[EM] IIAC. Juho: Census re-districting instead of PR for allocating seats to districts.

[Juho Laatu]

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...
>