourth count, the elimination of Mav and the distribution of his votes. This would go on until either five candidates had through surplus distribution or eliminations reached the quota or until the difference between the last three remaining candidates was such that even if the bottom candidate was eliminated and all their votes sent to the second placed candidate, that second placed candidate could not get ahead of the first placed candidate, in which case the last candidate would be declared elected "without having reached the quota".
Elections using PR.STV can be very exciting, with counts going on for hours, often until the ninth or tenth count. Its beauty is that most people's votes help get someone elected, whereas in plurality voting, often most people's votes have no impact whatsoever, as the candidate who wins wins with the biggest minority vote. If my first choice candidate is eliminated, they look at my ballot paper to see who was my second choice, if she is eliminated, they look at my third choice, etc etc until eventually my vote may help elect someone, even if it to get the eighth place candidate on my ballot elected if I prefer him to my nineth choice. It is one of the fairest electoral systems around, and also produces some of the most exciting electoral counts imaginable, often with the last seat going down to the wire with 50 votes or sometimes as little as 2 votes deciding who gets the last seat. FearÉIREANN 00:39 19 Jun 2003 (UTC)
That I don't know. I think it may be the mathematician who first drew up the formula but that is just a rough guess. FearÉIREANN 00:39 19 Jun 2003 (UTC)
Looks to me like the capitalization is pretty equally distributed between "Droop Quota" and "Droop quota", according to a google search (http://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=droop+quota&btnG=Google+Search). One site (http://accuratedemocracy.com/e_ler.htm) even calls it "Droop's quota." Also:
(from this site (http://accuratedemocracy.com/e_shares.htm)). So it would appear that the D should definitely be capitalized, but the Q need not be. -- Wapcaplet 14:14 24 Jun 2003 (UTC)
I removed some of the parentheses from the formula. According to a note on Evercat's talk page, all of the parentheses must be there, but I would like some clarification as to why this is so. All of the parentheses seem redundant to me (as they would to anyone with mathematical experience). Also, Jtdirl, if you have taught the DQ for 8 years, how come you didn't know who it was named after? I found that out in 20 seconds, and I've never heard of the Droop quota before today.
Finally, if the parentheses must be there, then why are they not present in the example given later in the article?
Shouldn't that be:
or
-- Wapcaplet 14:27 24 Jun 2003 (UTC)
Actually I wrote that bit... (based on JT's informal example) Evercat 14:29 24 Jun 2003 (UTC)
Ah. I guess the ultimate question is, how is:
ambiguous in any way? (unless we're talking about people who don't know that division has precedence over addition, or that the stuff on the bottom of the horizontal line has to be calculated before dividing the stuff on the top of the horizontal line by it. But then again, those people probably wouldn't know that parentheses take precedence over both, and/or wouldn't understand the remainder of the article.) How can this formula get a student failed? It expresses precisely the same quantity as the versions with extra parentheses. -- Wapcaplet 14:37 24 Jun 2003 (UTC)
I suppose some of the confusion may arise from the differences in how the TeX stuff is rendered (as PNG or HTML). Maybe we should format it without any math markup, to remove all doubt about how it's rendered and how it is to be calculated. Such as:
-- Wapcaplet 14:45 24 Jun 2003 (UTC)
BTW Wapcaplet, would a mathematician also be happy with this?
That's really the version that was most contoversial... Evercat 15:24 24 Jun 2003 (UTC)
And it is totally unambiguous, in my opinion, to anyone who has ever been exposed to basic arithmetical notation. -- The Anome 16:59 24 Jun 2003 (UTC)
The formula is always written with the brackets and never without. The reason is because students constantly don't understand the formula without them; ie the order in which the maths are done. Remember the students using the formula aren't mathematicians but students of political science or history. Without the brackets, people not understanding it sometimes add the final +1 to the votes total, or the seats +1. As a result, the brackets are thought so important that students who write the formula without the brackets in many colleges are automatically failed unless their answer in an exam shows they do know the order in which the maths are done. Recently a book about an Irish election had its first print-run pulped because the typesetter left out the brackets. A second print run was ordered with the brackets in place. It isn't a case of the brackets being optional, a matter of opinion. If they aren't there the formula is dismissed as wrong and if wiki can't even get the Droop Quota right it would instantly be dismissed by political scientists as an amateurish sourcebook that their students should not use. FearÉIREANN 18:16 24 Jun 2003 (UTC)
Well, after a number of false starts at math markup, I think I got something everyone can be happy with. Might need a bit of rephrasing here and there, and I've guessed at the rounding-down thing until it can be confirmed (btw, the example seems to round up, which may be in contradiction of the floor notation). -- Wapcaplet 01:51 25 Jun 2003 (UTC)
Ah, so it is. One month out of college and I already forgot how to add... -- Wapcaplet 17:20 25 Jun 2003 (UTC)
Re FearÉIREANN's "I taught students about DQ for 8 years" and yet not knowing the origin of the term, we see the hazards of waving academic credentials about. Wikipedia is just as open to input from the incompetent academic as from the qualified one, which is why we should be citing from the published works of accepted authorities rather than trying to claim personal authority. Any competent academic should be able to reel off the relevant chapters (if not page numbers and paragraphs!) of the authorities' works that are the basis of any assertion. Stan 04:27 25 Jun 2003 (UTC)
ow! i thought Henry Richmond Droop [?] was a piss-take -- but no, apparently he's real. Tangerine[?]
I would be interested to find an authoritative source on how the formula is calculated. The formula given in the article predominates in the google searches I've done; I have found one site which states that it's:
(from a Tasmanian House of Assembly (http://www.parliament.tas.gov.au/tpl/Backg/HAElections.htm) site, which is where I got some of the additions to the article). Anyhow, this explanation of the quota is highly ambiguous, since it can be interpreted as:
All of which are wrong, in comparison with the current formula; a fine example of the ambiguity of the English language :-) Anyway, this may cast into suspicion the other bits about Droop himself, so those may need editing by someone in the know.
Also, I found a Green Party of Canada (http://www.green.ca/english/convention2002/Res_D09.shtml) site which states that the formula is:
Which is subtly different from the interpretation we've used of rounding down, then adding one. This statement is worded more precisely than the previous one, and the only interpretation I can get out of this is that the quota is:
Mathematically, this is very slightly different from the round-down-then-add-one version. Specifically, if the part inside the brackets/floor/ceiling comes out to be an integer, this formula will give a result one less than the formula(s) used in the article.
Once again, not having studied (or even heard of) this quota before yesterday, I would appreciate some pointers towards a more authoritative source. By the way, IANAM, but I have a great appreciation for mathematically unambiguous (and preferably correct) formulas, even if they are in an article on politics. No sense in confusing even the non-mathematicians. -- Wapcaplet 17:43 25 Jun 2003 (UTC)
This last version can't be correct. Imagine there are 100,000 votes and 4 seats this time. Under this version, that gives a quota of 20,000. But it would be possible for 5 candidates to meet that quota. Evercat 17:56 25 Jun 2003 (UTC)
No. It is perfectly straightforward and foolproof, once the parentheses are left in. You increase the number of seats by one, divide the total votes by that number, then add one to the final total. That means 100,000 divided by 5 = 20,000, +1 gives the quota of 20,001. So that means that when 4 candidates reach 20,001, there are 19,996 votes left, not enough for a another quota. It is that straight forward. There is no question of rounding up or rounding down. The Droop Quota is only used with PR.STV and that is only used in the Republic of Ireland and Malta and it has one straight-forward formula. The parentheses are included to avoid the very confusion that seems to be cropping up on this page. FearÉIREANN 18:12 25 Jun 2003 (UTC)
Having thought about it, I think the version that rounds down first then adds one is always the lowest number that doesn't allow more candidates to win than there are seats... Evercat 17:58 25 Jun 2003 (UTC)
Reverting my version was uncalled for. I think it's very clear on all the issues discussed here.
Your version is factually wrong, your use of capitalisation is incorrect, you use the wrong quota. Your interpretation is flawed. FearÉIREANN 22:24 25 Jun 2003 (UTC)
This isn't a maths page, it is a page describing a formula used in political science to produce a quota for use in PR.STV. The formula I used is the formula used by political scientists. No other form of formula is used. Your formula may be the same in formal mathematics but this isn't about mathematics it is about a formula used in political science. As to the capitalisation, Droop Quota is treated as a proper noun and is written as such and should no more be decapitalised that President of the United States should be written as President of the united states. And the 'parenthesis babysitting' is simply ensuring that the formula is written as the formula is written and used by political science. Nothing more and nothing less. The problem with your text was that it turned something that is simply (simply!) describing a formula and how it relates to electoral politics into a mini-treatise on the theoretical mathematics behind it. While that has its uses, its effect was to turn a page meant to simply and straight-forwardly explain what the formula means by the people who would be seeking the information (people interested in the practicalities of electoral science) into something so complicated that non-mathematicians would run a mile from it. A daughter article could very well be constructed to analyse in mathematical terms the workings of the formulæ. But what you did inadvertently obscured the simple question of what is the Droop Quota and how is it used, by going in depth into information that people using the formula would not concern the formula, given that it is not used in mathematics but is simply used as part of a process of election. That is why I made the changes, and BTW I think we were both caught in an edit war and that may be the reason that your version was lost. Wiki is going so incredibly slow and I resorted to a cut and paste to save an extra couple of paragraphs I had added in before I got timed out or the modem started disconnecting. (Wiki is really infuriating right now with its slowness).
I do think a detailed of the mathematical nature of DQ might be useful, but be careful that it doesn't turn an article that is not about maths into a largely maths article. That isn't what people using the page would be using it for. The page would mostly be visited by students of electoral processes, not mathematicians (just as turning some maths page into a long treatise on how maths shaped elections might not be of much interest to maths fans and would be unlikely to be visited by political students. A linked daughter article explaining the mathematical theory behind it might make more sense. FearÉIREANN 23:37 25 Jun 2003 (UTC)
May I suggest as a compromise that we go back to the version that had both the brackety version and the mathematically precise version? Evercat 23:28 25 Jun 2003 (UTC)
That is OK with me. As I said we appear to have been caught in an edit conflict when I made changes. FearÉIREANN 23:37 25 Jun 2003 (UTC)
You are right above the above line. (I've just come to the page to remove the line and put an explanation here!) Basically, PR.STV is designed to ensure that party political support in a popularly elected house of parliament is relatively proportional to a party's percentage support base. Single party constituencies are thought likely to decrease the degree of relative proportionality, with the higher the number of seats per constituency, the greater the degree of proportionality achieved. The DQ is used as the means to achieve a quota which can only be achieved by the number of candidates identical to the number of seats available. For in a five seat constituency it is mathematically impossible for more than five candidates to achieve the quota and so be elected.
re the question - it isn't exactly stated where to round down - you don't. Ever. You never have to round up or down. By adding 1 to the final result when you divide the TVP by (seats +1), you get a number that can never be achieved by more candidates than the number of seats available. Rounding up or down never arises and never can arise.
As to your example: it uses terms that are never used in describing the workings of either the PR.STV or the DQ, its reference to 'rounding' is completely wrong, as is its mention of 'votes with positive weights' , 'depleted', 'floor' , 'decaying'. "Since votes with positive weights may become depleted . . ." what does that mean? I am rewriting my paragraph to make it clearer. FearÉIREANN 03:05 26 Jun 2003 (UTC)
Say the Droop Quota formula gives the value 5000.5 : does a candidate need to get 5000 or 5001 votes? Evercat 03:20 26 Jun 2003 (UTC)
I would advise against it. Millions of people cannot understand even the concept of the Droop Quota because their only experience is of electoral systems were quotas don't matter as the winner is the person with the largest number, even if it is the largest minority vote. So it is useful to explain on this page why and what a quota is, that means explaining that some electoral systems require them to function. Wiki is great for links, but one thing I think can be a problem is if we don't give enough info to grasp the basics but rely on links. It is all too east to be puzzled by something, hit a link, read a text, have to hit another one and end up a couple of links away where you started trying to work your way back. It turns reading wiki into attempting to do a jigsaw. I think every page should carry enough basic info so that someone reading the one page knows what the thing is and has a rough idea of the context in which it works. We should aim for each page to have enough info to ensure that someone when they leave that one page could explain the gist of what something is to a friend, not say "em I'm not sure. I have to explore a couple of links more before I can really know what it is all about." We can go into a lot more detail elsewhere but this page should allow someone to be able to walk away without leaving more confused than when they came in. FearÉIREANN 03:59 26 Jun 2003 (UTC)
I think the fundamental problem here is that various references disagree with one another. Therefore, attempting to clear away the confusion by giving a single clear answer is impossible. Some sources say that the Droop quota is the same as the Hagenbach-Bischoff quota, others give different formulae for the two, some even give entirely different formulae for the Droop quota: see the apparently authoritative http://www.aec.gov.au/_content/What/voting/elec_sys/03.htm for an example.
I think NPOV, rather than appeals to authority or credentials, is going to have to be used here. If we can point to a piece of Irish electoral legislation, and quote it as "in the Republic of Ireland, the Droop Quota (capitalized as a proper noun) is defined by the ... Act of 19xx as ...", and "according to the Australian Electoral Commission, the Droop quota is defined as ...". And of course, "In a paper entitled ..., written in 18xx, Henry Richmond Droop originally defined the Droop quota as ...". Doing this will require someone to actually look up the primary references, rather than citing secondary sources.
-- Anon.
See also these references:
--- Anon.
Whee, my library seems to have that last Journal - I'll try and grab it, tomorrow maybe... Evercat 14:56 26 Jun 2003 (UTC)
Search Encyclopedia
|
Featured Article
|