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

[Juho]

On May 3, 2010, at 2:07 PM, Raph Frank wrote:

> 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

(An alternative approach to defining the ideal winner sets would be  
{50}, {25, 75}, {17, 50, 83} etc., but this is not important in this  
example.)

>
> 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.

Yes, using a non-serial proportional method to get the ideally  
proportional council and then serialize its members using a serial  
proportional method would give ideal proportionality for the council.  
(PR-STV is however not ideally proportional but a practical method  
that has its own distortions, just like the serial ones have.) This  
approach has some other distortions. It may not elect the ideal  
president (or vice presidents) since one can only pick one among the  
council members. The sets of "n first presidents" could also be less  
proportional than in the case where one can elect the presidents from  
the full set of candidates.

We are thus talking about how to best allocate the inevitable small  
distortions that we must live with in any case.

The serial approach has the benefit of simplicity if the presidents  
will be elected in some serial style anyway. One should also note that  
the set of candidates is never ideal, and the border line between last  
elected and first not elected candidate may always be a bit violent  
with respect to proportionality. This means that to some extent the  
additional noise caused by the serial election style (of the full  
council) to some extent gets lost in the noise caused by other factors  
among the last elected / not elected candidates. We need to estimate  
the benefits and problems.

>
> 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.

Yes, although one alternative approach would also be to punish them  
for not setting many enough candidates and therefore electing more  
women than one otherwise would.

>
> 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.

You seem to assume here that the method would be based on serial  
elimination of the candidates.

Juho


>
> 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).