Talk:Sainte-Laguë method

message: who was Sainte Lague?  Who created this system?  Surely something should be put in about that.--Gregstephens 09:17, 10 Mar 2005 (UTC)
replies: text: 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)
thread_title:  who was Sainte-Lague 

message: 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)
replies: text: Premium seats? Nope. Well, not in New Zealand, anyway. In the unlikely event that a party with a slight majority of the votes didn't get a majority of the seats, they just don't get a majority of the seats. The modification itself (not used in New Zealand, which has a 5% threshold) has the effect of requiring a party to earn an entire seat before it gets one - it stops parties that earn, for example, three-quarters of a seat, from having it rounded up. And yes, you could just use a threshold, it's just a different way of doing it. Quadparty 03:57, 24 May 2007 (UTC)
replies: text: In some countries using Sainte-Lague there is a "premium seat" (e.g. in Germany, although there has never been a party with a majority in German federal elections anyway). The argument for using the modification is that under a pure S-L system without threshold, very small parties benefit from splitting themselves in two if they expect to get a vote share between 1.0 and 1.5 seats: they would usually only get one seat as a single party, but splitting into two equally-sized parties (i.e. each having a vote share between 0.5 and 0.75) would get them two seats. To avoid this incentive, the first divisor is increased from 0.5 to 0.75.--Roentgenium111 (talk) 18:29, 22 December 2010 (UTC)
thread_title: modification

message: 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 ), 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)
thread_title: proportionality

message: I don't understand why the method is called a "highest average method". From the following explanation how the seats are allocated it might be called a "highest quotient method". But the word "average" seems to be wrong, because no average is calculated.178.203.183.22 (talk) 10:37, 19 December 2010 (UTC)
thread_title:  Highest Average 

message: I don't think most people would get anything from it, and it doesn't help to explain the topic. Unless you where a programmer or learning programming, which is not most people. I would delete it myself but it seems like someone put a bit of work in to it, so I'll let them defend it. Dude2288 (talk) 00:01, 22 December 2010 (UTC)
replies: text: Ok, I think the python code is more easy to understand. --178.203.183.22 (talk) 20:35, 1 January 2011 (UTC)
thread_title:  Is the 'example C implementation' section necessary?  

message: As Denmark uses both D'Hondt (135 seats) and Sainte-Laguë (40) to (s)elect the 175 Danish members of the Folketing, I wonder whether it should figure on the list of countries in both articles - comments/discussions/pro et contra is referred to the talkpage for the D'Hondt method (section: "Denmark, D'Hondt and Sainte-Laguë") so as to keep everything together.
-- Mojowiha (talk) 09:55, 21 July 2014 (UTC)
replies: text: Done for this article. -- Picapica (talk) 21:25, 13 June 2015 (UTC)
thread_title:  Denmark, D'Hondt and Sainte-Laguë - see the article on D'Hondt 

message: 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)
thread_title:  Rename lemma to "Sainte-Laguë method"