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

[Peter Zbornik]

Dear Juho,

I attach a post scriptum to my email below (7.5.2010).

I wrote:
"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)."

A less ambiguous formulation is (changes in bold):
"The "unified" method for two seats without boundary conditions would select
BA (i.e.Schulze STV)*.*
Under the boundary condition *P>VP (the P is elected before the VP)* the
same "unified" method would select AC (i.e. Schulze proportional ranking)."

Best regards
Peter Zborník

On Fri, May 7, 2010 at 5:27 PM, Peter Zbornik <pzbornik at gmail.com> wrote:

> 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
>>
>
>
>
>
>
> ----
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>
>
>
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