Re: [Election-Methods] Determining representativeness of multiwinner methods

[Juho]

On Jun 27, 2008, at 13:54 , Kristofer Munsterhjelm wrote:

That could be one big poster where the candidates are listed on  
the right hand side and the left hand side is used for  
representing the tree structure (and the names of the parties and  
the subgroups).


That could work, at least in cases where there's only one district  
and the party limits the depth of the tree so it doesn't get too  
cluttered. I don't think it would be of much use in small-district  
elections, since either all subgroups would have to field  
candidates (making the regional lists very long), or only some  
subgroups would have candidates you could vote on.


To be absolutely safe, each party in party list PR would have to  
have at least as many candidates in the running for a region as  
there are seats in the region. If you want absolute representation  
not just between parties but within the party, each subgroup would  
have to do the same, which would add greatly to the count.


If needed some sensible limits could be set for each party, e.g. 5 +  
1.5 * number_of_current_representatives.


It could be solvable by something like MMP where you have one  
constituency (FPTP or STV) vote and one subgroup vote, where the  
subgroup totals propagate up the party -- or for an asset-flavored  
method, the subgroups negotiate with weighted votes as to how the  
list votes are to be divided up.


My default basic method is simply an open list method with hierarchy.  
The number of votes to individual candidates accumulates to subgroups  
and parties. Seats will be allocated starting from the root of the  
tree in reverse direction. My default assumption for regional  
proportionality is to have districts that have multiple seats. It is  
possible to distribute the seats country wide in the political  
hierarchy and at the same time make sure that also the regional  
proportionality requirements are met (in Finland there is a reform  
process going on at the moment, planning to move from the traditional  
open list based system in this direction).


Asset-flavored methods would have the same Fiji-type problems you  
referred to, however, if the candidates throw their weight behind  
something you don't support. One might say that feedback would make  
the voter trust the candidate less the next time around and thus  
keep them in line, but that argument could be made for Fiji, too,  
and observation shows that feedback isn't strong enough.


The substituted ranks (candidate-individual automatic how-to-vote  
cards) would nest outwards, from the small wings to the  
increasingly larger ones within the party itself, then on to  
other parties in preference. In a sense, they are "lists" of  
their own, and so the problem isn't completely avoided.
Are there some specific cases where the tree like inheritance  
order is clearly not sufficient?


Not really - it was more of an addon to increase the information  
given, with the idea that if the candidates transfer beyond their  
own party, then a socialist green could favor other socialist and  
green parties over conservative ones, for instance. Since I  
considered the tree-structure too complex, I thought that  
complexity wouldn't be an issue.


At least the rank substitution method gives a simple way of  
implementing such a nested party-list method. If candidates declare  
subgroups, and subgroups supergroups, then the rank votes are  
generated so that a list gives the ordering within subgroups, and  
then the ranked vote is [Candidates in subgroup] > [ Candidates in  
other subgroups ] > [ Candidates in other supergroups ] and so on.


That brings us to the original question, whether it'd be possible  
to simulate this method. If "tree-based party list" (as we may call  
it) is transformed to STV, then any question of proportionality of  
tree-based party list would be reduced to a subset of the questions  
of proportionality of STV alone, and so it wouldn't be necessary to  
test tree-based party list separately - at least not unless the  
structure mitigates some problem with ordinary STV representation.


The three / nested party-list style is a more limited version of the  
rank substitution style (the inheritance network is limited to form a  
tree structure). STV (unlike the previous ones, I guess) allows the  
voter to determine the inheritance order (and is therefore even less  
limited).


The more complex methods can simulate the simpler methods. The simple  
ones have the benefit of simplicity (easy to vote, easy to understand  
the position of the candidates, no need to check and compare the  
opinions of numerous candidates). The complex ones allow voters to be  
more expressive. The problem of the complex methods is complexity,  
e.g. in STV one would need to cast a quite complex vote to simulate  
the tree model => C1>S1=S2=S3>P1=P2=P3=...=P20>A1=A2=...=A50  
(C=Candidate S=Subgroup P=Party A=Alliance). (One could of course  
introduce also names for the grou

Re: [Election-Methods] Determining representativeness of multiwinner methods

[Kristofer Munsterhjelm]

That could be one big poster where the candidates are listed on the 
right hand side and the left hand side is used for representing the tree 
structure (and the names of the parties and the subgroups).


That could work, at least in cases where there's only one district and 
the party limits the depth of the tree so it doesn't get too cluttered. 
I don't think it would be of much use in small-district elections, since 
either all subgroups would have to field candidates (making the regional 
lists very long), or only some subgroups would have candidates you could 
vote on.


To be absolutely safe, each party in party list PR would have to have at 
least as many candidates in the running for a region as there are seats 
in the region. If you want absolute representation not just between 
parties but within the party, each subgroup would have to do the same, 
which would add greatly to the count.


It could be solvable by something like MMP where you have one 
constituency (FPTP or STV) vote and one subgroup vote, where the 
subgroup totals propagate up the party -- or for an asset-flavored 
method, the subgroups negotiate with weighted votes as to how the list 
votes are to be divided up.


Asset-flavored methods would have the same Fiji-type problems you 
referred to, however, if the candidates throw their weight behind 
something you don't support. One might say that feedback would make the 
voter trust the candidate less the next time around and thus keep them 
in line, but that argument could be made for Fiji, too, and observation 
shows that feedback isn't strong enough.


The substituted ranks (candidate-individual automatic how-to-vote 
cards) would nest outwards, from the small wings to the increasingly 
larger ones within the party itself, then on to other parties in 
preference. In a sense, they are "lists" of their own, and so the 
problem isn't completely avoided.


Are there some specific cases where the tree like inheritance order is 
clearly not sufficient?


Not really - it was more of an addon to increase the information given, 
with the idea that if the candidates transfer beyond their own party, 
then a socialist green could favor other socialist and green parties 
over conservative ones, for instance. Since I considered the 
tree-structure too complex, I thought that complexity wouldn't be an issue.


At least the rank substitution method gives a simple way of implementing 
such a nested party-list method. If candidates declare subgroups, and 
subgroups supergroups, then the rank votes are generated so that a list 
gives the ordering within subgroups, and then the ranked vote is 
[Candidates in subgroup] > [ Candidates in other subgroups ] > [ 
Candidates in other supergroups ] and so on.


That brings us to the original question, whether it'd be possible to 
simulate this method. If "tree-based party list" (as we may call it) is 
transformed to STV, then any question of proportionality of tree-based 
party list would be reduced to a subset of the questions of 
proportionality of STV alone, and so it wouldn't be necessary to test 
tree-based party list separately - at least not unless the structure 
mitigates some problem with ordinary STV representation.


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Re: [Election-Methods] Determining representativeness of multiwinner methods

[Juho]

On Jun 25, 2008, at 21:05 , Kristofer Munsterhjelm wrote:


Juho wrote:

On Jun 24, 2008, at 0:34 , Kristofer Munsterhjelm wrote:

What do you mean by "methods that allow candidates to form a
tree like structure"? Something like delegable proxy, or just
preference ballots with parties instead of candidates? Or
nontraditional nested democracy (groups elect members to an
assembly - groups of assemblies elect members to a second-
level assembly, onwards up to global issues)?
I was thinking about the traditional party structure and  
proportional methods and how they may provide quite exact  
proportionality between parties but how they can not provide  
proportionality in any more detailed level. In this set-up it is  
possible to split one party e.g. to the green wing and others, and  
then the green wing could consist of radical and moderate greens.  
A vote to the radical greens (of this party) would be a vote also  
to the green wing in general and to the party in general.
The point was that now you could have even the binary decisions  
"stacked" in the party hierarchy (at least if the tree would be a  
binary tree). In this model it would also make a difference if you  
vote the green wing of the socialists or the socialist wing of the  
greens (order of priority).


If the parties as well as their respective divisions (and  
subdivisions) were to produce their own party lists, that would be  
a whole lot of lists.


That could be one big poster where the candidates are listed on the  
right hand side and the left hand side is used for representing the  
tree structure (and the names of the parties and the subgroups).


One might be able to get the effect without all the lists by having  
a candidate ranking option, similar to "voting above the line" but  
with candidates instead of parties.


I'm not sure if I got this right. STV is one basic proportional  
method where candidates are ranked. The tree structure is simpler in  
the sense that the voter votes simply just one candidate. It may be a  
problem to the voters to evaluate all the numerous candidates  
separately (if there is no structure and no "lists"). The fact that  
candidates themselves determine the order of inheritance and that the  
structure is limited to a tree format may also be considered a  
simplifying factor from the voter point of view (sets some  
limitations too, but maybe not crucial). Candidates in a way commit  
to the policy that they state (e.g. "I'll fight for socialism and  
secondarily for green values"). The tree structure is interesting  
also in the sense that it allows voters to influence and determine  
the direction that each party will take better than currently typical  
monolithic parties (proportionality is not provided inside the parties).


A voter voting for a radical green submits an approval or plurality- 
type ballot for the radical green, and the system substitutes this  
with "RadicalGreen1(Party F) > RadicalGreen2(Party F) >  
ModerateGreen1 >  > Mainstream1(Party F) > ... > Whoever(Party  
X) > SomeoneElse(Party Y)". That is, the nesting is done implicitly  
in the ranking substitution, after which the ranked votes are input  
into your favorite multiwinner method.


I assume that the candidate provided the ranking order. This is more  
flexible than the tree structure but also more confusing from the  
voter point of view.


Fiji has btw had some problems with candidates (parties) that look  
like representing X but their votes are inherited by candidates that  
do not represent X. Reading all the inheritance lists (even more  
lists) and understanding the impact of vote transfers was obviously  
too difficult. 


The substituted ranks (candidate-individual automatic how-to-vote  
cards) would nest outwards, from the small wings to the  
increasingly larger ones within the party itself, then on to other  
parties in preference. In a sense, they are "lists" of their own,  
and so the problem isn't completely avoided.


Are there some specific cases where the tree like inheritance order  
is clearly not sufficient?


In an ideal world, one could argue that if voters assume a  
candidate is acceptable (if not, why would they vote for them?)  
then they could also reasonably assume that the candidate's premade  
substitute rank can be trusted. But in reality one may pick a  
candidate not because he's absolutely trustworthy, but because the  
others are worse, and the method in any case amplifies central  
power (like closed list PR does, and for pretty much the same reason).


The complexity of the inheritance lists, the amount of work that  
voters need to do to find their optimal vote and the Fiji case make  
the simple tree structure look more practical (although STV and the  
substituted ranks (inheritance lists on automatic how-to-vote cards)  
are more flexible). STV is used in practice though, so it can't be  
overly difficult to the vot

Re: [Election-Methods] Determining representativeness of multiwinner methods

[Kristofer Munsterhjelm]

Juho wrote:

On Jun 24, 2008, at 0:34 , Kristofer Munsterhjelm wrote:


What do you mean by "methods that allow candidates to form a
tree like structure"? Something like delegable proxy, or just
preference ballots with parties instead of candidates? Or
nontraditional nested democracy (groups elect members to an
assembly - groups of assemblies elect members to a second-
level assembly, onwards up to global issues)?


I was thinking about the traditional party structure and proportional 
methods and how they may provide quite exact proportionality between 
parties but how they can not provide proportionality in any more 
detailed level. In this set-up it is possible to split one party e.g. to 
the green wing and others, and then the green wing could consist of 
radical and moderate greens. A vote to the radical greens (of this 
party) would be a vote also to the green wing in general and to the 
party in general.


The point was that now you could have even the binary decisions 
"stacked" in the party hierarchy (at least if the tree would be a binary 
tree). In this model it would also make a difference if you vote the 
green wing of the socialists or the socialist wing of the greens (order 
of priority).


If the parties as well as their respective divisions (and subdivisions) 
were to produce their own party lists, that would be a whole lot of lists.
One might be able to get the effect without all the lists by having a 
candidate ranking option, similar to "voting above the line" but with 
candidates instead of parties. A voter voting for a radical green 
submits an approval or plurality-type ballot for the radical green, and 
the system substitutes this with "RadicalGreen1(Party F) > 
RadicalGreen2(Party F) > ModerateGreen1 >  > Mainstream1(Party F) > 
... > Whoever(Party X) > SomeoneElse(Party Y)". That is, the nesting is 
done implicitly in the ranking substitution, after which the ranked 
votes are input into your favorite multiwinner method.


The substituted ranks (candidate-individual automatic how-to-vote cards) 
would nest outwards, from the small wings to the increasingly larger 
ones within the party itself, then on to other parties in preference. In 
a sense, they are "lists" of their own, and so the problem isn't 
completely avoided.


In an ideal world, one could argue that if voters assume a candidate is 
acceptable (if not, why would they vote for them?) then they could also 
reasonably assume that the candidate's premade substitute rank can be 
trusted. But in reality one may pick a candidate not because he's 
absolutely trustworthy, but because the others are worse, and the method 
in any case amplifies central power (like closed list PR does, and for 
pretty much the same reason).


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Re: [Election-Methods] Determining representativeness of multiwinner methods

[Kristofer Munsterhjelm]

Terry Bouricius wrote:
That brings me to an interesting issue, which may be off-topic for this 
list..."sortition"...the selection of a legislative body by means of 
modern sampling methods that assure a fully representative body. There is 
an interesting history of the tension between sortition on one hand and 
election on the other (Athenian democracy used both), where sortition was 
seen as the more democratic method, with election being the lesser 
(because candidates with more money or fame had such an advantage over 
average citizens). It is the old question of whether representative 
democracy should be seen as "self-governance," or "consent of the 
governed."


Possibly taking this thread even further off topic, I could mention a 
hybrid I once thought of. If there's a legislature of 360 members (to 
use a highly composite number), use random sampling to construct 36 
groups - juries or citizens' assemblies - each of which elect ten from 
their own numbers to the main assembly.


Assuming the jury voters know what they're doing, the final 
representatives would have greater skills than a randomly selected 
assembly, yet they would not be as prone to corruption and 
"aristocratic" effects as a directly elected assembly (since nobody can 
tell who'll make up the first-round juries, and thus no shadowy group 
could run ads on the behalf of any of those candidates).


One disadvantage to this method is that minorities of less than a tenth 
of the population won't be represented (since each jury only elects ten 
members). Another is that it may be considered undemocratic since only 
(36 * members of each jury) have any say in the final outcome.


The size of the assemblies, and how many they elect, could be tuned as 
desired to reflect a particular position on the sortition-election spectrum.


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Re: [Election-Methods] Determining representativeness of multiwinner methods

[Juho]

I'm inclined to think the model where all voter groups get  
representatives that closely reflect their views as the default  
model. The model where the society is represented e.g. by a group of  
centrists works in many cases but it has also some problem cases that  
make it "an alternative" in my eyes.


Let's say there are three parties or segments: left (30%), centre  
(40%) and right (30%). There may be decisions that require 75%  
supermajority. If the left wing and right wing voters are (partly or  
fully) represented by the centrist canduidates then they will lost  
their minority position that would allow them to veto some major  
decisions.


In many opinions left and right are two extremes that can be summed  
up to a centrist opinion. In these cases we might as well let the  
centre section decide. There may however be questions where right and  
left have the same opinion (i.e. this issue is not on the traditional  
left-right axis but in some other opinion space). Maybe they both  
would like to give full rights to minorities in all matters while the  
centre segment would be happier to exclude minorities in some areas.  
Left and right have majority support among the voters but not among  
the representatives.


It is also possible that the centre segment makes decisions that  
benefit the centre. They might e.g. nominate all the key people in  
central positions from the centre party.



On Jun 25, 2008, at 16:58 , Steve Eppley wrote:

The argument that the public as a whole won't engage in robust  
debate is irrelevant, since robust debate takes place in many  
circles outside the legislature. (Internet email lists, for example.)


In the heat of the political debates the representatives might forget  
the Internet email lists since their fellow representatives are  
closer (and a problem that they want to solve first to get anywhere  
with their proposals).


Don't misconstrue my argument as pro status quo.  I favor inducing  
competition to be around the voters' medians by using Condorcetian  
voting methods such as MAM


Do you thus support single-winner methods for multi-winner elections?  
(i.e. not full proportionality, and favouring large parties and not  
the small ones) (maybe for U.S. but not for current multi-party  
countries)


Juho Laatu








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Re: [Election-Methods] Determining representativeness of multiwinner methods

[Kristofer Munsterhjelm]

Steve Eppley wrote:

Hi,

I prefer a definition of "representativeness" that differs from 
Kristofer's.  To me, the more similar the *decisions* of a legislature 
are to the decisions the people themselves would make collectively in a 
well-functioning direct democracy, the more representative is the 
legislature.
Given my definition, a non-proportional legislature comprised solely of 
centrist majoritarian compromise candidates may be very representative, 
since the people themselves would reach centrist compromises on the 
issues in a well-functioning direct democracy.  It might be more 
representative than a proportional legislature, since the proportional 
legislator could match her constituents' favorite position on every 
issue yet fail to match the way they would compromise.


By considering issue representativeness, I was trying to reduce the 
problem of deliberation within a representative assembly to that of a 
direct democracy. Whatever problems the assembly might have, the people 
would also have if a direct democracy on the scale in question would be 
feasible in the first place: problems like tipping-point coalitions 
having undue power (as the Banzhaf and SS indices try to measure) would 
exist in both cases.


However, that, as you say, depends on that issues are the only thing 
that matter. Now, the dynamics among the candidates could differ from 
those of the people, but I don't see how those dynamics could be 
simulated. In order to measure the proportionality of decisions alone, 
there would have to be some sort of "decision generator" that takes the 
dynamics into account.


Also, the centrist majority candidates you mention would have to be very 
good at being neutral, incorruptible, and not belong to the same 
majority. The feedback is much more direct in a proportional assembly: 
if one of the representatives start to diverge, their support wanes, and 
voters can discriminate between dropping support of one part of the 
assembly and of another. If the assembly consisted of centrists, a 
veering centrist could benefit more than he loses just by moving closer 
to a certain majority, since a majoritarian method would reward him for 
doing so.


Why should anyone care more about the legislature's proportionality than 
about their decisions?


If the issues are good predictors of decisions, one would care about 
issues for that reason alone.


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Re: [Election-Methods] Determining representativeness of multiwinner methods

[Kristofer Munsterhjelm]

Howard wrote:

Question to Kristofer

do you see the "issues" that you start off with as orthogonal?
i.e. do you see this only working in a world where the issues polled are 
independent.


The simulation I wrote assumes this, since it picks the proportion in 
favor on each issue independently. The simulation-idea itself could work 
with non-orthogonal issues, where one programs the individual issue 
profile generator to select true on an issue with a probability that's 
correlated (or reversely correlated) with the probability of selecting 
true on some other issue.


The concept works with non-orthogonal issues. The implementation doesn't.

also, how it would be decided what issues are polled? even in a 
simulation this is important.


I take a best-case approach here: every voter knows the issue profiles 
of every candidate. That's not how it would happen in reality, but it 
can only make the simulated scores better than in reality, not worse.


Ultimately there are a large election there are wide variety of issues 
and it is impossible for any one candidate or voter to be aware of all 
of them much less have an opinion on them all.


Perhaps there could be a switch where, if turned on, the simulation only 
compares subsets of issue profiles. A noise parameter would determine 
how large a subset is compared. One would have to make assumptions as to 
the correlation of subsets, though - do voters compare on the same 
subsets (what's being advertised, for instance), or do they compare on 
different subsets (their special interests)? In hoping that the results 
can be generalized, picking random subsets may suffice.


I think the generalization you propose below to a range of values is 
probably worth while.
it might then also be able to address not only proportionality on views 
of the legislature, but also proportionality on the thrust of the 
legislature.
i.e. it is all well and good to say you are for some position but if the 
legislature never proposes a new law or regulation around this position 
it is of little use to the people.


How would you treat the case where the assembly doesn't care about a 
certain issue, but the voters do? Range-style "only count those with an 
opinion" would produce an undefined proportion in favor of the issue at 
that point (because of a division by zero). I'm not sure what the best 
approach would be in that case.


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Re: [Election-Methods] Determining representativeness of multiwinner methods

[Steve Eppley]

 have 
been better represented by any 150 people selected at random than by its 
elected "representatives" (of course Vermont uses FPTP winner-take-all 
elections).


That brings me to an interesting issue, which may be off-topic for this 
list..."sortition"...the selection of a legislative body by means of 
modern sampling methods that assure a fully representative body. There is 
an interesting history of the tension between sortition on one hand and 
election on the other (Athenian democracy used both), where sortition was 
seen as the more democratic method, with election being the lesser 
(because candidates with more money or fame had such an advantage over 
average citizens). It is the old question of whether representative 
democracy should be seen as "self-governance," or "consent of the 
governed."


Sorry if this is too off-topic.

Terry Bouricius


----- Original Message ----- 
From: "Steve Eppley" <[EMAIL PROTECTED]>

To: <[EMAIL PROTECTED]>
Sent: Monday, June 23, 2008 11:20 PM
Subject: Re: [Election-Methods] Determining representativeness of 
multiwinner methods



Hi,

I prefer a definition of "representativeness" that differs from
Kristofer's.  To me, the more similar the *decisions* of a legislature
are to the decisions the people themselves would make collectively in a
well-functioning direct democracy, the more representative is the
legislature.

Given my definition, a non-proportional legislature comprised solely of
centrist majoritarian compromise candidates may be very representative,
since the people themselves would reach centrist compromises on the
issues in a well-functioning direct democracy.  It might be more
representative than a proportional legislature, since the proportional
legislator could match her constituents' favorite position on every
issue yet fail to match the way they would compromise.

Why should anyone care more about the legislature's proportionality than
about their decisions?

Regards,
Steve

Kristofer Munsterhjelm wrote:
  

Hello all,

(says the newcomer.)

I think I have found a metric for comparing multiwinner systems, at
least as these pertain to proportional representation, when all votes
are honest.

The advantage of the metric is that, if what it measures is desirable,
it gives an idea of how good the system performs - how representative
it is - and thus its best case performance. In contrast, criterion
failure shows how bad a system can get in the worst case.

The broad idea is this: The most proportional assembly is the one
which reflects the population on all issues. In other words, if a
fraction p of the population is of a certain position on a binary
opinion, it is better (ceteris paribus) for a council to have, of that
opinion, a fraction close to p than one far away from it.

Thus we could make a simulation. First, set that there are n binary
issues. Each of the voters then have an issue profile which consists
of n booleans. Set these randomly with different biases for each issue
(so that, for instance, on the first issue, 70% may hold the "true"
position, while on another, only 23% do).

Counting the proportion that hold the true-position for each issue
gives the popular issue profile. In general, the issue profile of a
certain subset takes the form of n numbers (for n issues), where each
number is equal to the proportion that holds the true-position for the
issue in question.

Then a perfectly representative assembly has an issue profile that is
equal to the issue profile of the people. So now we have a measure of
how well the assembly or council represents the people: the more its
issue profile differs from that of the people, the less representative
it is.

However, this presents a problem. How does one aggregate the
difference on each issue into a single score? Is a one-percent
difference on a single issue better than 1/n percent difference on all
issues? One way to solve this is to just settle on an aggregation
measure (like root-mean-square) and hope the results can be
generalized across; another is to use Pareto-domination as a measure
instead, in saying that councils produced by a method A is better than
councils produced by a method B to the extent that A-councils lie
strictly closer to the population profile than does B. That approach
can give no information on the cases where some issues are closer by
method A and some are closer by B (mutual nondomination).

Putting all of the pieces together, to figure out the scores, a
simulation would do something like this:
- Generate issue vectors for all of the people, and get the
popular issue profile.
- Choose a subset of the people as candidates.
- Generate ballots for each voter of all the candidates.
- For a great number of random assemblies:
- Get the issue profile of this assembly, and calculate
the sim

Re: [Election-Methods] Determining representativeness of multiwinner methods

[Juho]

On Jun 24, 2008, at 15:44 , Terry Bouricius wrote:

That brings me to an interesting issue, which may be off-topic for  
this

list..."sortition"...the selection of a legislative body by means of
modern sampling methods that assure a fully representative body.  
There is
an interesting history of the tension between sortition on one hand  
and
election on the other (Athenian democracy used both), where  
sortition was

seen as the more democratic method, with election being the lesser
(because candidates with more money or fame had such an advantage over
average citizens). It is the old question of whether representative
democracy should be seen as "self-governance," or "consent of the
governed."

Sorry if this is too off-topic.


Very on-topic.

Another reason why sampling could be considered better is that in  
elections people that want to become elected and are ready to fight  
their way through and spend few years doing so are more likely to  
become candidates and finally representatives. That has both positive  
and negative impacts, but in any case this means one kind of bias in  
the representation.


One intermediate approach is to combine the two approaches and first  
nominate a pool of candidates that people want to represent them and  
then elect among these by lottery (or maybe even the other way  
around, first pick random candidates and then arrange an election  
(maybe this method would be less good)). This method has the benefit  
that the representatives are likely to be reasonably competent too,  
and if the nomination process is reasonably open, then also people  
that are competent and willing but that would not fight their way  
through could be elected (nomination by few neighbours might be enough).


Juho






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Re: [Election-Methods] Determining representativeness of multiwinner methods

[Juho]

On Jun 24, 2008, at 0:34 , Kristofer Munsterhjelm wrote:


What do you mean by "methods that allow candidates to form a
tree like structure"? Something like delegable proxy, or just
preference ballots with parties instead of candidates? Or
nontraditional nested democracy (groups elect members to an
assembly - groups of assemblies elect members to a second-
level assembly, onwards up to global issues)?


I was thinking about the traditional party structure and proportional  
methods and how they may provide quite exact proportionality between  
parties but how they can not provide proportionality in any more  
detailed level. In this set-up it is possible to split one party e.g.  
to the green wing and others, and then the green wing could consist  
of radical and moderate greens. A vote to the radical greens (of this  
party) would be a vote also to the green wing in general and to the  
party in general.


The point was that now you could have even the binary decisions  
"stacked" in the party hierarchy (at least if the tree would be a  
binary tree). In this model it would also make a difference if you  
vote the green wing of the socialists or the socialist wing of the  
greens (order of priority).


Juho









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Re: [Election-Methods] Determining representativeness of multiwinner methods

[Juho]

One reason why districts have been kept is that if there were no  
districts then voters would have some tendency to vote for the  
capital area candidates that have typically better access to TV etc.  
There are typically also more popular figures in general at the  
capital region. The risk is thus that the distribution (without  
districts) would not be a random distribution but would favour the  
central regions.


Juho



On Jun 24, 2008, at 6:18 , Howard wrote:


>One more observation. Nowadays many methods actually try to meet two
>kind of proportionality requirements, political/ideological
>proportionality (typically based on the party structure) and regional
>proportionality (typically implemented by mandating all to vote at
>their own home district for the local candidates there). These
>scenarios may be out of the scope of the proposed metric because of
>the mandated nature of the regional representation, but regional
>proportionality is one interesting and maybe also measurable
>criterion for proportionality.

I feel that the need to look for and design a system around  
geographic proportionality is a waist of time (except as a sales  
pitch).
I believe that geographic proportionality would naturally come out  
of a truly proportional system (if it was important to the voters)  
where the proportionality of all issues important to the voters are  
taken into account.
As an example, if a large number of voter care about the number of  
pot holes on bank street it is likely that many of these voters  
live or work near bank street. and thus would elect at least some  
politicians that live near bank street.


Geographic location is a hold over from the days when communication  
was limited to a local area is largely irrelevant today.


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list info




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Re: [Election-Methods] Determining representativeness of multiwinner methods

[Abd ul-Rahman Lomax]

At 11:18 PM 6/23/2008, Howard wrote:
I feel that the need to look for and design a system around 
geographic proportionality is a waist of time (except as a sales pitch).
I believe that geographic proportionality would naturally come out 
of a truly proportional system (if it was important to the voters) 
where the proportionality of all issues important to the voters are 
taken into account.
As an example, if a large number of voter care about the number of 
pot holes on bank street it is likely that many of these voters live 
or work near bank street. and thus would elect at least some 
politicians that live near bank street.


Geographic location is a hold over from the days when communication 
was limited to a local area is largely irrelevant today.


I agree. It's quite possible to design a system that is, for most 
voters, geographically proportional, but, for a few, is politically 
proportional, and that is, again for most voters, both geographically 
and politically proportional.


I don't see any sign that he realized the possibilities, but Charles 
Dodgson first proposed the key concept in about 1884, as a tweak to 
Single Transferable Vote.


He suggested that, in lieu of exhausting a ballot with a bullet vote, 
the candidate receiving the vote would be able to "spend" the ballot 
"as if it were the candidate's personal property." This is the same 
metaphor used by Warren Smith in his Asset Voting publication of 
(2004?). The method was also called Candidate Proxy by Mike Ossipoff 
in a post to this list before 2000. It is related to Delegable Proxy, 
my own invention, independently invented by others as well; but the 
Asset form is, as proposed, for multiwinner elections, used to create 
a peer assembly, which has certain functional advantages over pure 
proxy systems for public use.


Consider the simplest Asset system: voters vote for one candidate, 
and that candidate becomes their proxy for the purpose of determining 
representation. If the candidate gains a quota of votes, the 
candidate is automatically elected (or may, at will, elect someone 
else), and any leftover votes are then disposable for the purpose of 
creating more seats when combined with the votes held by other candidates.


What prior writers did not seem to realize was that such a system 
would gravitate toward the voter voting for the single person they 
most trust, both to function in the assembly themselves, should that 
occur, or for the purpose of choosing who will represent the voter, 
ultimately. I would expect direct election in the "primary" to become 
increasingly rare, for there will arise very good reasons to vote for 
someone you personally know and can reliably communicate with. This 
person, who is a public voter, I call an "elector," will be known to 
the holder of the seat as the one who directed votes to him or her. 
Thus Asset will set up filtered communication channels between voters 
and seats, thus resolving an old problem with deliberative and 
representative democracy, the problem of scale and communications 
breakdown resulting from it.


Now, an elector will have a list of precincts from which his or her 
votes came. The elector may have a good idea who these people are, 
but that isn't verifiable, votes in the primary remain secret. 
However, the elector *may* choose to assign votes, in cooperation 
with other electors, so that seats have a maximized relationship with 
the precincts from which the votes came. Thus there may be, for a 
large population city, a number of seats representing relatively 
common different political positions, whereas some seats for small 
minority political positions may cover an entire state, and a few 
seats may be a kind of catchall seat, likewise drawn from the whole 
state, being representatives who have promised, perhaps, to represent 
diverse positions in the Assembly. "Represent" here means to ensure 
that positions are represented in debate. I'd presume that the seat 
would vote the conscience of the seat, which *might* represent, for 
example, "far left" or "far right," though, in reality, political 
positions are only grossly represented by such categories.


("Libertarian" for example, is in some ways "right," and in some ways 
"left." There are, in fact, different axes of polarity.)


What Asset Voting does is to increase, to maximize, "chosen 
representation" that doesn't represent the majoritarian compromise; 
such majoritarian compromises, when involved in the creation of 
seats, tend to take place on grossly oversimplified levels. The 
result can be serious loss of representation.


Asset Voting actually would make possible something very close to 
direct democracy, without the known problems. It's hybrid 
direct/representative democracy, all the more so if electors, who are 
now public voters (like seats are), have the right to vote in 
Assembly decisions. Not participate in deliberation: they would not 
have the right to enter motions or debate on th

Re: [Election-Methods] Determining representativeness of multiwinner methods

[Terry Bouricius]

Steve,

I can speak first-hand about the reason to have a legislature that is as 
broadly diverse as the population, rather than made up of centrist 
majoritarians... (I served ten years as a third party member of the 
Vermont House of Representatives in the USA).

Society benefits from robust debate, and the consideration of ideas and 
perspectives beyond what is currently the majority view. The quality of 
decisions a legislature makes will be better if these alternate views are 
part of the in-legislature debate. The public as a whole does not engage 
in robust debate that may result in the evolution of current majority 
views (and our mass media certainly don't help), and new issues come up 
that were not issues during the election, so no majoritarian selection 
resulted from that election.

If a majority of residents in a society happen to be home-owners with 
health insurance, and decent jobs, would a legislature made up of 100% 
such people be more or less likely to tackle the issues of renters, 
without insurance and no jobs? And if they did tackle those issues, would 
they become sensitized to the perspective of those on the short end of the 
stick? When I served in the Vermont House, out of 150 members, there was 
only a single renter, and renters' rights were completely ignored (though 
30% of Vermonters are renters). I often observed that Vermont would have 
been better represented by any 150 people selected at random than by its 
elected "representatives" (of course Vermont uses FPTP winner-take-all 
elections).

That brings me to an interesting issue, which may be off-topic for this 
list..."sortition"...the selection of a legislative body by means of 
modern sampling methods that assure a fully representative body. There is 
an interesting history of the tension between sortition on one hand and 
election on the other (Athenian democracy used both), where sortition was 
seen as the more democratic method, with election being the lesser 
(because candidates with more money or fame had such an advantage over 
average citizens). It is the old question of whether representative 
democracy should be seen as "self-governance," or "consent of the 
governed."

Sorry if this is too off-topic.

Terry Bouricius


- Original Message - 
From: "Steve Eppley" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Monday, June 23, 2008 11:20 PM
Subject: Re: [Election-Methods] Determining representativeness of 
multiwinner methods


Hi,

I prefer a definition of "representativeness" that differs from
Kristofer's.  To me, the more similar the *decisions* of a legislature
are to the decisions the people themselves would make collectively in a
well-functioning direct democracy, the more representative is the
legislature.

Given my definition, a non-proportional legislature comprised solely of
centrist majoritarian compromise candidates may be very representative,
since the people themselves would reach centrist compromises on the
issues in a well-functioning direct democracy.  It might be more
representative than a proportional legislature, since the proportional
legislator could match her constituents' favorite position on every
issue yet fail to match the way they would compromise.

Why should anyone care more about the legislature's proportionality than
about their decisions?

Regards,
Steve

Kristofer Munsterhjelm wrote:
> Hello all,
>
> (says the newcomer.)
>
> I think I have found a metric for comparing multiwinner systems, at
> least as these pertain to proportional representation, when all votes
> are honest.
>
> The advantage of the metric is that, if what it measures is desirable,
> it gives an idea of how good the system performs - how representative
> it is - and thus its best case performance. In contrast, criterion
> failure shows how bad a system can get in the worst case.
>
> The broad idea is this: The most proportional assembly is the one
> which reflects the population on all issues. In other words, if a
> fraction p of the population is of a certain position on a binary
> opinion, it is better (ceteris paribus) for a council to have, of that
> opinion, a fraction close to p than one far away from it.
>
> Thus we could make a simulation. First, set that there are n binary
> issues. Each of the voters then have an issue profile which consists
> of n booleans. Set these randomly with different biases for each issue
> (so that, for instance, on the first issue, 70% may hold the "true"
> position, while on another, only 23% do).
>
> Counting the proportion that hold the true-position for each issue
> gives the popular issue profile. In general, the issue profile of a
> certain subset takes the form of n numbers (for n issues), where each
> number is equal to the

Re: [Election-Methods] Determining representativeness of multiwinner methods

[James Gilmour]

Howard > Sent: Tuesday, June 24, 2008 4:18 AM
> I feel that the need to look for and design a system around geographic 
> proportionality is a waist of time (except as a sales pitch).
> I believe that geographic proportionality would naturally come out of a 
> truly proportional system (if it was important to the voters) where the 
> proportionality of all issues important to the voters are taken into account.
> As an example, if a large number of voter care about the number of pot 
> holes on bank street it is likely that many of these voters live or work 
> near bank street. and thus would elect at least some politicians that 
> live near bank street.

And that is what you would get with STV-PR, so why the need to re-invent this 
particular wheel?

James Gilmour

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Re: [Election-Methods] Determining representativeness of multiwinner methods

[Steve Eppley]

Hi,

I prefer a definition of "representativeness" that differs from 
Kristofer's.  To me, the more similar the *decisions* of a legislature 
are to the decisions the people themselves would make collectively in a 
well-functioning direct democracy, the more representative is the 
legislature. 

Given my definition, a non-proportional legislature comprised solely of 
centrist majoritarian compromise candidates may be very representative, 
since the people themselves would reach centrist compromises on the 
issues in a well-functioning direct democracy.  It might be more 
representative than a proportional legislature, since the proportional 
legislator could match her constituents' favorite position on every 
issue yet fail to match the way they would compromise.


Why should anyone care more about the legislature's proportionality than 
about their decisions?


Regards,
Steve

Kristofer Munsterhjelm wrote:

Hello all,

(says the newcomer.)

I think I have found a metric for comparing multiwinner systems, at 
least as these pertain to proportional representation, when all votes 
are honest.


The advantage of the metric is that, if what it measures is desirable, 
it gives an idea of how good the system performs - how representative 
it is - and thus its best case performance. In contrast, criterion 
failure shows how bad a system can get in the worst case.


The broad idea is this: The most proportional assembly is the one 
which reflects the population on all issues. In other words, if a 
fraction p of the population is of a certain position on a binary 
opinion, it is better (ceteris paribus) for a council to have, of that 
opinion, a fraction close to p than one far away from it.


Thus we could make a simulation. First, set that there are n binary 
issues. Each of the voters then have an issue profile which consists 
of n booleans. Set these randomly with different biases for each issue 
(so that, for instance, on the first issue, 70% may hold the "true" 
position, while on another, only 23% do).


Counting the proportion that hold the true-position for each issue 
gives the popular issue profile. In general, the issue profile of a 
certain subset takes the form of n numbers (for n issues), where each 
number is equal to the proportion that holds the true-position for the 
issue in question.


Then a perfectly representative assembly has an issue profile that is 
equal to the issue profile of the people. So now we have a measure of 
how well the assembly or council represents the people: the more its 
issue profile differs from that of the people, the less representative 
it is.


However, this presents a problem. How does one aggregate the 
difference on each issue into a single score? Is a one-percent 
difference on a single issue better than 1/n percent difference on all 
issues? One way to solve this is to just settle on an aggregation 
measure (like root-mean-square) and hope the results can be 
generalized across; another is to use Pareto-domination as a measure 
instead, in saying that councils produced by a method A is better than 
councils produced by a method B to the extent that A-councils lie 
strictly closer to the population profile than does B. That approach 
can give no information on the cases where some issues are closer by 
method A and some are closer by B (mutual nondomination).


Putting all of the pieces together, to figure out the scores, a 
simulation would do something like this:

- Generate issue vectors for all of the people, and get the
popular issue profile.
- Choose a subset of the people as candidates.
- Generate ballots for each voter of all the candidates.
- For a great number of random assemblies:
- Get the issue profile of this assembly, and calculate
the similarity measure for that with regards to
the popular issue profile.
- If the similarity measure is more similar or less
similar than any random assembly we've seen so
far, update the worst (respectively best)
record.

- For each multiwinner election system:
- Feed the ballots into the system.
- Get the issue profile of the elected assembly, and
calculate the similarity measure for that with
regards to the popular issue profile.
- Normalize the similarity measure with regards to the
worst and best random councils.
- Add the normalized similarity measure to that system's
runningtotal.

To be robust, it would do this a lot of times with various population 
sizes, council sizes, and issue numbers (n). With a similarity 
measure, 0 would be perfect (impossible most of the time), and 1 (or 
infinity, depending on the measure) be the worst possible.


The only thing remaining is to find out how to generate ballots for 
each voter. A reasonable assumption is that voters are going to prefer 
the c

Re: [Election-Methods] Determining representativeness of multiwinner methods

[Howard]

Question to Kristofer

do you see the "issues" that you start off with as orthogonal?
i.e. do you see this only working in a world where the issues polled are 
independent.


also, how it would be decided what issues are polled? even in a 
simulation this is important.


Ultimately there are a large election there are wide variety of issues 
and it is impossible for any one candidate or voter to be aware of all 
of them much less have an opinion on them all.


I think the generalization you propose below to a range of values is 
probably worth while.
it might then also be able to address not only proportionality on views 
of the legislature, but also proportionality on the thrust of the 
legislature.
i.e. it is all well and good to say you are for some position but if the 
legislature never proposes a new law or regulation around this position 
it is of little use to the people.


Kristofer Munsterhjelm wrote:

How do see the role of parties here? Do you use e.g. a binary
decision between left wing and right wing? Or maybe support or no
support to party P? Or maybe you don't measure party support at all
but just separate binary questions.


Parties aren't explicitly included. Implicitly and ideally, a party would 
be a vector quantization center in issue-space, which is to say, a 
provider of a popular combined platform. In reality, parties aren't 
perfect and face distortions both because of their own nature and 
because of the dynamics of the environment in which they exist.


The latter should be well known to list readers - one dynamics 
example is that of Duverger's law. Another would be the median voter

theorem for what election method is being used. I think Warren Smith
argued that any preferential election method would produce a 2:3:2 
ratio on a one-dimensional political spectrum - one major party and two

lesser ones - but I can't verify that.

But to get back to the question: The binary issues are issues. Parties 
present issue-bundles and therefore don't relate to the model. As such, 
the model is more simple than reality, but not enough to invalidate it.


In an approval-type scenario, some of the binary issues could be 
support/no support (as you say) above pure issue-agreement, but since 
Hamming distance measures all differences equally, that means party 
loyalty is the same for all parties with regard to all other parties. It's 
better, I think, to just leave the parties as issue-bundles.


Any opinions on how to treat different levels of importance of 
different criteria to the voter (and to the candidates)?


There are two questions here. I'm not sure which you mean, so I'll 
answer them both.


The first is how much inter-issue differences matter in contrast to 
intra-issue differences. To take an individual example, consider a 
picky people that isn't bothered if the assembly is slightly disproportionate 
on any issue, but finds the assembly unworthy if it errs very much 
on a single issue. This is the matter which changes based on what
error measure is used. I don't know which error measure is closest 
to reality, so in keeping with the simple nature of the model, I used
RMSE. One could argue in favor of, and use, absolute error, the 
Sainte-Lague index, Gini, or many others.


The second is of how to handle the case where some issues are
unimportant to a voter. A simple extension to the binary issue profiles 
would be a ternary profile: 1 for agree, -1 for disagree, and 0 for no 
opinion. Then one could count the discrepancy of assembly and 
people on each issue, taking only into account those who have an 
opinion (in either assembly or among the people), kind of like the 
"no opinion" score in Range. But what does it mean for an assembly 
to have no opinion on a single issue? Directly speaking, it means that 
they don't consider the issue, it takes no part in the deliberation. But 
how does one compare the "error" of the assembly with regards to 
the people in that case? I don't have an answer to that, so I didn't 
implement it. (Perhaps it'd count maximally, since both those in 
favor and against would be unhappy? Perhaps it'd count as if it was 
50%, assuming the assembly members would make decisions that

impact this issue randomly, half the time in support by coincidence,
and half the time against it by coincidence...) 


How about traditional party list based multi-winner methods? I find
methods that allow candidates to form a tree like structure (instead
of the typical flat party structure) where different branches reflect
different opinions on different key questions interesting from this
proportionality point of view.


Party list needs parties, and there's also the question of open versus 
closed list. Both open and closed list have to have a list in the first 
place, and the nature of that list is complex, often shaped by the 
interplay of power within the party.


But perhaps parties could be added by having a "preround" where
one runs k-means clustering (vector quantiz

Re: [Election-Methods] Determining representativeness of multiwinner methods

[Howard]

>One more observation. Nowadays many methods actually try to meet two
>kind of proportionality requirements, political/ideological
>proportionality (typically based on the party structure) and regional
>proportionality (typically implemented by mandating all to vote at
>their own home district for the local candidates there). These
>scenarios may be out of the scope of the proposed metric because of
>the mandated nature of the regional representation, but regional
>proportionality is one interesting and maybe also measurable
>criterion for proportionality.

I feel that the need to look for and design a system around geographic 
proportionality is a waist of time (except as a sales pitch).
I believe that geographic proportionality would naturally come out of a 
truly proportional system (if it was important to the voters) where the 
proportionality of all issues important to the voters are taken into 
account.
As an example, if a large number of voter care about the number of pot 
holes on bank street it is likely that many of these voters live or work 
near bank street. and thus would elect at least some politicians that 
live near bank street.


Geographic location is a hold over from the days when communication was 
limited to a local area is largely irrelevant today.


Election-Methods mailing list - see http://electorama.com/em for list info

Re: [Election-Methods] Determining representativeness of multiwinner methods

[Kristofer Munsterhjelm]

>How do see the role of parties here? Do you use e.g. a binary
>decision between left wing and right wing? Or maybe support or no
>support to party P? Or maybe you don't measure party support at all
>but just separate binary questions.

Parties aren't explicitly included. Implicitly and ideally, a party would 
be a vector quantization center in issue-space, which is to say, a 
provider of a popular combined platform. In reality, parties aren't 
perfect and face distortions both because of their own nature and 
because of the dynamics of the environment in which they exist.

The latter should be well known to list readers - one dynamics 
example is that of Duverger's law. Another would be the median voter
theorem for what election method is being used. I think Warren Smith
argued that any preferential election method would produce a 2:3:2 
ratio on a one-dimensional political spectrum - one major party and two
lesser ones - but I can't verify that.

But to get back to the question: The binary issues are issues. Parties 
present issue-bundles and therefore don't relate to the model. As such, 
the model is more simple than reality, but not enough to invalidate it.

In an approval-type scenario, some of the binary issues could be 
support/no support (as you say) above pure issue-agreement, but since 
Hamming distance measures all differences equally, that means party 
loyalty is the same for all parties with regard to all other parties. It's 
better, I think, to just leave the parties as issue-bundles.

>Any opinions on how to treat different levels of importance of 
>different criteria to the voter (and to the candidates)?

There are two questions here. I'm not sure which you mean, so I'll 
answer them both.

The first is how much inter-issue differences matter in contrast to 
intra-issue differences. To take an individual example, consider a 
picky people that isn't bothered if the assembly is slightly disproportionate 
on any issue, but finds the assembly unworthy if it errs very much 
on a single issue. This is the matter which changes based on what
error measure is used. I don't know which error measure is closest 
to reality, so in keeping with the simple nature of the model, I used
RMSE. One could argue in favor of, and use, absolute error, the 
Sainte-Lague index, Gini, or many others.

The second is of how to handle the case where some issues are
unimportant to a voter. A simple extension to the binary issue profiles 
would be a ternary profile: 1 for agree, -1 for disagree, and 0 for no 
opinion. Then one could count the discrepancy of assembly and 
people on each issue, taking only into account those who have an 
opinion (in either assembly or among the people), kind of like the 
"no opinion" score in Range. But what does it mean for an assembly 
to have no opinion on a single issue? Directly speaking, it means that 
they don't consider the issue, it takes no part in the deliberation. But 
how does one compare the "error" of the assembly with regards to 
the people in that case? I don't have an answer to that, so I didn't 
implement it. (Perhaps it'd count maximally, since both those in 
favor and against would be unhappy? Perhaps it'd count as if it was 
50%, assuming the assembly members would make decisions that
impact this issue randomly, half the time in support by coincidence,
and half the time against it by coincidence...) 

>How about traditional party list based multi-winner methods? I find
>methods that allow candidates to form a tree like structure (instead
>of the typical flat party structure) where different branches reflect
>different opinions on different key questions interesting from this
>proportionality point of view.

Party list needs parties, and there's also the question of open versus 
closed list. Both open and closed list have to have a list in the first 
place, and the nature of that list is complex, often shaped by the 
interplay of power within the party.

But perhaps parties could be added by having a "preround" where
one runs k-means clustering (vector quantization codebook 
generation) to find the best party platforms, and then create lists 
based on distance from that platform, where voters vote on the 
list according to the platform's distance from their own views. 
That would be complex, but yes, interesting. Such a party model 
would also support simulations of "voting above the line" and MMP,
but again I'm not sure whether the results would be close enough
to reality to be any good.

What do you mean by "methods that allow candidates to form a 
tree like structure"? Something like delegable proxy, or just 
preference ballots with parties instead of candidates? Or 
nontraditional nested democracy (groups elect members to an 
assembly - groups of assemblies elect members to a second-
level assembly, onwards up to global issues)?

>One more observation. Nowadays many methods actually try to meet two
>kind of proportionality requirements, political/ideological
>propor

Re: [Election-Methods] Determining representativeness of multiwinner methods

[Kristofer Munsterhjelm]

Hi again,

>- When you presents simulation results, is the best method the one with
>greatest or smallest score? IRV is considered the best majoritarian method
>but its score is between Nauru-Borda and Plurality

Oops, that was an error on my part. Since the scores are normalized 
root-mean-square error measurements between the assembly and public issue 
profiles, lower is better. 

>- In some countries, particularly federative ones, many issues are highly
>correlated to subnational territories. Because of this, in real scenarios
>majoritarian methods are a bit more proportional than in simulations where
>all political factions are equally spread within all the country. Had you
>considered some correlation with distribution of issue vectors and electoral
>districts?

Since the simulation runs a given election method only once per evaluation, 
it elects the entire assembly from a single set of ballots, which means it 
doesn't know anything about regionality. It shouldn't be too hard to implement 
district votes: simply have q districts and q mini-elections for their parts of 
the assembly. 

In the case of a nationwide vote (single election to entire assembly) with 
correlation of issue vectors and electoral districts, I don't think the results 
would differ much, since the largest district or group of districts would trump
the other districts.

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Re: [Election-Methods] Determining representativeness of multiwinner methods

[Diego Santos]

Hi, Kristofer, your idea seems interesting, but I couldn't understand some
points:

- When you presents simulation results, is the best method the one with
greatest or smallest score? IRV is considered the best majoritarian method
but its score is between Nauru-Borda and Plurality

- In some countries, particularly federative ones, many issues are highly
correlated to subnational territories. Because of this, in real scenarios
majoritarian methods are a bit more proportional than in simulations where
all political factions are equally spread within all the country. Had you
considered some correlation with distribution of issue vectors and electoral
districts?

Diego Santos

2008/6/20 Kristofer Munsterhjelm <[EMAIL PROTECTED]>:

> Hello all,
>
> (says the newcomer.)
>
> I think I have found a metric for comparing multiwinner systems, at least
> as these pertain to proportional representation, when all votes are honest.
>
> The advantage of the metric is that, if what it measures is desirable, it
> gives an idea of how good the system performs - how representative it is -
> and thus its best case performance. In contrast, criterion failure shows how
> bad a system can get in the worst case.
>
> The broad idea is this: The most proportional assembly is the one which
> reflects the population on all issues. In other words, if a fraction p of
> the population is of a certain position on a binary opinion, it is better
> (ceteris paribus) for a council to have, of that opinion, a fraction close
> to p than one far away from it.
>
> Thus we could make a simulation. First, set that there are n binary issues.
> Each of the voters then have an issue profile which consists of n booleans.
> Set these randomly with different biases for each issue (so that, for
> instance, on the first issue, 70% may hold the "true" position, while on
> another, only 23% do).
>
> Counting the proportion that hold the true-position for each issue gives
> the popular issue profile. In general, the issue profile of a certain subset
> takes the form of n numbers (for n issues), where each number is equal to
> the proportion that holds the true-position for the issue in question.
>
> Then a perfectly representative assembly has an issue profile that is equal
> to the issue profile of the people. So now we have a measure of how well the
> assembly or council represents the people: the more its issue profile
> differs from that of the people, the less representative it is.
>
> However, this presents a problem. How does one aggregate the difference on
> each issue into a single score? Is a one-percent difference on a single
> issue better than 1/n percent difference on all issues? One way to solve
> this is to just settle on an aggregation measure (like root-mean-square) and
> hope the results can be generalized across; another is to use
> Pareto-domination as a measure instead, in saying that councils produced by
> a method A is better than councils produced by a method B to the extent that
> A-councils lie strictly closer to the population profile than does B. That
> approach can give no information on the cases where some issues are closer
> by method A and some are closer by B (mutual nondomination).
>
> Putting all of the pieces together, to figure out the scores, a simulation
> would do something like this:
>- Generate issue vectors for all of the people, and get the
>popular issue profile.
>- Choose a subset of the people as candidates.
>- Generate ballots for each voter of all the candidates.
>- For a great number of random assemblies:
>- Get the issue profile of this assembly, and calculate
>the similarity measure for that with regards to
>the popular issue profile.
>- If the similarity measure is more similar or less
>similar than any random assembly we've seen so
>far, update the worst (respectively best)
>record.
>
>- For each multiwinner election system:
>- Feed the ballots into the system.
>- Get the issue profile of the elected assembly, and
>calculate the similarity measure for that with
>regards to the popular issue profile.
>- Normalize the similarity measure with regards to the
>worst and best random councils.
>- Add the normalized similarity measure to that system's
>running total.
>
> To be robust, it would do this a lot of times with various population
> sizes, council sizes, and issue numbers (n). With a similarity measure, 0
> would be perfect (impossible most of the time), and 1 (or infinity,
> depending on the measure) be the worst possible.
>
> The only thing remaining is to find out how to generate ballots for each
> voter. A reasonable assumption is that v

Re: [Election-Methods] Determining representativeness of multiwinner methods

[Juho]

On Jun 21, 2008, at 1:09 , Kristofer Munsterhjelm wrote:


Hello all,

(says the newcomer.)


Welcome.

First, set that there are n binary issues. Each of the voters then  
have an issue profile which consists of n booleans.


How do see the role of parties here? Do you use e.g. a binary  
decision between left wing and right wing? Or maybe support or no  
support to party P? Or maybe you don't measure party support at all  
but just separate binary questions.


However, this presents a problem. How does one aggregate the  
difference on each issue into a single score? Is a one-percent  
difference on a single issue better than 1/n percent difference on  
all issues? One way to solve this is to just settle on an  
aggregation measure (like root-mean-square) and hope the results  
can be generalized across;


Any opinions on how to treat different levels of importance of  
different criteria to the voter (and to the candidates)?


Best of all were the "proper" methods implemented: STV (with  
Senatorial rules) and QLTD-PR, which uses Woodall's QLTD instead of  
IRV as its basis: it adds fractional votes until someone gets above  
the quota, then reweights the voters who contributed to that one,  
basing the weighting on the candidate's surplus.


How about traditional party list based multi-winner methods? I find  
methods that allow candidates to form a tree like structure (instead  
of the typical flat party structure) where different branches reflect  
different opinions on different key questions interesting from this  
proportionality point of view.



One more observation. Nowadays many methods actually try to meet two  
kind of proportionality requirements, political/ideological  
proportionality (typically based on the party structure) and regional  
proportionality (typically implemented by mandating all to vote at  
their own home district for the local candidates there). These  
scenarios may be out of the scope of the proposed metric because of  
the mandated nature of the regional representation, but regional  
proportionality is one interesting and maybe also measurable  
criterion for proportionality.


Sorry about being "speculation oriented only" instead of making some  
more concrete proposals/claims :-).


Juho







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