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

[Raph Frank]

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.