Talk:Gallagher Index
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I'm not certain of the accuracy of the table. I tried to calculate the Index for the UK 2005 General Election on Edexcel, and came up with 16.8
This was worked out as follows (although I used many smaller parties in order to improve accuracy, these will have comparitively little impact and so I have not listed them, and have rounded the numbers greatly – should it become apparent that I am correct, and have not made some mistake, I shall write the calculation more fully): Labour has 35% of the vote and 55% of the seats. This is a difference of about -20, which squares to 400.
Conservative has 32% of the vote and 30% of the seats. This is a difference of about 2, which squares to 4.
Liberal Democrats have 22% of vote and 10% of seats. This is a difference of about 12, which squares to 144.
The sum of these three is 548. Half of this is 274. The root of this is 16.6 (and would be 16.8 had I not rounded, and had I listed all parties involved) comment by user:Ronald Collinson Sept 25/05
- Hi, there! Just as a quick first note, it's helpful to sign your talk page contributions, especially on more heavily used talk pages. Just type four tilde signs (~~~~) and an automagic date, time and signature stamp will appear.
- I suppose my first question is whether you've misread the table; you calculate a rough value for the 2005 UK election as 16.6%, and seem to consider it close enough to 16.8% (your 'unrounded' value), but the table gives the value as 16.9%, which is certainly close as well - are you perhaps looking at the 18.0% score from the 2001 election? Alternately, is it simply that you're dealing with the percents as whole numbers, rather than as decimals, which is the common method used in engineering and science? Taking Labour as an example, they have 0.35 of the vote, and 0.55 of the seats (also commonly written as 35% and 55%). The difference would be -0.2, squaring to 0.04. In other words, 0.169 = 16.9%.
- As far as the specific values, they do depend on rounding and the list of parties; if all parties in this election that failed to win seats were combined as a single monolithic "others" category, a score of 0.169362 results. Taking all parties singly, I get 0.166868, rounded to 0.167. The exact value seems to be dependent on this rounding; the point of the Gallagher Index is, in my opinion, not in quibbling over 0.166 versus 0.169 versus somewhere in between, but much more to enable us to say that the 2005 UK election was more representative than the previous one, but was much less representative than those in, say, the Netherlands or Germany.
- Anyways, in view of the fact that we seem to be agreeing (that the proper result for that election is somewhere around 0.168), I'll edit the main page, to both remove the dispute tag and update the 2005 election result to the value of 0.167, which is closer to your calculations than to my original result, and seems to be better, in that it includes all parties, assuming the current table on the election results page is, in fact, correct.ByeByeBaby 05:36, 26 September 2005 (UTC)
Ronald Collinson 20:40, 26 September 2005 (UTC)
- Ah, clearly my mistake was indeed to deal with the percents as whole numbers. Thanks for clearing that up.
hang on, you are meant to use the percentages as whole numbers. Check Arjend Lijphart's 1994 book to see it in action. The UK should be around 16 percent, as that indicates that it's system is 16% disproportional. Redo the table. It is currently incorrect.--LeftyG 01:10, 16 October 2005 (UTC)
I've created an example of how to calculate proportionality in place of the previous table which was clearly wrong. Hopefully someone can redo the old table so that it is actually correct. NB: NZ had a very proportional election and thus the figure is low. Most FPP elections (such as the UKs) will be somewhere btwn 10 and 20% disproportional.
The table needs a bit of clean up at some point of time, but my feeling is not many people actually look at this page.--LeftyG 04:22, 2 January 2006 (UTC)
Also, can people please calculate for elections the disproportionality? That way, we could ultimately have a wiki-list of the most proportional countries. --LeftyG 04:31, 2 January 2006 (UTC)
[edit] Formula
The current formula for the index is
this is not the standard least squares formula which is either
In a sense this calculates the average of the squrard differences. Using this formula will require the totals in the table to be recalculated. --Salix alba (talk) 13:32, 13 March 2006 (UTC)
- what exactly does the n mean? Would it make a difference that both votes and seats need to add to 100%? Cheers for this check though. --Midnighttonight 03:59, 30 March 2006 (UTC)
n is the number of parties. For most situations your wish to find the average deviation from expectation, see Root mean square. How you choose the divisor can affect the results, leading to some bias, when trying to compare elections with different numbers of parties, say 3 as opposed to 4. There is some justification for using 2 parties as the first two parties tend to get the most votes, with 10 parties dividing by n-1 would over correct. Hence I'm not sure what Gallagher actually intended. From a statistical POV the Sainte-Laguë Index is a better measure. --Salix alba (talk) 07:59, 30 March 2006 (UTC)
I just got a reply from the man himself, seem like it should be 2.
- Thanks for your message. I can confirm that the demoninator is 2; the index measures total disproportionality per election, not disproportionality per unit (eg party), so it would not make sense to divide by the number of units. Division by 2 ensures that the value of the index ranges between 0 and 100.
- I took a look at the wikipedia address and the article makes good sense to me. Under 'References', you could add the following, which fleshes out the index somewhat and refines the calculation of it:
- Michael Gallagher and Paul Mitchell (eds), The Politics of Electoral Systems (Oxford: Oxford University Press, 2005), Appendix B. (http://www.oup.co.uk/isbn/0-19-925756-6)
- Sorry to say I don't have the 1991 paper in electronic form. Best wishes Michael Gallagher
--Salix alba (talk) 23:35, 3 April 2006 (UTC)
[edit] Fascinating page
Thanks for this information. I knocked up an index for the Australian federal election, 2007 located here, and note that the example gives a low rating, with the article stating the result ranges 0-100. The one I knocked up gives a rating of 10.28 - ok, it's low in terms of 100, but high in terms of the example. Google doesnt seem to show up much for the index, can anyone point me toward some sort of list of ratings so I know what sort of context to put that result in? Thanks. Timeshift (talk) 13:07, 9 May 2008 (UTC)
