Talk:Hagenbach-Bischoff system

Citations

The article gives a bibliography, but it doesn't specify the source for the individual component parts. I'd like to see some footnotes. Though perhaps this was the author's intention, students use Wikipedia as a substitute for proper research. While responsible ones take the time to note the citation and go to the original when writing a paper, it's not unheard of for them to just copy the citation to make it look like the went to the library to get a book or logged on to JSOR. Are there any concurring/dissenting opinions on the need for footnotes? (Or are you guys all Chicago-style inliners⸮) Petropetro (talk) 12:10, 22 January 2013 (UTC)[reply]

Math

Would it be good to include some math into the page that proves equal results to the straight D'Hondt method?

In the Jefferson/D'Hondt method, a quota range is found, where all seats are filled. Quotas above this range will fill less seats than needed. Quotas below this range will fill more seats than needed.
If the Hagenbach-Bischoff system produces a quota too high, there is no problem. Because of dropping decimal parts, results will be the same as from a higher quota, namely a quota which happens to be the most efficient for one candidate. Its just like how being within the Jefferson range is fine, as opposed to only being at the precise higher end of range. By most efficient it is meant that the candidate has no "wasted votes", because the quota is equal to the candidate's votes divided by the amount of seats that the candidate won. In this case, at least another round of the D'Hondt method would be needed to fill all available seats.
The Hagenbach-Bischoff quota cannot be less than the lower end of the Jefferson method range. The Jefferson method's lower limit is equal to the most efficient quota for a candidate, which fills all seats + 1. That means the total vote must be at least as big as that lower limit times the sum of amount of seats plus one. The Hagenbach-Bischoff quota is equal to total vote divided by the sum of amount of seats plus one. Therefore, the Hagenbach-Bischoff quota cannot be less than the Jefferson method's lower limit.
Jefferson method's lower limit * (Amount of seats + 1) + "wasted votes" = Total vote
"wasted votes" = Total vote - Jefferson method's lower limit * (Amount of seats + 1)
0 ≤ "wasted votes"
0 ≤ Total vote - Jefferson method's lower limit * (Amount of seats + 1)
Jefferson method's lower limit * (Amount of seats + 1) ≤ Total vote
Jefferson method's lower limit ≤ Total vote / (Amount of seats + 1)
Hagenbach-Bischoff quota = Total vote / (Amount of seats + 1)
Jefferson method's lower limit ≤ Hagenbach-Bischoff quota

Let me know what you think 104.33.114.195 (talk) 01:34, 11 June 2019 (UTC)[reply]

also, in the case that

Jefferson method's lower limit = Hagenbach-Bischoff quota

one seat in excess gets filled by the Hagenbach-Bischoff system. It must also be true with the D'Hondt method. The above situation must mean that there are 0 "wasted votes." Every candidate's votes must therefore equal an integer multiple of the Hagenbach-Bischoff quota. That must mean there were multiple winners from the preceding D'Hondt method round. The D'Hondt method skipped the target amount of seats, also, by awarding multiple winners in some round. 104.33.114.195 (talk) 16:06, 11 June 2019 (UTC)[reply]

Merge into D'Hondt?

As far as I can tell, H-B seems to describe the exact same method as D'Hondt (in that the same number of seats are assigned to each party in the end). If that's the case, H-B is just a computation/implementation detail that lets you determine an initial allocation for all parties. This would deserve some mention in the D'Hondt article, but not an article of its own. Closed Limelike Curves (talk) 19:00, 27 December 2023 (UTC)[reply]