Thanks for the useful information (and thaks to Warren too for making such fact sheets). I guess most of the historical apportionment methods have some good arguments why they were invented in the first place.
Juho On 25.6.2012, at 22.50, Kristofer Munsterhjelm wrote: > On 06/25/2012 09:29 AM, Juho Laatu wrote: >> On 25.6.2012, at 4.50, Michael Ossipoff wrote: >> >>> Do you have an exact formulation on what you think is the crucial >>> property that makes SL optimal or best in "equal representation" >>> that all should follow (at least when compared to LR)? You focus >>> very much on optimization of seats per quota, although you also >>> agree that not even SL does perfect job here. >>> >>> So what if SL isn't optimal for equality of S/Q? It does dramatically >>> better than LR in that regard, and that's sufficient for this discussion. >>> You ask for an exact formulation of the crucial property that makes SL >>> [not optimal, but better than LR] in equal representation for people. >> >> Ok, that's a good definition. There is no "SL's optimal proportionality" >> and it is not "optmal for equality of S/Q" but to you it is important >> that it is better in S/Q than LR. > > I would like to point out that there are measures which Sainte-Lague > (uniquely) optimizes. Some are given on Warren's page about divisor methods, > here: http://rangevoting.org/Apportion.html . > > The global optimality property that Sainte-Lague/Webster meets, that it > minimizes the variance of the seat-share, seems most relevant in this case. > That is, if you call S_k the number of seats for the kth group (party, state, > etc), and P_k the number of voters for that group, and the total number of > seats (resp. voters) is S (resp. P), Sainte-Lague minimizes > > sum over k > > P_k * (S_k / P_k - S/P)^2 > > so in one sense, people get as equal shares of the legislature as possible. > > Similarly, if you pick two states/parties j and k, Webster minimizes the > absolute value of S_j/P_j - S_k/P_k, i.e. the difference between "seats per > population" (share of influence per person) of state j and k. > > The page also gives optimality properties satisfies by other apportionment > methods. If you with to minimize the difference not between seats per > population but between population per seat, then pick Dean instead of > Webster. And so on... > ---- Election-Methods mailing list - see http://electorama.com/em for list info
