Sorry about some delay in answering the mail. I was celebrating the midsommer out of the reach of proper internet connections. I think we are already on the second round of this topic (divisor methods and ratios vs. quota based methods and number of people) but here are some comments from a more Largest Remainder oriented point of view.
Let's say one quota is 1000 votes, and the district populations are A:50332, B: 1335, C:1333. If we allocate the seats 50-2-1, differences from accurate PR will be 332-665-333 persons. If we allocate the seats 51-1-1, differences from accurate PR will be 668-335-333 persons. I don't think the idea of allocating the seats so that the sum of overrepresentations and underrepresentations is as small as possible is an arbitrary way to allocate seats. Quite natural, don't you think. Divisor methods focus on ratios of people and representatives. Why should that be the only approach that people should use? If we measure the biggest difffereces in persons (i.e. not in ratios like you did), then the differences are 997 (min -332, max +665) and 1003 (min -335, max +668) Ratios are a bit different approach in how they treat small and large groups. Let's say some small group has 1.5 quotas. Somewhere around that point we might consider giving it its second representative. Its S/Q value with one representative is 0.667. Then we have another larger group that has already 10 representatives. How many quotas would it need to reach the same S/Q value that the small group has? It would need 15 quotas to get the same S/Q value. A person that puts weight on the number of people who are possibly left unrepresented might have guessed 10.5 quotas. The ratios change so easily when the numbers are small. >From the other direction, if the larger group has 10,5 quotas, how many quotas >does the smaller group need to reach the same S/Q value (0.952). It needs 1.05 >quotas (5% of the next quota). One more way to read your example is to assume that district A first had first exactly 50 quotas and 50 seats, and B had 1 quota and 1 seat. Then we annex some new areas to those districts (332 and 335 persons). The question is why the 335 extra (over 1 quota) people in district B are "less valuable" than the extra 332 (over 50 quota) of district A? Isn't this a valid concern, at least from one point of view? > Surely no one would deny that the number of representatives that a Hare quota > of people has is its "representation". I note that although you wrote these words to support Saint-Laguë, they work also against it. Let's say we have proportions 61-13-13-13. SL allocates the seats 2-1-1-1. The number of quotas of each district/party has is 3.05 - 0.65 - 0.65 - 0.65. The third full quota of the largest district/party does not get its seat. Shouldn't all quotas get their representation? Is this in line with "SL's optimal proportionality"? SL is one good allocation method (for certain needs) but I have hard time defining it as optimal. Juho On 20.6.2012, at 19.24, Michael Ossipoff wrote: > Juho: > > Ok, I'll let this subject go, but I just want to say one more thing, > and then show an example. > > Your justifications for LR sound arbitrary. Just as you said, anyone > could express preference for any sort of standard, and no one can say > that your standard isn't right for you. That's why it's best to look > at _objective_ standards that we can all agree on. > > Say a Hare quota of people has a certain number of representatives. > Another Hare quota has a different number of representatives. > > Surely no one would deny that the number of representatives that a > Hare quota of people has is its "representation". > Now, if a Hare quota of people in your district has more > representation than a Hare quota of people in my district, that's what > we want to avoid in PR. > > We could speak of the difference or the ratio of your and my > representatives per Hare quota, but, as I said, difference is what is > relevant in Congressional and Parliamentary voting. > > In the following example, Hall's method gives the same seat allocation > as Sainte-Lague/Webster. > > To dramatically bring out the difference between LR and SL, this > example has districts greatly differing in size. > > In this example election, there are 3 districts, A, B, and C. > > S/Q means seats per Hare quota. > > Largest-Remainder: > > District......Hare.Quotas.......Seats......S/Q > A................50.332................50............9934 > B................1.335...................2.............1.498 > C................1.333...................1...............0.75 > > > Sainte-Lague/Webster: > > A................50.332................51............1.0133 > B.................1.335.................1...............0.749 > C.................1.333.................1...............0.75 > > Difference between largest and smallest S/Q: > > SL: .2643 > LR: .748 > > The difference in the representation per Hare quota, between the best > and least represented districts, is about three times as great with > LR, in comparison to SL. > > In LR, you'd have Hare quotas in those two districts differing in > their representaton by 3/4 of a seat. Is that really what you think is > fair? > > Mike Ossipoff > ---- > Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
