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 <[email protected]> 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 <[email protected]> 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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