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...
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