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

[Peter Zbornik]

Dear all,

A mathematically more sound notation of the importance of the functions of
the council members would be the following:
M1>M2=M3>M4=M5=M6=M7, where Mn is a member of the set of all council
members.
instead of P>[VPa, VPb]>[Ma, Mb, Mc, Md].

The "unified method" is called Schulze generalized proportional ranking.
This method would repeatedly apply the fill the not yet elected (vacant)
seats of councils, that are
elected by STV method (FVSSTV).
Schulze describes his method in chapter 7 of
http://m-schulze.webhop.net/schulze2.pdf

<http://m-schulze.webhop.net/schulze2.pdf>
Best regards
Peter Zborník



On Fri, May 7, 2010 at 10:11 PM, Raph Frank <raphfrk at gmail.com> wrote:

> On Fri, May 7, 2010 at 4:27 PM, Peter Zbornik <pzbornik at gmail.com> wrote:
> > The proportional ranking needed is not P>VPa>VPb>Ma>Mb>Mc>Md,
> > but P>[VPa, VPb]>[Ma, Mb, Mc, Md].
> > Let us call this required ranking for "boundary conditions".
>
> Schulze's method can do that too.
>
> Step 1: Elect the Schulze single seat method winner as President
> Step 2: Elect a 3 person council using Schulze-STV, but the President
> must be a member
> Step 3: Elect a 7 person council using Schulze-STV, but the President
> + VPs must be members.
>
> I think this is what you meant by your unified method?
>
> Schulze rankings is just Schulze-STV, except you elect councils that
> increase in size by one each iteration, and members elected in
> previous iterations must be members of subsequent councils.
>
> > Example (from an email by Schulze):
> > "40 ABC
> > 25 BAC
> > 35 CBA
> > The Schulze proportional ranking is BAC.
> > However, for two seats, Droop proportionality, requires that A and C are
> > elected."
> >
> > The "unified" method for two seats without boundary conditions would
> select
> > BA (i.e.Schulze STV)
>
> Schulze-STV meets the Droop criterion, so would elect A and C in a 2 seat
> race.
>
> Schulze-rankings elects B and then A as you say.
>
> There are 2 steps:
>
> *** Work out A's score vs C:  ***
>
> We split the voters in 2 groups
>
> Voters who prefer B to A: 60
> Voters who prefer C to A: 35
>
> There are no options in which group each voter can be placed, as no
> voter is eligible for both groups.
>
> The smallest group has 35 voters so, A better than than C gets 35 votes
>
> *** Work out C's score vs A ***
>
> Again we split into 2 groups
>
> Voters who prefer only B to C: 0
> Voters who prefer only A to C: 0
> Voters who prefer both to C: 65
>
> Thus we split the third group into 2 parts, as they can be placed in
> either group.
>
> Voters who prefer B to C: 32.5
> Voters who prefer A to C: 32.5
>
> The smallest group has 32.5 voters so, C better than A gets 32.5 votes
>
> Thus the result is
>
> A gets 35 votes and C get 32.5 votes, so A wins the 2nd seat.
>
> Anyway, I think the rankings method can be generalised to allow groups
> of candidates to be elected at once, rather than electing them one at
> a time.
>
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