# Talk:Highest averages method

First, I can't tell you how happy that user:Ruhrjung added this page, and the sainte-lague one, and that we've had all these people working on these pages.  I'm going to suggest that we replace the example with the following made-up one: apportioning seats to states for an 8-seat council of New England states.  The reasons I'd want to make the change are: 1) the "preferences" (in this case, population) aren't made up, so nobody has to account for "is this a realistic spread of preferences or is this tailored", and 2) it emphasises the difference between d'H and S-L (that's why I chose not to use modified S-L).  
However, I'm not going to be bold because Ruhrjung clearly put in a lot of work to make the existing example (whose table structure I have copied) and I don't want to offend him.  Is this okay?  Which example do you think is better?

Also, whichever example we use, I want to use and explain a table like this:

Seats=seats allocated under this system
Ratio=Total Seats to allocate*State Population/N.E. Population
Diff.= Seats-Ratio
-- User:DanKeshet
Go along.
I'm busy at work for the next three days - probably without any time to "recover" in front of the computer.
Your proposed addition is quite in line with my thoughts on what's relevant and interesting. I had a thought with the made up number of votes, namely that they make percentage-comparisons easy for the untrained, as the total number of casted votes was set to 100.000. And as quite a few elections in the last 30 years (i.e. in my lifetime:-) has been done with these methods, it never occured to me that one of them ought to be taken as an example. By making up the numbers, the which-and-why question was avoided. :-)
My idea was to add rows to the tables with approximately the following information:

const.                     result in percentage 
size         d'Hondt                              Sainte-Laguë
         party 1    party 2,   party 3...       party 1,  party 2,  party 3...
 1       100% (1)                               100% (1)
 2       100% (2)                               100% (2)
 3        67% (2)    33% (1)                     67% (2)   33% (1)
 4        50% (2)    25% (1)    25% (1)          50% (2)   25% (1)   25% (1)
 5
 6
 7
 8      
 9
10

I had further had the idea to have two sections in the article with two headings: One for comparing the unmodified Sainte-Laguë method, and one (as I had started) for the method with the first divisor set equal to 1.4 - and how unlikely it might now ever seem, I had actually finished that work when my computer locked, and the work was lost, ...and I soured.
Do as you like with the figures. I wouldn't advice you to use any New England example, as the whole wikipedia project already as it is is pretty much US-centered, which isn't always a good thing, and as it might seem odd to list half-a-dozen of non-US countries where the method is in uncontroversial use, and then give an example from USA. However, I'm glad someone more than me has found it relevant to work on these articles, and I'm sure the end result will become pretty good whatever you choose to do of your New England idea. 
best regards!
-- Ruhrjung 17:52 28 Jul 2003 (UTC)

Uf!  I'm sorry to hear about your computer lockup!  I look forward to the text being regenerated.  So, I agree about the US-centrism, and I'll drop the New England example, but I still think it's better to use a "real-life" made-up example (EU?  AU?) than an out-of-the-blue made-up example.  
By the way, do you know about Wikipedia:WikiProject Voting Systems?  You don't need to know anything about the project in order to participate, but if we want project-wide standards, then that could be a place we work them out.    
See you,
DanKeshet 04:35, 29 Jul 2003 (UTC)
One more step taken, on the outlined road, but the weather is nice, and the summer short up here in the North, why I refuse to hide indoors more. :))
-- Ruhrjung 09:05, 5 Aug 2003 (UTC)

No worries.  Relax, take your time, it will still be here when you get back.  I have added a section on the other way of conceiving of the highest averages methods.  I understand that nobody who didn't already understand what I wrote will probably gain an understanding, but I meant it as starter text which can be ruthlessly rewritten until it actually explains the reasoning behind the procedures. DanKeshet 17:49, 6 Aug 2003 (UTC)
I saw that. The colour is nice. Your attempt to explain the method as if it was largest remainder method is maybe not quite simple to understand, that's true, but if so, it can surely be mended in due time. I'm for instance pretty fond of the following sparse wording, quoted from http://www.barnsdle.demon.co.uk/vote/appor.html:

That was the quota definition of Webster's method. Webster actually worded his own definition slightly differrently, in a way that's very brief: To determine each party's seats:
Divide each party's votes by the same number & round off.
This common divisor is chosen so that the total number of seats awarded equals the desired house (or district) size.
Again, this common divisor is a common ratio between seats & votes, and rounding off puts each party's seats as close as possible to what that common ratio calls for.
Some object that the divisor definition is unclear because it orders division by an as-yet unspecified number, unlike the quota definition. But Webster's divisor definition has the best brevity.
-- Ruhrjung 13:58, 7 Aug 2003 (UTC)
Would it be useful to mention minor methods like Hill's method? (Hill's method is used for assigning representatives to US states, and has the property that every "party" gets at least one representative.) Rob Speer 08:04, Jul 17, 2004 (UTC)

Im having trouble understanding the exact rationale behind these methods. Why do seemingly provisionaly choosen divisors result in a proportional result? Also, why are such complicated ways of allocation used at all; it would seem that simply dividing the number of votes each party won with the total votes and multiplying this with the number of available seets, rounded down, and then largest remaining fractions up to the remaining number of seets chosen (if you write this out, it is mathematically equivalent to Hare quota) would by definition result in the most proportional results, and its the most intuitive - mathematically most evident - way of doing this. --195.29.116.30 04:54, 19 July 2006 (UTC)

Thaat is a largest remainder method and is not mathematically equivalent.--Rumping (talk) 10:17, 5 June 2009 (UTC)

You’re describing Largest-Remainder. Its departures from proportionality are universally agreed to be much greater than those of Webster/Sainte-Lague. …& that’s not even counting Largest-Remainder’s nonmonoticity (negative response).

But you started right: X% of the vote should get X% of the seats. So yes, multiply each party’s vote % by the desired house-size, to get the parties’ “ Rightful seats”.

Rightful seats typically ends in a fraction, so round to the nearest whole number. Assign to the party that number of seats.

Due to vagaries of rounding, the total assigned seats might not sum to the desired house-size. No problem:

Before rounding, multiply each party’s rightful-seats by the same number (the “multiplier”).

If the total allocation was too low, the multiplier should be a bit greater than 1. If the total allocation was too high, the multiplier should be a by less then 1.

Then, as before, round to the nearest whole number, & give the party that number of seats.

So, the house-size is adjusted by multiplying each party’s rightful seats by some same number before rounding.

By trial-&-error, find the multiplier that gives the desired house-size.

That gives the Webster/Sainte-Lague allocation.

If, instead of rounding to the nearest whole number, you round everyone up, that’s Adams.

…or if you round everyone down, Jefferson/d’Hondt.
 2600:6C55:7900:2B8:5514:AAA9:18DB:87CB (talk) 22:03, 23 December 2024 (UTC)
For the (necessary) SL modification, the 1st rounding-point is changed from.5 to .7 2600:6C55:7900:2B8:5514:AAA9:18DB:87CB (talk) 22:15, 23 December 2024 (UTC)

____________
Let’s suppose those figures:
A: 340,000	B: 280,000	C: 160,000	D: 60,000	E: 15,000
The result using Sainte-Laguë method would be: 3, 2, 1, 1
If we use D'Hond method, then: 2, 2, 2, 1.
It seems to contradict the idea of a 'more proportional' system.
Thanks.  —Preceding unsigned comment added by 81.35.196.9 (talk) 15:03, 13 November 2008 (UTC) 

You may have made an error with your D'Hondt calculations: I make it 3,3,1,0 as 340000/3 > 280000/3 > 160000/2 > 60000/1.  As for which is more proportional, I have my doubts about any system which does not guarantee that a party with more than half the votes will win at least half the seats. --Rumping (talk) 10:17, 5 June 2009 (UTC)

Sorry for writing after the GA review has concluded, but after reading the great book Electoral systems by Lebeda and co. I stumbled upon this article and it's assosiates and was quite astonished by how 'pro-divisor' this and all the other articles are.
Though after going through the references, it started to make sense, considering that the only two larger sources cited are pretty much just Pukelsheim, who is very reliable on a susceptibility to paradoxes (which isn't bad, but there are two sides to the story) and Balinski (whom I didn't read, so perhaps he makes great arguments, sorry if the does). I'd say one needs a bit more than that to claim that divisor methods are "generally preferred by social choice theorists" (which changes to mathematicians in the latter part of the article), especially considering that when describing d'Hondt, Gallagher is cited with "However, Jefferson's method performs poorly when judged by most metrics of proportionality".
In my opinion, the parts of the article where the comparison is made, should be edited as to include a more neutral overview of the topic. Using Gallagher's work (for example Gallagher 1992) for a bit more balanced outlook or Lijphart (Lijphart 1994) for a bit more pro-quota outlook to balance things out.
To be clear, I do not admonish divisors or love quotas (my belief is that STV rules anyways and for regular PR Sainte-Laguë might just be the best of both worlds), but the current text is lopsided.
In summary, making the text more neutral on the divisor/quota divide would be of use. Quotas have their problems (population and Alabama paradoxes (though sidenote, I don't think participation can be called as a paradox intrinsic to quotas, as unrounded quotas or Hare-Niemeyer don't produce it)) and Divisors have theirs (breaking the quota rule obviously, generally considered less proportional, because we use Hare as a point of reference most of the time (though again, consult Gallagher for a better explanation)), so that should be included. In my experience and from my reading I have not encountered a broad consensus that divisors are inherently superior. JerenMapper (talk) 10:28, 23 August 2024 (UTC)

Excuse me, but aren’t the divisor-methods the topic of this article?? …& the meaning of the article’s title?
Discussion of STV & Largest-Remainder have no place here.
There are other Wikipedia articles about them, or about the larger general topic of Proportional Representation & the relative-merits of its types.
2600:6C55:7900:2B8:89A7:F9D5:59FC:4E65 (talk) 10:32, 24 December 2024 (UTC)

User:Closed Limelike Curves, WP:ENGVAR is not an excuse to replace the terms commonly used in present-day literature (d'Hondt method, Sainte-Laguë method) with terms that are mainly used in old articles about U.S. congressional apportionment (Jefferson method, Webster method).
I would like, once again, to refer to this note from the talk page for "Sainte-Laguë method":

In literature "Webster/Sainte-Laguë method" is rarely used. I found 30 results in time frame since 2015 for "Webster/Sainte-Laguë method" seat allocation, 97 results for "Webster method" seat allocation and 265 results for "Sainte-Laguë method" seat allocation. Seems "Sainte-Laguë method" is the most used lemma. HudecEmil (talk) 12:18, 19 February 2023 (UTC)
Glide08 (talk) 15:03, 7 January 2025 (UTC)

97 results for "Webster method" seat allocation and 265 results for "Sainte-Laguë method"So in other words, Sainte-Laguë is about 2.5× as common (the same order-of-magnitude). Webster is the most common name in the US, and Sainte-Laguë is the most-common name in Europe. Possible arguments for using the US names are precedence (Webster invented the method first) and familiarity—many people know who Daniel Webster is, and "Webster" is an easier name for English-speakers than Sainte-Laguë. An additional argument is the lack of European names for many apportionment methods (e.g. Hamilton's method or Adams' method).I don't think any of these arguments is decisive, so WP:ENGVAR applies: use either US English or UK English, but do so consistently. – Closed Limelike Curves (talk) 17:13, 7 January 2025 (UTC)
I apologize if my joining this discussion late means that I have missed some relevant information.  That said ... if each of these names is most common in a non-trivial context — obviously different contexts for each — then let's use both.  To me, the argument boils down to whether we should use "Webster/Sainte-Laguë" or "Sainte-Laguë/Webster".   —Quantling (talk | contribs) 17:29, 7 January 2025 (UTC)
Somewhat agree, in the sense that both of these names should be explained to be synonyms; however, typing "Webster/Sainte-Laguë" or vice-versa every time is a big pain, so I've stuck to just doing it in titles, labels, and first mentions. The article's body sticks to "Webster" because the article written in American English. – Closed Limelike Curves (talk) 17:53, 7 January 2025 (UTC)
Learn to use copy & paste. —David Eppstein (talk) 18:26, 7 January 2025 (UTC)
I don't think even American papers use Webster as much nowadays. Glide08 (talk) 20:11, 7 January 2025 (UTC)
And I'd also add that these names aren't exclusively European - even in Latin America, where you'd logically expect Jefferson and Webster to be used more, the names d'Hondt and Sainte-Laguë are used almost exclusively (e.g. the Library of the Chilean Congress ("El sistema electoral proporcional chileno usa un mecanismo llamado coeficiente D’Hondt."), a news site from the Dominican Republic ("Una iniciativa […] busca reemplazar el método d’Hondt por el método Sainte-Laguë."), the National University of Colombia (porque en Colombia se aplica la fórmula d´Hondt,)) Glide08 (talk) 20:25, 7 January 2025 (UTC)