Talk:Stable winner set
Limitations
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.