[EM] Proportional election method needed for the Czech Green party - Council elections

[Juho]

On May 7, 2010, at 6:27 PM, Peter Zbornik wrote:

> Our main problem with the proposal of Schulze, is that it gives us  
> more hierarchy than we usually need, and that it drops  
> proportionality unnecessarily much.
> Let's for the sake of the argument say, that we want to select the  
> Green regional party council in Prague, which (as an exception) has  
> two vice presidents, without internal ordering and seven members.
> Thus this council looks like the following: P, VPa, VPb, Ma, Mb, Mc,  
> Md (Ma means Member a).
>
> The proportional ranking needed is not P>VPa>VPb>Ma>Mb>Mc>Md,
> but P>[VPa, VPb]>[Ma, Mb, Mc, Md].

In my definition I missed this variant. In this case 3) and 4) should  
be replaced with

3) Elect the vice presidents (all at one round) so that set of P 
+VP1+...+VPn is as proportional as possible based on V1


> An other example where this ranking would be needed could for  
> instance be the national council with two presidents (party  
> leaders), whch is a common leaderhip structure in the green parties  
> in some countries.
> Thus, let us for instance assume the following structure:
> [Pa, Pb]>VPa>VPb>[Ma, Mb, Mc]
> In the case of two presidents, Shulze's proportional ranking fails  
> to elect the "most proportional" "Condorcet" presidential pair (I  
> have no clue of how to be able to find the "most proportional  
> Condorcet presidential pair"), since it imposes an unnecessary  
> condition that one president should be ranked ahead the secon.
> Maybe the presidential pair or Prague regional council of the Greens  
> could be good examples to focus on.

Let's make a generic model. Your notation is a good start.

I see "proportional ranking" and "proportional election" as two  
alternative schemes that differ so that
- proportional election elects the best proportional set of n candidates
- proportional ranking does the same but in a serial way so that it  
first elects one representative, then two representatives with the  
restriction that the first representative has already been fixed, and  
so on until all representatives have been elected

There could be also intermediate forms where the serial process e.g.  
uses some forward looking techniques to balance the bias caused by the  
decisions that can not be fixed later. Some proportional election  
techniques are also computationally complex and therefore proportional  
ranking or some intermediate approaches may help (e.g. elect  
representatives in smaller groups, or even so that the decisions can  
be partially reversed later, there are many alternative ways).

Your notation could in this light be read as follows. [Pa,  
Pb]>VPa>VPb>[Ma, Mb, Mc] says: use PE to elect Pa and Pb; continue  
with PR to elect VPa; continue with PR to elect VPb; continue with PE  
to elect Ma, Mb and Mc (with the limitation that the already elected  
representatives must be kept). This is based on the assumption that  
same votes are used in all phases. The PR steps are actually just PE  
steps that elect only one additional representative. We can thus in  
principle use the same PE method all the time. Relation ">" refers to  
a serial process and "[ , ]" refers to electing multiple  
representatives at one round.

Juho


P.S. I note that you already covered this approach in your later mail.  
This approach applies to all proportional methods that can add members  
to some already fixed set of representatives (not only to the one that  
Markus Schulze proposed).