Talk:Highest averages method

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You have new messages (last change).

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?

d'Hondt method   Sainte-Laguë method
States MA CT ME NH RI VT MA CT ME NH RI VT
Pop. (1000s) 6,349 3,405 1,274 1,235 1,048 608 6,349 3,405 1,274 1,235 1,048 608
mandate quotient
     
1 6,349 3,405 1,274 1,235 1,048 608 6,349 3,405 1,274 1,235 1,048 608
2 3,175 1,703 637 2,116 1,135 425 412
3 2,116 1,135 1,270 681
4 1,587 907
5 1,270
seat seat allocation
1 6,349             6,349          
2 3,405          3,405         
3 3,175          2,116        
4 2,116             1,274      
5 1,703          1,270          
6 1,587               1,235    
7   1,274         1,135        
8 1,270                  1,048  

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

d'Hondt

method

 Sainte-Laguë method
States MA CT ME NH RI VT MA CT ME NH RI VT
Seats 5 2 1 0 0 0 3 2 1 1 1 0
Ratio 3.65 1.96 0.73 0.71 0.60 0.35 3.65 1.96 0.73 0.71 0.60 0.35
Diff. +1.35 +0.04 +0.27 -0.71 -0.60 -0.35 -0.65 +0.04 +0.27 +0.29 +0.40 -0.35
  • 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)

[edit] why?

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)

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