Talk:Sainte-Laguë method
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The method used in Sweden is a modified version of Sainte-Laguë with 1.4 as the first divisor. I think Bosnia and Herzegovina uses unmodified Sainte-Laguë. I don't know about the other countries. Maybe this should be clarified in the article. Nicke Lilltroll 21:33, 21 Sep 2004 (UTC)
The graph on how to use SL is a bit confusing. Prehaps using a true example of an election could help, such as the 2002 New Zealand election. If people want more on SL try Elections NZ. --210.86.91.61 07:35, 21 Feb 2005 (UTC)
I think Norway is using modified version of Sainte-Läguë formula. And I think that Hungary is using its own modification of formula, with 1.5 as first divisor.
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[edit] who was Sainte-Lague
who was Sainte Lague? Who created this system? Surely something should be put in about that.--Gregstephens 09:17, 10 Mar 2005 (UTC)
- and how is his name spelled? Google shows more hits on Saint-Laguë than on Sainte-Lagues, but Wikipedia redirects in the opposit direction. A report from the Canadian Parliament O'Neil, Electoral Systems, 1993, p. 9 uses both spellings in the same heading. Is there an explanation? Jesper Carlstrom 09:15, 30 March 2007 (UTC)
[edit] modification
why is the formula modified anyways? It affects only the ease of getting the first seat - if it aims to eliminate the smallest parties, wouldnt applying a threshold give the same result - that would at leas make its aim more explicit, instead of burying it deep in the seat allocation process? Also the article says that the modification gives a slight prefference to larger parties - but this doesnt seem a clear enough formulation to me. Since it modifies only the first divisor, it gives no prefferences to larger parties in allocation of aditional seats. It only makes getting the first seat harder. So a smaller party would not be the least bit disadvantaged with the modified version if its only big enough to ensure the first seat. d'Hondt on the other hand, would disadvantage the smaller party in every case, cuz it would effectively round down, to its disadvantage. What isnt mentioned here is that Sainte Lague doesnt ensure majority rule - a party with a (slight) majority of votes could win a minority of seats. Id love to know how this is dealt with in countries that use Sainte Lague. Do winning parties get some premium seats, for instance?--Aryah 03:14, 19 July 2006 (UTC)
[edit] proportionality
supposing this set of 1000 votes divided to parties: (501,77,76,75,74,73,72,52) S-L divisons of the first would give (/3)167,(/5)100,2 (/7)71,57.. (btw why are the divisions usually in integers?) . So if 9 seats are ellected, minor parties but the smallest would each get a seat - alltogether 6 seats, and the large party would get 3 seats, although it has absolute majority. Now I do understand how in this situation a truly proportional system would not guarantee the absolute majority to a party that has majority of votes, if it rounds the fractions fairly. However, I dont understand how the large party is getting 3, instead of 4 seats. The obvious definition of proportionality would be that each party gets the proportion of seats equal, within rounding margin of error, of the proportion of its votes, right? If one were to implement this definition directly, it would mean calculating the percentage of votes of each party (Vp/Vt), and then multiplying that with the number of seats ((Vp/Vt)*S=(Vp*S)/Vt) Vp being the votes a party won, Vt the total num of cast votes and S the num of seats to allocate. This is identical to applying the Hare quota (where Vp is divided with Vt/S, giving Vp/(Vt/S)=(Vp*S)/Vt ), which would mean that Hare quota is by definition of proportionality the most proportional method. And the rounding can be done by choosing the remainders (remainding votes, if using Hare quota, or remainding fractions of a seat if applying the definition directly) that are the largest, untill no more seats are available - just as its done with Hare. If this were applied to this situation, it would give the largest party 4 seats, and to others, but the 2 smallest ones , one seat each, which would (by definition) be more proportional mathematically. The situation is even worse in the case where the smallest party would not run, making the total number of votes 948. Sainte Lague would still give 3 seats to the largest party, and a single seat to each other party. However, Hare quota would be 948/9=105.333... , giving 4 seats (421.333..) to the largest party, and a reminder of 501-421.333...=79.666, thus giving it a fifth seat before giving any seats to other parties - so the smallest, 72, would not get a seat. Again, this is, by the obvious definition given above, the most proportional possible result. One would equivalently found that Vt/Vp=1000/501=0,501 (50,1%); 0.501*9=4.509 , assuring the 4th seat (and (77/1000)*9=0,693 for the largest minor party). It would also give some justification to the empirically found need for modifying Sainte Langue (though not justifying the ad-hoc sollution to it). So this would mean that Sainte Lague is certaly not the most proportional method, this by definition of proportionality must be Hare quota, but that Sainte Lague indeed unduly favours small parties in giving first seats. I have not been able to replicate this discrepency with the 2. seat allocation, where Sainte-Lague seems to give proportional results (though modified Sainte Lague did seem unjust in late-allocating the 1. seat), identical to Hare results. However there seem to be cases where another discrepency arises - if there were 918 votes, cast (509,132,131,130,16) and 9 seats, the hare quota would be 918/9=102, giving 4 seats to the largest party and one seat to each minor party, but the smallest. The largest party would have 101, allmost the quota remaining, giving it the 5. seat. The largest small party would have 30 remaining, and it would get the last seat. However, if S-L were applied, (and also, if S-L were applied only to the remainders, with 101/3=33.66..!, and the largest minor party having 30 remainder), that seat would instead also go to the largest party (w largest party divisions (/3)169,66.. (/5)101,8 , (/7)72,714.. , (/9) 56,55.. , (/11) 46,2727.. and largest minor party division 132/3=44). Since the circling by allocationg the remaining seats simply to the largest remainders in order of their size is a bit ad-hoc sollution, and S-L is equivalent to rounding to the nearest whole number (as explained here [1]), though I dont know, I wouldnt be suprised if the S-L result is more proportional (though giving 6:3 instead of 5:4 allocation for only 55+% majority?), but applying Hare and then S-L to its remainders seems even if that were tha case superior to only S-L, because of the previous problem with S-L's undue allocation of the first seat to small parties. Im sorry if I made some calculation mistake that would invalidate these examples - though i would expect these kind of result to be possible even if I did make such a mistake. In either case, it would suffer from Alabama paradox et all, though would ensure low quota (or both high and low quota), which could possibly be a reason for small party problems? Not sure if its worth the change in the place of using just S-L (but was thinking in application to no-party list systems, which suffer this anyways). Does using S-L with no quota then ensure monotoniciy for a STV/QPQ-like system?... --Aryah 08:09, 19 July 2006 (UTC)
[edit] Another idea for a highest averages system
I've got another idea - how about one with the divisors going in a Fibonacci-like pattern.
Here's how it works (I'll take it over 50 seats so you see a pattern:)
| Brazil | Italy | Germany | Argentina | Uruguay | |
| Votes | 340,000 | 280,000 | 160,000 | 60,000 | 15,000 |
| Seat 1 | 340,000 | 280,000 | 160,000 | 60,000 | 15,000 |
| Seat 2 | 170,000 | 280,000 | 160,000 | 60,000 | 15,000 |
| Seat 3 | 170,000 | 140,000 | 160,000 | 60,000 | 15,000 |
| Seat 4 | 113,333 | 140,000 | 160,000 | 60,000 | 15,000 |
| Seat 5 | 113,333 | 140,000 | 80,000 | 60,000 | 15,000 |
| Seat 6 | 113,333 | 93,333 | 80,000 | 60,000 | 15,000 |
| Seat 7 | 68,000 | 93,333 | 80,000 | 60,000 | 15,000 |
| Seat 8 | 68,000 | 56,000 | 80,000 | 60,000 | 15,000 |
| Seat 9 | 68,000 | 56,000 | 53,333 | 60,000 | 15,000 |
| Seat 10 | 42,500 | 56,000 | 53,333 | 60,000 | 15,000 |
| Seat 11 | 42,500 | 56,000 | 53,333 | 30,000 | 15,000 |
| Seat 12 | 42,500 | 35,000 | 53,333 | 30,000 | 15,000 |
| Seat 13 | 42,500 | 35,000 | 32,000 | 30,000 | 15,000 |
| Seat 14 | 26,153 | 35,000 | 32,000 | 30,000 | 15,000 |
| Seat 15 | 26,153 | 21,538 | 32,000 | 30,000 | 15,000 |
| Seat 16 | 26,153 | 21,538 | 20,000 | 30,000 | 15,000 |
| Seat 17 | 26,153 | 21,538 | 20,000 | 20,000 | 15,000 |
| Seat 18 | 16,190 | 21,538 | 20,000 | 20,000 | 15,000 |
| Seat 19 | 16,190 | 13,333 | 20,000 | 20,000 | 15,000 |
| Seat 20 | 16,190 | 13,333 | 12,307 | 20,000 | 15,000 |
| Seat 21 | 16,190 | 13,333 | 12,307 | 12,000 | 15,000 |
| Seat 22 | 10,000 | 13,333 | 12,307 | 12,000 | 15,000 |
| Seat 23 | 10,000 | 13,333 | 12,307 | 12,000 | 7,500 |
| Seat 24 | 10,000 | 8,235 | 12,307 | 12,000 | 7,500 |
| Seat 25 | 10,000 | 8,235 | 7,619 | 12,000 | 7,500 |
| Seat 26 | 10,000 | 8,235 | 7,619 | 7,500 | 7,500 |
| Seat 27 | 6,181 | 8,235 | 7,619 | 7,500 | 7,500 |
| Seat 28 | 6,181 | 5,090 | 7,619 | 7,500 | 7,500 |
| Seat 29 | 6,181 | 5,090 | 4,705 | 7,500 | 7,500 |
| Seat 30 | 6,181 | 5,090 | 4,705 | 4,615 | 7,500 |
| Seat 31 | 6,181 | 5,090 | 4,705 | 4,615 | 5,000 |
| Seat 32 | 3,820 | 5,090 | 4,705 | 4,615 | 5,000 |
| Seat 33 | 3,820 | 3,145 | 4,705 | 4,615 | 5,000 |
| Seat 34 | 3,820 | 3,145 | 4,705 | 4,615 | 3,000 |
| Seat 35 | 3,820 | 3,145 | 2,909 | 4,615 | 3,000 |
| Seat 36 | 3,820 | 3,145 | 2,909 | 2,857 | 3,000 |
| Seat 37 | 2,361 | 3,145 | 2,909 | 2,857 | 3,000 |
| Seat 38 | 2,361 | 1,944 | 2,909 | 2,857 | 3,000 |
| Seat 39 | 2,361 | 1,944 | 2,909 | 2,857 | 1,875 |
| Seat 40 | 2,361 | 1,944 | 1,797 | 2,857 | 1,875 |
| Seat 41 | 2,361 | 1,944 | 1,797 | 1,764 | 1,875 |
| Seat 42 | 1,459 | 1,944 | 1,797 | 1,764 | 1,875 |
| Seat 43 | 1,459 | 1,201 | 1,797 | 1,764 | 1,875 |
| Seat 44 | 1,459 | 1,201 | 1,797 | 1,764 | 1,153 |
| Seat 45 | 1,459 | 1,201 | 1,111 | 1,764 | 1,153 |
| Seat 46 | 1,459 | 1,201 | 1,111 | 1,090 | 1,153 |
| Seat 47 | 901 | 1,201 | 1,111 | 1,090 | 1,153 |
| Seat 48 | 901 | 742 | 1,111 | 1,090 | 1,153 |
| Seat 49 | 901 | 742 | 1,111 | 1,090 | 714 |
| Seat 50 | 901 | 742 | 686 | 1,090 | 714 |
| Total Seats | 12 | 12 | 11 | 9 | 6 |
Althogh this is not part of the method, 10 more "repechage" seats are going to be allocated. For the starting figures, we will divide the remaining quotients by the seats earned so far and multiply the result by 1,000, but we will restart the divisors at 2.
| Brazil | Italy | Germany | Argentina | Uruguay | |
| Old quotients | 901 | 742 | 686 | 674 | 714 |
| Seat 1 | 75,083 | 61,833 | 62,363 | 74,888 | 119,000 |
| Seat 2 | 75,083 | 61,833 | 62,363 | 74,888 | 59,500 |
| Seat 3 | 37,541 | 61,833 | 62,363 | 74,888 | 59,500 |
| Seat 4 | 37,541 | 61,833 | 62,363 | 37,444 | 59,500 |
| Seat 5 | 37,541 | 61,833 | 31,181 | 37,444 | 59,500 |
| Seat 6 | 37,541 | 30,916 | 31,181 | 37,444 | 59,500 |
| Seat 7 | 37,541 | 30,916 | 31,181 | 37,444 | 39,666 |
| Seat 8 | 37,541 | 30,916 | 31,181 | 37,444 | 23,800 |
| Seat 9 | 25,027 | 30,916 | 31,181 | 37,444 | 23,800 |
| Seat 10 | 25,027 | 30,916 | 31,181 | 24,962 | 23,800 |
| New Seats | 2 | 1 | 1 | 2 | 3 |
| Total Seats | 14 | 13 | 12 | 11 | 9 |
—The preceding unsigned comment was added by Scott Gall (talk • contribs) 06:26, 21 January 2007 (UTC).
