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Text and/or other creative content from this version of Electoral system was copied or moved into Comparison of electoral systems with this edit on 20 March 2017. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
The main article "Electoral Systems" primarily contrasts Majoritarian vs Proportional. It seems to me the primary subject of this article would therefore be the tradeoffs between proportional vs majoritarian - i.e. local representation.
For example, problems with proportional representation, such as the debate of extremist legislators:
http://www.tandfonline.com/doi/abs/10.1080/00344890408523252?journalCode=rrep20
On the hand, proportional representation greater representation of women and minorities:
Filingpro ( talk) 01:09, 16 April 2017 (UTC)
If you click on the LIIA heading in the table, it takes you to a wiki page which says, in part,
> LIIA is weaker than IIA because satisfaction of IIA implies satisfaction of LIIA, but not vice versa.
Note that on this table, Schulze is marked as satisfying IIA but not LIIA. Something is wrong here. — Preceding unsigned comment added by 100.14.179.139 ( talk) 11:55, 24 July 2018 (UTC)
"Semi-honest" and "No favorite betrayal" are two terms that this article uses, seemngly without any clear explanation. They should either be linked to an article or article section that explains them, or else there should at least be a footnote that clearly explains them. (There may well also be other terms in need of explanation). Tlhslobus ( talk) 05:14, 1 September 2018 (UTC)
I am so sorry to describe here that I am totally flabbergasted that this article is not what the title purports it to be. Where is the true comparison of systems? Where is the heart of the matter?
Who wrote this? What is going on in the mind of people that wrote/supported this page as it exists now?
I am going to make a few edits. Please help me turn this page into something worth reading.
FredrickS
When I first started digging around here, I was, like most people probably are, taken in by the nice pretty green strips across the comparison table which some of the different voting systems produce. You would naturally assume that a voting system that meets more of the criteria must be "better", however it has come to my attention that this may be far from the case.
Point in case: https://arxiv.org/ftp/arxiv/papers/1606/1606.04371.pdf
He demonstrates clearly, using a relatable example, of how the commonly accepted "desirable" criteria may lead to nonsensical results in practical terms, and how violating those properties under specific conditions can lead to superior results. Apparently Tideman (the creator of the Ranked Pairs method) has also raised similar objections. It's amazing the kind of things you can stumble across on google scholar. :P
Anyway I think we may want to reconsider how the information is presented and add notes about the controversy surrounding some of the criteria. Some methods fail at certain criteria in a bad way, or when they have no theoretical reason to (ie a non-condorcet method failing participation), while others fail the criteria only in specific situations, and do so beneficially, and we should probably make finer distinctions about that.
I should also mention that I've noticed a few errors in the table, as well as important criteria which are missing (ie the weak condorcet criterion) that really ought to be fixed/included. MarcT 107.129.249.144 ( talk) 07:37, 15 May 2019 (UTC)
can 'vulnerability to free riding' be a criteria in the table for multi-winner methods? not a simple yes/no answer but there are papers comparing different methods through simulation. 2A02:C7D:8A9:6700:4082:5C5:DABF:ADCE ( talk) 18:22, 15 November 2022 (UTC)
Douglas Woodall shows that clone independence is incompatible with the Droop proportionality criterion here: http://www.votingmatters.org.uk/ISSUE3/P5.HTM
As such, the clone independence column should be removed from the "Compliance of non-majoritarian party agnostic multi-winner methods" section because it would be uninformative: every Droop-proportional method fails it, and probably so does every proportional method in general. The gist of Woodall's observation is that suppose some coalition X has fielded too few candidates (e.g. it has 80% support but only a single candidate in a 10-winner election). Then cloning X will always make both X and the clone win, and that happens at the expense of some other candidate, hence a violation of clone independence.
Woodall suggests replacing clone independence with three criteria (clone-no-harm, clone-no-help and clone-in), but I don't know any sources that have done so.
In addition, that every method is claimed as being clone-proof despite Woodall's impossibility observation suggests that more of the data may be suspect as well, and so the claims made could use more references in general. 82.164.37.138 ( talk) 12:26, 23 August 2019 (UTC)
Quoting the original paper by Burt Monroe [1]:
"Let us first establish some definitions. We assume that we can quantify the misrepresentation of voter v_a when represented by candidate x_i; call this mu_ia. Further assume that for reasons of voter equality, the scale of mu_ia across voters can be normalized and then compared."
(under "The Pure Fully Proportional Representation Concept")
"For m = 1, the pure FPR system is equivalent to the Borda count. In this example, the Independent is the clear Borda winner. All of the advantages and disadvantages of the Borda rule are inherent in ordinal FPR (...)"
(under "An Example")
In the abstract of Brams and Potthoff's paper "Proportional Representation: Broadening the Options" [2], the authors write:
Under Monroe's system and our generalizations of it, one minimizes total misrepresentation, where misrepresentation is based on approval votes, the rankings of candidates, or other ballot information.
Monroe's method can thus be applied to any weighted points system, and in fact, Monroe uses Borda in his example. Calling only the particular version that uses Approval or Range scores "Monroe" is like saying that Minmax must always use pairwise opposition and thus that Minmax always passes the Favorite Betrayal criterion. 46.66.178.159 ( talk) 08:38, 6 September 2019 (UTC)
References
Could one of you add an explanation or chart for the color scheme in the comparison charts? There are 2 colors for "No" and 2 colors for "Yes". HSukePup ( talk) 23:26, 17 October 2019 (UTC)
The article claims that highest median satisfies resolvability. Could please someone elaborate this claim? Markus Schulze 18:09, 13 December 2020 (UTC)
The color scheme in the comparison table indicates the following scale:
This implies that score-based voting systems are superior to ranked voting systems. In the literature, Approvals are considered a floor/ceiling score based system; and score systems are considered highly vulnerable to strategy and generally unable to provide good electoral outcomes in practice. Strictly speaking, the literature suggests score-based systems are among the worst systems, barring single-mark systems. I am uncertain if general consensus as such is representative of what may be considered facts, or if presentation is suggested to be neutral in such a way that Wikipedia would present global warming skepticism as equally valid as the mainstream scientific consensus on climate change; but as it stands, the color scheme—which has now been rolled back from an earlier edit to clarify—gives the automatic impression that global warming is fake news, so to speak, regarding scored versus ranked systems.
Given the literature and the use of a four-scale color scheme, I suggest the below is more scientific and less blatantly biased:
Even this is generous to scores, and only because approvals are considered scores in the literature and are reasonably so. The literature isn't the problem on Wikipedia, though; between FairVote and the few Score vote supporters who started their own barely-existent advocacy groups, there is a lot of subtle tweaking to cover up flaws and elevate the status of one voting system over another as an ongoing propaganda campaign. It is perfectly reasonable and in fact important to discuss some systems as being better than others, so long as this can be backed up with literature weighted for methodological quality and general consensus, and fits with consistent normative values Wikipedia assumes are used for such evaluation or else with declared criteria constituting "better." It is also reasonable to expect presentation will be interpreted by the reader and so can convey things the words don't strictly say. Tables are quite nice, as it's hard to twist bare facts when presented without interpretation (even though these tables don't give weighting to the importance of criterion or their probabilistic failure rates and practical considerations); but apparently there are ways to manipulate that as well. John Moser ( talk) 15:10, 14 March 2021 (UTC)
If I were a Wikipedia editor I would be put the "This article has multiple issues..." health warning at the top. However, I am not a Wikipedia editor and I say instead that this article contains some serious, industrial strength, claptrap.
I came here (to this article) for enlightenment - and I do know a thing or two about electoral systems. But this article does not enlighten me. So far I have got as far as the section, "Direct comparisons between first-past-the-post and proportional voting" and I make the following comments--
1. The statement, "With proportional voting, virtually every voter can point to the representative they voted for" is just plainly not true. That the opposite is true is the main drawback of proportional voting.
2. The statement,
"if a seat is obtained with 20 percent of the vote (which can occur), and a decision is subsequently made with 40 percent of the council members, then the voters' input can be declared as diminished, since about 12 percent of voters have indirectly made the winning decision. If decisions made in proportional voting are won with an absolute majority of the votes by the people who got their seats based on the direct distribution of the constituents' votes, then there is at worst a 50 percent weakening in the representation of voters' opinions, in the sense that a decision represents (indirectly, via the representatives) at least 50 percent of the voters"
needs some serious clarification. How on earth do these numbers tie together? There is no reasoning to support the figures and no reference to seek further clarification.
3. The statement,
"This shows how one system is more accustomed to having a more vertical power structure whereas the other is more collaborative or horizontal in nature."
is nonsense. Please clarify what vertical and horizontal power structure are.
4. The statement,
"In general, the two major parties will have no problem absorbing third-party issues as their own, covering any gaps both forgot to cover collectively. Both parties may therefore deliver close to what the voters want."
is pure unalloyed claptrap - it is a statement of opinion that no third party in the UK (for example) would agree with.
If this section is indicative of the rest of the article it will not be worth reading. — Preceding unsigned comment added by 146.200.235.218 ( talk • contribs)
My translation was correct, as is confirmed by published sources (eg. Szpiro’s book: “Essay on the application of probability analysis to majority decisions”). The title in the Condorcet article seems to have been copied from Google translate by someone with no knowledge of the language. Is duck à l’orange “duck to the orange”? Colin.champion ( talk) 13:32, 22 July 2021 (UTC)
I’ve added a table showing the relative accuracies of a few ranked voting methods. I originally intended it for the ranked voting article, where there was some discussion (see the talk) but I got cold feet and thought that it was better to put it somewhere which provides more context. Colin.champion ( talk) 10:36, 9 August 2021 (UTC)
n method
|
5 | 25 | 125 |
---|---|---|---|
FPTP | 55.6 | 52.3 | 51.2 |
AV/IRV | 61.9 | 60.1 | 60.2 |
Coombs | 66.6 | 61.8 | 60.8 |
Borda | 71.9 | 71.2 | 71.2 |
Minimax | 65.7 | 65.1 | 65.1 |
Copeland | 67.9 | 65.7 | 65.4 |
The article previously devoted a lot of space to a discussion of metrics. This seemed misguided to me – the metrics are almost wholly presentational whereas the substance of a comparison lies in the model. A pattern emerged from Bordley’s and Merrill’s evaluations of utilitarian metrics favouring the Borda count over Condorcet methods.
Bordley’s result is genuine but nothing to do with metrics: he essentially used a jury model, and it has been known for some time that the Borda count is approximately optimal under it. I coded up Bordley’s evaluation for σ2=0 and varying numbers of voters; some results are shown here. (There are 5 candidates. The numbers in the table are the percentages of cases in which the best candidate is elected. The Copeland tie-break is to choose the Copeland winner with the largest number of first and second preferences combined.)
I’ve added a brief discussion of jury models to the article since they’re interesting in their own right. The arctan formulae for p play no part in the argument; they make use of an integral which will be found on stackechange.
Merrill’s results are based on a spatial model. So far as I can see his margin between Borda and Condorcet is less than experimental error, and maybe much less, so it probably doesn’t mean anything. I find it incredible that a small change in metric should overturn the superiority of Condorcet methods, and when I look into the question myself in one dimension I find that Condorcet methods continue to outperform the Borda count. I illustrate this by a mini-table in the article. It requires a few extra lines in my software, which follows. The formula for the metric uses the fact that the average distance from x to a point in a standard Gaussian distribution is .
C program
|
---|
#include <math.h> #define pi 3.141592653589793 double rtlnorm(double),gaussv() ; static double qk = sqrt(2/pi) ; int fptp(int **bal,double *qwt,int nbal,int m) { double q,*score=vector(m) ; int t,winner ; for(t=0;t<nbal;t++) score[bal[t][0]] += qwt[t] ; for(q=winner=t=0;t<m;t++) if(t==0||score[t]>q) { winner = t ; q = score[t] ; } free(score) ; return winner ; } int borda(int **bal,double *qwt,int nbal,int m) { double q,*score=vector(m) ; int balno,t,winner,*b ; for(balno=0;balno<nbal;balno++) for(q=qwt[balno],b=bal[balno],t=0;t<m-1;t++) score[b[t]] += q * ((m-1)-t) ; for(q=winner=t=0;t<m;t++) if(score[t]>q) { winner = t ; q = score[t] ; } free(score) ; return winner ; } int minimax(int **bal,double *qwt,int nbal,int m) { double q,*qmin=vector(m),**r=matrix(m,m),qmax ; int i,j,balno,t,winner,*b ; for(balno=0;balno<nbal;balno++) for(q=qwt[balno],b=bal[balno],i=0;i<m-1;i++) for(j=i+1;j<m;j++) r[b[i]][b[j]] += q ; for(i=0;i<m;i++) for(qmin[i]=1,j=0;j<m;j++) if(i!=j&&r[i][j]<qmin[i]) qmin[i] = r[i][j] ; for(qmax=winner=t=0;t<m;t++) if(qmin[t]>qmax) { winner = t ; qmax = qmin[t] ; } free(qmin) ; freematrix(r) ; return winner ; } int av(int **bal,double *qwt,int nbal,int m) { int t,tau,balno,winner,loser,mleft,**b=imatrix(nbal,m) ; double qmin,*score=vector(m) ; for(balno=0;balno<nbal;balno++) for(t=0;t<m;t++) b[balno][t] = bal[balno][t] ; for(mleft=m;mleft>0;mleft--) // mleft is the number of remaining candidates { for(balno=0;balno<m;balno++) score[balno] = 0 ; for(balno=0;balno<nbal;balno++) score[b[balno][0]] += qwt[balno] ; for(qmin=loser=t=0;t<mleft;t++) if(t==0||score[b[0][t]]<qmin) { loser = b[0][t] ; qmin = score[loser] ; } for(balno=0;balno<nbal;balno++) for(tau=t=0;t<mleft;t++) if(b[balno][t]!=loser) b[balno][tau++] = b[balno][t] ; } winner = b[0][0] ; free(score) ; freeimatrix(b) ; return winner ; } int main(int argc,char **argv) { int (*alg[])(int **,double *,int,int) = { borda , fptp , minimax , av , 0 } ; char *algname[] = { "borda" , "fptp" , "condorcet" , "av" , 0 } ; int testno,i,j,t,l,r,ntests=1000000,nalg,rightful,winner ; for(nalg=0;alg[nalg];nalg++) ; int m = (argc>=2?atoi(argv[1]):3) , m2 = (m*(m-1)) / 2 ; double offs=(argc>=3?atof(argv[2]):0) ,ql,qr,q ; int *win = ivector(nalg) , *ballot = ivector(m) , **bal = imatrix(m2+1,m) ; double *c = vector(m) , *qwt = vector(m2+1) , *qdist = vector(nalg) ; xi *cm = xivector(m2) ; for(testno=0;testno<ntests;testno++) { for(i=0;i<m;i++) c[i] = gaussv() + offs ; realsort(c,m) ; for(t=i=0;i<m-1;i++) for(j=i+1;j<m;j++,t++) cm[t] = xi((c[i]+c[j])/2,(i<<8)|j) ; xisort(cm,m2) ; for(i=0;i<m;i++) ballot[i] = i ; for(ql=1,i=0;i<=m2;i++,ql=qr) { if(i==m2) qr = 0 ; else qr = rtlnorm(cm[i].x) ; qwt[i] = ql - qr ; for(t=0;t<m;t++) bal[i][t] = ballot[t] ; if(i==m2) break ; l = cm[i].i >> 8 ; r = cm[i].i & 255 ; for(t=0;t<m-1&&ballot[t]!=l;t++) ; swap(ballot[t],ballot[t+1]) ; } for(q=rightful=t=0;t<m;t++) if(t==0||fabs(c[t])<q) { rightful = t ; q = fabs(c[t]) ; } for(t=0;t<nalg;t++) { winner = alg[t](bal,qwt,m2+1,m) ; if(rightful==winner) win[t] += 1 ; q = c[winner] ; qdist[t] += q*(1-2*rtlnorm(q)) + qk*exp(-q*q/2) ; } } printf("m=%-2d, x=%.2f",m,offs) ; for(t=0;t<nalg;t++) printf(" | %s: %4.1f",algname[t],win[t]*100.0/ntests) ; printf("\n") ; for(t=0;t<nalg;t++) printf(" | %s: %5.3f",algname[t],qdist[t]/ntests-qk) ; printf("\n") ; } |
The table at the start of the article, in which 22 experts were asked which voting methods they would each endorse, does not qualify as encyclopedic content and should be removed.
If there were a well-conducted survey of a large number of voting theorists, representative of the overall opinion of the academic field, the results of that survey would be encyclopedic content and would deserve its own section in this article.
However, the table simply conveys the opinions of 22 people who just happened to be attending the same workshop as each other. The source of the table (Laslier, "And the Loser is... Plurality Voting", 2011) does not claim to be the consensus opinion of the academic field. Without additional context, the table could easily be misinterpreted as such.
Ancophosep ( talk) 18:40, 27 September 2021 (UTC)
{{
cite book}}
: |journal=
ignored (
help)@ JusticeShampoo: added a sentence to the lead para mentioning that STAR had been first proposed in 2014, presumably as an explanation for its absence from the table of methods assessed by Laslier et al. It would be very cumbersome if every method invented since 2010 needed to be mentioned in this way. On the other hand the table isn’t presented as authoritative on the relative values of voting systems, and I don’t think any reader would interpret it otherwise.
There are similar tables elsewhere on Wikipedia. There have been surveys of economists trying to find what common ground exists between them (“is government spending a stimulus?”) and these have not been caveated more heavily than the table in this article. Colin.champion ( talk) 08:51, 16 October 2021 (UTC)
It seems to me that the summability criterion needs to be added to the table comparing various methods. Who's going to take that on? -- RobLa ( talk) 04:22, 9 February 2022 (UTC)
@ Closed Limelike Curves: Which sources cited in this article are not reliable? Jarble ( talk) 15:33, 13 March 2024 (UTC)
Hi,
the multiwinner part of the article currently seems of very very low quality. Dubious methods, original research, even more dubious axioms. I feel like currently it might be better to just delete it and then start to restructure stuff a bit. @ Closed Limelike Curves@ Wotwotwoot Jannikp97 ( talk) 19:22, 5 April 2024 (UTC)
This article is rated C-class on Wikipedia's
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Text and/or other creative content from this version of Electoral system was copied or moved into Comparison of electoral systems with this edit on 20 March 2017. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
The main article "Electoral Systems" primarily contrasts Majoritarian vs Proportional. It seems to me the primary subject of this article would therefore be the tradeoffs between proportional vs majoritarian - i.e. local representation.
For example, problems with proportional representation, such as the debate of extremist legislators:
http://www.tandfonline.com/doi/abs/10.1080/00344890408523252?journalCode=rrep20
On the hand, proportional representation greater representation of women and minorities:
Filingpro ( talk) 01:09, 16 April 2017 (UTC)
If you click on the LIIA heading in the table, it takes you to a wiki page which says, in part,
> LIIA is weaker than IIA because satisfaction of IIA implies satisfaction of LIIA, but not vice versa.
Note that on this table, Schulze is marked as satisfying IIA but not LIIA. Something is wrong here. — Preceding unsigned comment added by 100.14.179.139 ( talk) 11:55, 24 July 2018 (UTC)
"Semi-honest" and "No favorite betrayal" are two terms that this article uses, seemngly without any clear explanation. They should either be linked to an article or article section that explains them, or else there should at least be a footnote that clearly explains them. (There may well also be other terms in need of explanation). Tlhslobus ( talk) 05:14, 1 September 2018 (UTC)
I am so sorry to describe here that I am totally flabbergasted that this article is not what the title purports it to be. Where is the true comparison of systems? Where is the heart of the matter?
Who wrote this? What is going on in the mind of people that wrote/supported this page as it exists now?
I am going to make a few edits. Please help me turn this page into something worth reading.
FredrickS
When I first started digging around here, I was, like most people probably are, taken in by the nice pretty green strips across the comparison table which some of the different voting systems produce. You would naturally assume that a voting system that meets more of the criteria must be "better", however it has come to my attention that this may be far from the case.
Point in case: https://arxiv.org/ftp/arxiv/papers/1606/1606.04371.pdf
He demonstrates clearly, using a relatable example, of how the commonly accepted "desirable" criteria may lead to nonsensical results in practical terms, and how violating those properties under specific conditions can lead to superior results. Apparently Tideman (the creator of the Ranked Pairs method) has also raised similar objections. It's amazing the kind of things you can stumble across on google scholar. :P
Anyway I think we may want to reconsider how the information is presented and add notes about the controversy surrounding some of the criteria. Some methods fail at certain criteria in a bad way, or when they have no theoretical reason to (ie a non-condorcet method failing participation), while others fail the criteria only in specific situations, and do so beneficially, and we should probably make finer distinctions about that.
I should also mention that I've noticed a few errors in the table, as well as important criteria which are missing (ie the weak condorcet criterion) that really ought to be fixed/included. MarcT 107.129.249.144 ( talk) 07:37, 15 May 2019 (UTC)
can 'vulnerability to free riding' be a criteria in the table for multi-winner methods? not a simple yes/no answer but there are papers comparing different methods through simulation. 2A02:C7D:8A9:6700:4082:5C5:DABF:ADCE ( talk) 18:22, 15 November 2022 (UTC)
Douglas Woodall shows that clone independence is incompatible with the Droop proportionality criterion here: http://www.votingmatters.org.uk/ISSUE3/P5.HTM
As such, the clone independence column should be removed from the "Compliance of non-majoritarian party agnostic multi-winner methods" section because it would be uninformative: every Droop-proportional method fails it, and probably so does every proportional method in general. The gist of Woodall's observation is that suppose some coalition X has fielded too few candidates (e.g. it has 80% support but only a single candidate in a 10-winner election). Then cloning X will always make both X and the clone win, and that happens at the expense of some other candidate, hence a violation of clone independence.
Woodall suggests replacing clone independence with three criteria (clone-no-harm, clone-no-help and clone-in), but I don't know any sources that have done so.
In addition, that every method is claimed as being clone-proof despite Woodall's impossibility observation suggests that more of the data may be suspect as well, and so the claims made could use more references in general. 82.164.37.138 ( talk) 12:26, 23 August 2019 (UTC)
Quoting the original paper by Burt Monroe [1]:
"Let us first establish some definitions. We assume that we can quantify the misrepresentation of voter v_a when represented by candidate x_i; call this mu_ia. Further assume that for reasons of voter equality, the scale of mu_ia across voters can be normalized and then compared."
(under "The Pure Fully Proportional Representation Concept")
"For m = 1, the pure FPR system is equivalent to the Borda count. In this example, the Independent is the clear Borda winner. All of the advantages and disadvantages of the Borda rule are inherent in ordinal FPR (...)"
(under "An Example")
In the abstract of Brams and Potthoff's paper "Proportional Representation: Broadening the Options" [2], the authors write:
Under Monroe's system and our generalizations of it, one minimizes total misrepresentation, where misrepresentation is based on approval votes, the rankings of candidates, or other ballot information.
Monroe's method can thus be applied to any weighted points system, and in fact, Monroe uses Borda in his example. Calling only the particular version that uses Approval or Range scores "Monroe" is like saying that Minmax must always use pairwise opposition and thus that Minmax always passes the Favorite Betrayal criterion. 46.66.178.159 ( talk) 08:38, 6 September 2019 (UTC)
References
Could one of you add an explanation or chart for the color scheme in the comparison charts? There are 2 colors for "No" and 2 colors for "Yes". HSukePup ( talk) 23:26, 17 October 2019 (UTC)
The article claims that highest median satisfies resolvability. Could please someone elaborate this claim? Markus Schulze 18:09, 13 December 2020 (UTC)
The color scheme in the comparison table indicates the following scale:
This implies that score-based voting systems are superior to ranked voting systems. In the literature, Approvals are considered a floor/ceiling score based system; and score systems are considered highly vulnerable to strategy and generally unable to provide good electoral outcomes in practice. Strictly speaking, the literature suggests score-based systems are among the worst systems, barring single-mark systems. I am uncertain if general consensus as such is representative of what may be considered facts, or if presentation is suggested to be neutral in such a way that Wikipedia would present global warming skepticism as equally valid as the mainstream scientific consensus on climate change; but as it stands, the color scheme—which has now been rolled back from an earlier edit to clarify—gives the automatic impression that global warming is fake news, so to speak, regarding scored versus ranked systems.
Given the literature and the use of a four-scale color scheme, I suggest the below is more scientific and less blatantly biased:
Even this is generous to scores, and only because approvals are considered scores in the literature and are reasonably so. The literature isn't the problem on Wikipedia, though; between FairVote and the few Score vote supporters who started their own barely-existent advocacy groups, there is a lot of subtle tweaking to cover up flaws and elevate the status of one voting system over another as an ongoing propaganda campaign. It is perfectly reasonable and in fact important to discuss some systems as being better than others, so long as this can be backed up with literature weighted for methodological quality and general consensus, and fits with consistent normative values Wikipedia assumes are used for such evaluation or else with declared criteria constituting "better." It is also reasonable to expect presentation will be interpreted by the reader and so can convey things the words don't strictly say. Tables are quite nice, as it's hard to twist bare facts when presented without interpretation (even though these tables don't give weighting to the importance of criterion or their probabilistic failure rates and practical considerations); but apparently there are ways to manipulate that as well. John Moser ( talk) 15:10, 14 March 2021 (UTC)
If I were a Wikipedia editor I would be put the "This article has multiple issues..." health warning at the top. However, I am not a Wikipedia editor and I say instead that this article contains some serious, industrial strength, claptrap.
I came here (to this article) for enlightenment - and I do know a thing or two about electoral systems. But this article does not enlighten me. So far I have got as far as the section, "Direct comparisons between first-past-the-post and proportional voting" and I make the following comments--
1. The statement, "With proportional voting, virtually every voter can point to the representative they voted for" is just plainly not true. That the opposite is true is the main drawback of proportional voting.
2. The statement,
"if a seat is obtained with 20 percent of the vote (which can occur), and a decision is subsequently made with 40 percent of the council members, then the voters' input can be declared as diminished, since about 12 percent of voters have indirectly made the winning decision. If decisions made in proportional voting are won with an absolute majority of the votes by the people who got their seats based on the direct distribution of the constituents' votes, then there is at worst a 50 percent weakening in the representation of voters' opinions, in the sense that a decision represents (indirectly, via the representatives) at least 50 percent of the voters"
needs some serious clarification. How on earth do these numbers tie together? There is no reasoning to support the figures and no reference to seek further clarification.
3. The statement,
"This shows how one system is more accustomed to having a more vertical power structure whereas the other is more collaborative or horizontal in nature."
is nonsense. Please clarify what vertical and horizontal power structure are.
4. The statement,
"In general, the two major parties will have no problem absorbing third-party issues as their own, covering any gaps both forgot to cover collectively. Both parties may therefore deliver close to what the voters want."
is pure unalloyed claptrap - it is a statement of opinion that no third party in the UK (for example) would agree with.
If this section is indicative of the rest of the article it will not be worth reading. — Preceding unsigned comment added by 146.200.235.218 ( talk • contribs)
My translation was correct, as is confirmed by published sources (eg. Szpiro’s book: “Essay on the application of probability analysis to majority decisions”). The title in the Condorcet article seems to have been copied from Google translate by someone with no knowledge of the language. Is duck à l’orange “duck to the orange”? Colin.champion ( talk) 13:32, 22 July 2021 (UTC)
I’ve added a table showing the relative accuracies of a few ranked voting methods. I originally intended it for the ranked voting article, where there was some discussion (see the talk) but I got cold feet and thought that it was better to put it somewhere which provides more context. Colin.champion ( talk) 10:36, 9 August 2021 (UTC)
n method
|
5 | 25 | 125 |
---|---|---|---|
FPTP | 55.6 | 52.3 | 51.2 |
AV/IRV | 61.9 | 60.1 | 60.2 |
Coombs | 66.6 | 61.8 | 60.8 |
Borda | 71.9 | 71.2 | 71.2 |
Minimax | 65.7 | 65.1 | 65.1 |
Copeland | 67.9 | 65.7 | 65.4 |
The article previously devoted a lot of space to a discussion of metrics. This seemed misguided to me – the metrics are almost wholly presentational whereas the substance of a comparison lies in the model. A pattern emerged from Bordley’s and Merrill’s evaluations of utilitarian metrics favouring the Borda count over Condorcet methods.
Bordley’s result is genuine but nothing to do with metrics: he essentially used a jury model, and it has been known for some time that the Borda count is approximately optimal under it. I coded up Bordley’s evaluation for σ2=0 and varying numbers of voters; some results are shown here. (There are 5 candidates. The numbers in the table are the percentages of cases in which the best candidate is elected. The Copeland tie-break is to choose the Copeland winner with the largest number of first and second preferences combined.)
I’ve added a brief discussion of jury models to the article since they’re interesting in their own right. The arctan formulae for p play no part in the argument; they make use of an integral which will be found on stackechange.
Merrill’s results are based on a spatial model. So far as I can see his margin between Borda and Condorcet is less than experimental error, and maybe much less, so it probably doesn’t mean anything. I find it incredible that a small change in metric should overturn the superiority of Condorcet methods, and when I look into the question myself in one dimension I find that Condorcet methods continue to outperform the Borda count. I illustrate this by a mini-table in the article. It requires a few extra lines in my software, which follows. The formula for the metric uses the fact that the average distance from x to a point in a standard Gaussian distribution is .
C program
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#include <math.h> #define pi 3.141592653589793 double rtlnorm(double),gaussv() ; static double qk = sqrt(2/pi) ; int fptp(int **bal,double *qwt,int nbal,int m) { double q,*score=vector(m) ; int t,winner ; for(t=0;t<nbal;t++) score[bal[t][0]] += qwt[t] ; for(q=winner=t=0;t<m;t++) if(t==0||score[t]>q) { winner = t ; q = score[t] ; } free(score) ; return winner ; } int borda(int **bal,double *qwt,int nbal,int m) { double q,*score=vector(m) ; int balno,t,winner,*b ; for(balno=0;balno<nbal;balno++) for(q=qwt[balno],b=bal[balno],t=0;t<m-1;t++) score[b[t]] += q * ((m-1)-t) ; for(q=winner=t=0;t<m;t++) if(score[t]>q) { winner = t ; q = score[t] ; } free(score) ; return winner ; } int minimax(int **bal,double *qwt,int nbal,int m) { double q,*qmin=vector(m),**r=matrix(m,m),qmax ; int i,j,balno,t,winner,*b ; for(balno=0;balno<nbal;balno++) for(q=qwt[balno],b=bal[balno],i=0;i<m-1;i++) for(j=i+1;j<m;j++) r[b[i]][b[j]] += q ; for(i=0;i<m;i++) for(qmin[i]=1,j=0;j<m;j++) if(i!=j&&r[i][j]<qmin[i]) qmin[i] = r[i][j] ; for(qmax=winner=t=0;t<m;t++) if(qmin[t]>qmax) { winner = t ; qmax = qmin[t] ; } free(qmin) ; freematrix(r) ; return winner ; } int av(int **bal,double *qwt,int nbal,int m) { int t,tau,balno,winner,loser,mleft,**b=imatrix(nbal,m) ; double qmin,*score=vector(m) ; for(balno=0;balno<nbal;balno++) for(t=0;t<m;t++) b[balno][t] = bal[balno][t] ; for(mleft=m;mleft>0;mleft--) // mleft is the number of remaining candidates { for(balno=0;balno<m;balno++) score[balno] = 0 ; for(balno=0;balno<nbal;balno++) score[b[balno][0]] += qwt[balno] ; for(qmin=loser=t=0;t<mleft;t++) if(t==0||score[b[0][t]]<qmin) { loser = b[0][t] ; qmin = score[loser] ; } for(balno=0;balno<nbal;balno++) for(tau=t=0;t<mleft;t++) if(b[balno][t]!=loser) b[balno][tau++] = b[balno][t] ; } winner = b[0][0] ; free(score) ; freeimatrix(b) ; return winner ; } int main(int argc,char **argv) { int (*alg[])(int **,double *,int,int) = { borda , fptp , minimax , av , 0 } ; char *algname[] = { "borda" , "fptp" , "condorcet" , "av" , 0 } ; int testno,i,j,t,l,r,ntests=1000000,nalg,rightful,winner ; for(nalg=0;alg[nalg];nalg++) ; int m = (argc>=2?atoi(argv[1]):3) , m2 = (m*(m-1)) / 2 ; double offs=(argc>=3?atof(argv[2]):0) ,ql,qr,q ; int *win = ivector(nalg) , *ballot = ivector(m) , **bal = imatrix(m2+1,m) ; double *c = vector(m) , *qwt = vector(m2+1) , *qdist = vector(nalg) ; xi *cm = xivector(m2) ; for(testno=0;testno<ntests;testno++) { for(i=0;i<m;i++) c[i] = gaussv() + offs ; realsort(c,m) ; for(t=i=0;i<m-1;i++) for(j=i+1;j<m;j++,t++) cm[t] = xi((c[i]+c[j])/2,(i<<8)|j) ; xisort(cm,m2) ; for(i=0;i<m;i++) ballot[i] = i ; for(ql=1,i=0;i<=m2;i++,ql=qr) { if(i==m2) qr = 0 ; else qr = rtlnorm(cm[i].x) ; qwt[i] = ql - qr ; for(t=0;t<m;t++) bal[i][t] = ballot[t] ; if(i==m2) break ; l = cm[i].i >> 8 ; r = cm[i].i & 255 ; for(t=0;t<m-1&&ballot[t]!=l;t++) ; swap(ballot[t],ballot[t+1]) ; } for(q=rightful=t=0;t<m;t++) if(t==0||fabs(c[t])<q) { rightful = t ; q = fabs(c[t]) ; } for(t=0;t<nalg;t++) { winner = alg[t](bal,qwt,m2+1,m) ; if(rightful==winner) win[t] += 1 ; q = c[winner] ; qdist[t] += q*(1-2*rtlnorm(q)) + qk*exp(-q*q/2) ; } } printf("m=%-2d, x=%.2f",m,offs) ; for(t=0;t<nalg;t++) printf(" | %s: %4.1f",algname[t],win[t]*100.0/ntests) ; printf("\n") ; for(t=0;t<nalg;t++) printf(" | %s: %5.3f",algname[t],qdist[t]/ntests-qk) ; printf("\n") ; } |
The table at the start of the article, in which 22 experts were asked which voting methods they would each endorse, does not qualify as encyclopedic content and should be removed.
If there were a well-conducted survey of a large number of voting theorists, representative of the overall opinion of the academic field, the results of that survey would be encyclopedic content and would deserve its own section in this article.
However, the table simply conveys the opinions of 22 people who just happened to be attending the same workshop as each other. The source of the table (Laslier, "And the Loser is... Plurality Voting", 2011) does not claim to be the consensus opinion of the academic field. Without additional context, the table could easily be misinterpreted as such.
Ancophosep ( talk) 18:40, 27 September 2021 (UTC)
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ignored (
help)@ JusticeShampoo: added a sentence to the lead para mentioning that STAR had been first proposed in 2014, presumably as an explanation for its absence from the table of methods assessed by Laslier et al. It would be very cumbersome if every method invented since 2010 needed to be mentioned in this way. On the other hand the table isn’t presented as authoritative on the relative values of voting systems, and I don’t think any reader would interpret it otherwise.
There are similar tables elsewhere on Wikipedia. There have been surveys of economists trying to find what common ground exists between them (“is government spending a stimulus?”) and these have not been caveated more heavily than the table in this article. Colin.champion ( talk) 08:51, 16 October 2021 (UTC)
It seems to me that the summability criterion needs to be added to the table comparing various methods. Who's going to take that on? -- RobLa ( talk) 04:22, 9 February 2022 (UTC)
@ Closed Limelike Curves: Which sources cited in this article are not reliable? Jarble ( talk) 15:33, 13 March 2024 (UTC)
Hi,
the multiwinner part of the article currently seems of very very low quality. Dubious methods, original research, even more dubious axioms. I feel like currently it might be better to just delete it and then start to restructure stuff a bit. @ Closed Limelike Curves@ Wotwotwoot Jannikp97 ( talk) 19:22, 5 April 2024 (UTC)