# Talk:Stable winner set

## Limitations[edit | edit source]

The example I added illustrates how there can be examples where the committee is in the core but it does not "seem fair". User:Kristomun added the further specification that it is not proportional. Being in the core is the strictest form of proportionality and implies more standard ones like Justified representation. I think it would be a mistake to say that the committee is not proportional. None of the underserved groups are a quota in size. Can we remove this claim? --Dr. Edmonds (talk) 16:07, 15 June 2022 (UTC)

- Sure; I was thinking of disproportionality in a setwise sense. In the example, as k->infty, the faction who gets every candidate contains almost none of the voters. If we consider there to be two factions: the c1...ck faction and the "anyone but these" faction, then the distribution of power is anything but proportional in these factions: the second faction's share can grow as large as you wish without getting any representation. No proportionality violation exists in the sense of a quota violation, but divisor methods would select some non-c_1..c_k candidates in this scenario, e.g.

- k = 3, L = 10,
- 10: A1 = A2 = A3
- 9: B1
- 9: B2
- 1: C1
- 1: C2

- Then Sainte-Laguë would elect one from A1, one from B1, and one from B2.

- The problem is analogous that the Droop proportionality criterion just says (if there were 10+epsilon voters): "the A group must get at least one candidate elected" without specifying anything about the representation of the other groups in aggregate.

- I'll rephrase by removing the term as the argument may require a different definition of proportionality. Kristomun (talk) 17:40, 15 June 2022 (UTC)

- Thanks Kristomun, this is better. Proportionality is not really a well defined term so it was ambiguous. While I have you. I did not get the size of the image right. It should be smaller to match the rest of the text better. Do you know how to fix this? --Dr. Edmonds (talk) 05:00, 16 June 2022 (UTC)

- I don't think there's a satisfactory solution because text in an image can't flow the way other text does. E.g. it's hard to find a relative size so that it looks right both in portrait and landscape. I'll try rephrasing it in text: the reference link is still available for anyone who would like to read the source. Feel free to revert if it doesn't look right. Kristomun (talk) 16:13, 16 June 2022 (UTC)

- I think the best solution would be to make it smaller so that it looks like a caption in all aspects. I thought about writing it out and only taking the actual image but the though of all that formatting scared me off. Can you just make it half size or something? --Dr. Edmonds (talk) 16:24, 16 June 2022 (UTC)

- Thinking about it a little more, the best solution is probably to use vector graphics and rescale to an appropriate size, while minimizing the amount of text in it. That is, restating/rephrasing as much as possible as article text and keeping the rest in the vector image itself. I tried to convert the relevant PDF page to SVG for this purpose, but inkscape consistently crashed on me. (Inkscape's option to render text glyphs directly worked, but wasted a lot of space and is quite inelegant anyway.) Kristomun (talk) 17:12, 27 June 2022 (UTC)

- I appreciate the effort but this is well outside my skill set so I cant help. --Dr. Edmonds (talk) 07:20, 29 June 2022 (UTC)