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

[Raph Frank]

2010/5/3 Juho <juho4880 at yahoo.co.uk>:
> (What I mean by "distorting effect" is that if you have left, centre and
> right, and centre has less first place support than the other two, then a
> good approach may be to elect C if one elects only one representative. But
> if one elects two then one could pick L and R (to be proportional). This
> means that the proportional ranking (or locking) approach always makes a
> mistake, either in the case of one or two representatives. But in the case
> of electing the presidents it may be well justified to elect C as president
> (the most important job, expected to represent all sections of the party)
> and then elect either L or R as the first vice president. And the other one
> as third. Fair enough although the "team of two" is not proportional.)

Looking it purely on the number line is like trying to slot in new
candidates at each step.

For example, assuming that each voter/candidate is scored from 0 to
100 and new candidates are added one at a time.

Round 1:
The most representative candidate would be placed at 50.

Winners: 50
Ideal result: 50

Round 2
The ideal result would be one candidate at 33 and one at 67.  However,
the winner from round 1must be included.

I am going to assume 33 wins the tie-break with 67.

Winners: 50, 33
Ideal: 67, 33

Round 3
The ideal would be 25, 50, 75

Since 33 was elected, 75 wins against 25.

Winners: 33, 50, 75
Ideal: 25, 50, 75

As you add more members, the differences between ideal and actual is
reduced, but it is never eliminated.

Also, if there is no need for rankings, then it is better to just
elect the remaining candidates proportionally.

> This kind of a method provides a complete proportional ranking of the
> elected council members. This is quite unnecessary towards the end of the
> list, but what is interesting at the beginning of the list is that there is
> no need to define the exact number of vice presidents since one can just
> pick as many of them from the chain as needed.

Right, if there is a desire for an ordered list and proportionality,
then proportional ordering methods are a good idea.

However, they do sacrifice some proportionality for being able to rank
the candidates.

> If the requirement of conservative / already used methods (like STV) is not
> strict, then one could well use some Condorcet method as a basis in the
> serialization.

This might be the simplest.  Just elect the council using PR-STV and
then rank them in condorcet order.

However, that does mean that the condorcet winner isn't guaranteed to
be the President.

> You mentioned also the possibility of additional requirements (in the P.S.
> mail). It is possible e.g. to elect certain minimum number of males and
> females. In the serial approach that was discussed above one simple approach
> would be to just eliminate all remaining male or female candidates at some
> appropriate in the serial process when all the remaining representatives
> must be of same sex.

So assume that the rules were 8 member council and at least 3 men and
at least 3 women.

If a 5th man is elected, then all further men are eliminated before
the next round.  Similarly, if a 5th woman is elected, all remaining
women are eliminated.

You also need a rule which says that members of a particular gender
would be automatically elected.  For example, if there is 1 man
elected and 2 unelected men remaining, then those 2 men are
automatically elected.

This could cause strategic effects and problems with quota.

It might be better to say that men are protected from elimination if
there are only 4 remaining men and likewise only 4 remaining women,
except in the last round (when there are 9 remaining candidates).
Also, all men or eliminated if 5 of their gender are elected.

This guarantees at least 3 of each are elected, which still having the
same effective quota for each (except if the 5 elected rule kicks in).