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

[Peter Zbornik]

Dear Juho,

thanks for taking the time to formalize the requirements and the discussion
so far.
I would like to put some ideas into the ether, which extend the approach of
Schulze in some directions.
It is worth emphasizing that I presently do not in any way recommend any of
the approaches below before Shulze's proportional ranking, and that they are
just some ideas, which I would like to get out of my head.
Thus in this email I deliberately leave the "procurement process" for a
proportional election system for the Czech green party in order to indulge
in some academic speculation.

---

Extension suggestion:
The Schulze proportional rankig method is good, but has one weakness, which
I will try to examplify below.

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].
Let us call this required ranking for "boundary conditions".

I will discuss some ideas to address this issue by with a little
inspiration from the world of statistics.

---

 In statistics, the top-down and bottom-up approach correspond to two
heuristics often used to select variables to a regression model from a large
number of candidate variables, specifically to forward and backward
selection, see (http://en.wikipedia.org/wiki/Stepwise_regression):

In statistics <http://en.wikipedia.org/wiki/Statistics>, *stepwise
regression* includes regression models in which the choice of predictive
variables is carried out by an automatic
procedure.[1]<http://en.wikipedia.org/wiki/Stepwise_regression#cite_note-0>
[2] <http://en.wikipedia.org/wiki/Stepwise_regression#cite_note-1>[3]<http://en.wikipedia.org/wiki/Stepwise_regression#cite_note-2>Usually,
this takes the form of a sequence of
F-tests <http://en.wikipedia.org/wiki/F-test>, but other techniques are
possible, such as t-tests <http://en.wikipedia.org/wiki/T-test>, adjusted
R-square <http://en.wikipedia.org/wiki/R-square>, Akaike information
criterion <http://en.wikipedia.org/wiki/Akaike_information_criterion>, Bayesian
information criterion<http://en.wikipedia.org/wiki/Bayesian_information_criterion>,
Mallows' Cp <http://en.wikipedia.org/wiki/Mallows%27_Cp>, or false discovery
rate <http://en.wikipedia.org/wiki/False_discovery_rate>.

The main approaches are:

   - Forward selection, which involves starting with no variables in the
   model, trying out the variables one by one and including them if they are
   'statistically significant'.
   - Backward elimination, which involves starting with all candidate
   variables and testing them one by one for statistical significance, deleting
   any that are not significant.

An other method (the exhaustive search), which can be used for a moderate
number of candidate variables and variables in the model, is to evaluate all
possible variable combinations. I.e. in the case where we are looking for a
model with two variables, and we have four candidate variables (a,b,c,d),
then we evaluate the model for the variables (a,b), (a,c), (a,d), (b,c),
(b,d), (c,d).

A combination of the forward selection approach and the exhaustive search
would take as imput information on how many candidate variables to evaluate
in each step, for instance, Step 1: one variable, step 2: two variables,
step 3: four variables (the Green regional party council in Prague)

---

The underlying idea from the combine statistical approach in the previous
paragraph, could be used combine top-down and
bottom-up ranking, by modifying or generalize the Schulze proportional
ranking (which I understand a little) and Schulze STV (which I haven't
studied) to one "universal" top-down method.
The unified method would have the Schulze proportional ranking as a special
case, when the bondary conditions would be a<...<n and speculatively Schulze
STV as a special case, when there would be no boundary conditions.
The Schulze unified method would borrow the following ideas
(i) the hierarchy approach from Schulze proportional ranking as specified by
the "boundary conditions", and
(ii) more than one hopefuls can be elected at once, as in Schulze STV, while
keeping the already elected stable.

For this approach to work, we might need to introduce "proportionality" as a
"performance criterion" (as R-square in regression), which is able to say,
that we always elect all the seats in one hierarchy group simultaneously.

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)
Under the boundary condition A>B (A is elected before B) the same "unified"
method would select AC otherwise (i.e. Schulze proportional ranking).

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.

---

So much the academic debate.
For me, my priority is to better understand the Schulze proportional ranking
method, and gather up enogh courage and time to attempt to read his paper.

I hope to open the second "tender" for primary elections soon, where
Schulze's method seems to be the natural departing point.

Best regards
Peter Zborník


On Fri, May 7, 2010 at 3:57 PM, Juho <juho4880 at yahoo.co.uk> wrote:


> Based on my best understanding of the requirements here is an exact but
> partial definition of the ideal method, with the assumption that all votes
> are sincere.
>
> V1 = set of ranked ballots that indicate who would be the best president /
> vice presidents
> V2 = set of ranked ballots that indicate who would be the best council
> members
>
> 1) If there is a Condorcet winner in V1, that candidate will be the
> president (P)
> 2) If there is no Condorcet winner in V1, then ... will be the president
> (P)
>
> 3) Elect the first vice president (VP1) so that the pair P+VP1 is as
> proportional as possible based on V1
> 4) Elect other possible vice presidents one by one so that at each round
> the set of P+VP1+...+VPn is as proportional as possible based on V1
>
> 5) Elect the remaining council members (all at one round) so that set of
> council members (that includes P+VP1+...+VPn) is as proportional as possible
> based on V2
>
> 6) The method must guarantee that the council will have at least the agreed
> minimum number of both male and female representatives. The resulting
> distortion should be minimized.
>
> - Maybe "as proportional as possible" is clear enough so that I don't need
> to define it here :-)
> - Minimal distortion caused by the male/female rule is a more vague
> concept. It could mean minimal changes in the most important seats or in all
> the seats in average. The required forced selections could be pushed to the
> last seats or spread to all of them.
> - If this is a correct reflection of the requirements then this definition
> hopefully helps in discussing the properties of different candidate methods
> or method categories
> - I used the assumption that the method uses ranked ballots, but that
> should not exclude other approaches (=> differences to be described)
> - Note that V1 could be chosen to be the same as V2 but that means a minor
> deviation from the ideal method
> - Note also that this definition means that the proportionality of the full
> council is not perfect since the P+VPs are elected using a proportional
> ranking based method
> - I assumed sincere votes. Possible strategic concerns (free riding,
> burying,...) might lead to using some other method than the one that gives
> optimal results with sincere votes. This doesn't seem to be a strong trend
> however.
>
> The only detailed proposal so far is the one that Markus Schulze proposed
> in
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026087.html.
> I'll comment it shortly in the light of the definition above.
> - In the proposed method V1=V2
> - It is Condorcet compliant (1)
> - In (2) it follows the logic on the (single-winner) Schulze method (good
> or bad)
> - It is quite good in (3) and (4) (but see also the male/female rule below)
> - It does not strictly follow (5) since it uses a proportional ranking
> based approach for the whole council (the results may not be radically
> different though)
> - In (6) the distortion is not minimal. The method could e.g. change the
> third candidate to opposite sex needlessly (the whole council could contain
> sufficient number of both sexes also without that change).
>
> - There are also many other proportional ranking based methods or variants
> of this proposal that would meet the criteria the same way or better. One
> could e.g. improve the male/female algorithm, or use some other Condorcet
> method than the (single-winner) Shulze method below the proportional ranking
> part.
> - Another direction would be to use different approaches in the P+VPs
> election (that according to the requirements above should pretty much follow
> the "proportional ranking style") and in the "rest of the council" election.
> The proportional ranking only approach is simpler but is that a good enough
> reason to allow the minor distortion in proportionality?
>
> Juho
>
>
>
>
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>
>
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