Matthew Welland | 1 May 07:21 2006

Looking for a little voting insight...

I am putting together a web site which will, in addition to some other things, 
illustrate different voting methods. I have approval and plurality voting 
done and was starting to look at Condorcet voting and a couple of questions 
came up. BTW I will probably use the rubyvote code as a starting point.

Questions:

1. Rubyvote has pure condorcet and cloneproof schwartz sequential available. I 
want to keep things simple. Does it matter which method I choose? Is there a 
cpu load difference?

2. Votes will be updated on the fly - does this distort or invalidate the 
Condorcet method in any way? I.e. the voter can see the current results and 
use that information in choosing their vote(s).

This is really only for fun but I am curious to hear whatever opinions people 
have.

By the way it has been interesting to play with approval vs plurality voting 
and to notice my own response.  Having both available now leaves me quite 
annoyed when faced with a plurality only vote. However I'm noticing in some 
approval voting scenarios I really wish I could articulate a hierarchy of 
preference.

Matt
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Simmons, Forest | 1 May 21:29 2006

Re: Proportional Condorcet Voting

Antonio Oneala lamented that proportional Condorcet methods tend to be intractable.  This is because if
there are N candidates from which to choose K winners, there are  C(N,K)=N!/(K!*(N-K)!) subsets to be
compared pairwise, for a total of  C(C(N,K),2) pairwise comparisons of subsets.

However, suppose that instead of comparing all C(N,K) of the K candidate subsets, we just compare all
submitted proposals, including those sets that would be elected by STV under various rules (Droop Quota,
etc.).  There might be ten thousand such proposals. But that would only require  C(10000, 2) = 49995000
comparisons, a few seconds of CPU time on a second rate computer.

Forest
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Paul Kislanko | 1 May 21:51 2006
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Re: Proportional Condorcet Voting

>From a theoretical standpoint, this may look intractactable, but for any
finite N,K the problem is solvable in polynomial time in a manner that
depends only upon N, K, and the number of voters. From a practical
standpoint, the calculation is not difficult for up to N,K=293 by
demonstation (I do that daily in my report of records vs common opponents
for division 1 american college baseball teams on a Dell laptop. It takes a
few minutes to run only because it is also producing 294 web pages, and all
that I/O slows it down).

  _____  

From: election-methods-bounces <at> electorama.com
[mailto:election-methods-bounces <at> electorama.com] On Behalf Of Simmons,
Forest
Sent: Monday, May 01, 2006 2:29 PM
To: election-methods <at> electorama.com
Subject: Re: [EM] Proportional Condorcet Voting

Antonio Oneala lamented that proportional Condorcet methods tend to be
intractable.  This is because if there are N candidates from which to choose
K winners, there are  C(N,K)=N!/(K!*(N-K)!) subsets to be compared pairwise,
for a total of  C(C(N,K),2) pairwise comparisons of subsets.

However, suppose that instead of comparing all C(N,K) of the K candidate
subsets, we just compare all submitted proposals, including those sets that
would be elected by STV under various rules (Droop Quota, etc.).  There
might be ten thousand such proposals. But that would only require  C(10000,
2) = 49995000 comparisons, a few seconds of CPU time on a second rate
computer.

(Continue reading)

Abd ul-Rahman Lomax | 1 May 21:56 2006

Re: Proportional Condorcet Voting

At 03:29 PM 5/1/2006, Simmons, Forest wrote:
>However, suppose that instead of comparing all C(N,K) of the K 
>candidate subsets, we just compare all submitted proposals, 
>including those sets that would be elected by STV under various 
>rules (Droop Quota, etc.).  There might be ten thousand such 
>proposals. But that would only require  C(10000, 2) = 49995000 
>comparisons, a few seconds of CPU time on a second rate computer.

Yes, the objections to Condorcet proposals based on computational 
intractability are pretty silly, based only on a theoretical idea 
that all possible rankings will exist in the ballot population. But 
the ballot population is a limited set, with almost certainly a high 
degree of reduncancy. Systems that require all voters to rank all 
candidates make it worse, to be sure, but even that will have a lot 
of redundancy in it.

However, I'm not sure why one needs Condorcet Voting for PR.

Asset Voting should create a very accurate, non-party-list PR 
assembly rather directly. Asset Voting, though, requires a 
deliberative or bargaining step, which is a rather new idea, as the 
election method itself does not suffice, without candidate action 
after the election, to determine all the winners (it only determines 
those who gain the quota in the initial balloting).

However, if Published Rankings are provided by candidates prior to 
the poll and are used to automatically reassign votes, it might be 
possible to have direct winner determination.

All excess or unused votes would be subject to reassignment. There 
(Continue reading)

Markus Schulze | 1 May 11:14 2006
Picon

Re: Looking for a little voting insight...

Dear Matthew Welland,

you wrote (30 April 2006):

> Rubyvote has pure condorcet and cloneproof schwartz
> sequential available. 

At Wikipedia, "pure Condorcet" is called "Minimax
Condorcet":

http://en.wikipedia.org/wiki/Minimax_Condorcet

At Wikipedia, "cloneproof Schwartz sequential dropping"
is called "Schulze method":

http://en.wikipedia.org/wiki/Schulze_method

******************************************

You wrote (30 April 2006):

> I want to keep things simple.
> Does it matter which method I choose?

Yes, it does matter. Minimax and Schulze are different
methods.

Example:

   3   A > B > D > C
(Continue reading)

Antonio Oneala | 1 May 23:52 2006
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Re: Proportional Condorcet Voting



"Simmons, Forest" <simmonfo <at> up.edu> wrote:
Antonio Oneala lamented that proportional Condorcet methods tend to be intractable. This is because if there are N candidates from which to choose K winners, there are C(N,K)=N!/(K!*(N-K)!) subsets to be compared pairwise, for a total of C(C(N,K),2) pairwise comparisons of subsets.

However, suppose that instead of comparing all C(N,K) of the K candidate subsets, we just compare all submitted proposals, including those sets that would be elected by STV under various rules (Droop Quota, etc.). There might be ten thousand such proposals. But that would only require C(10000, 2) = 49995000 comparisons, a few seconds of CPU time on a second rate computer.

Forest
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After reading up on the CPO-STV method, the mehtod I've just come up with actually seems to be simpler.  CPO-STV involves a complicated comparison of outcomes and the transferring of all votes to certain areas in each of these outcomes; mine only involves a complicated comparison of outcomes, giving a score to each outcome based on how many candidates are preferred more than the other outcome in the score according to the D'Hondt or Webster quotas, adding all of these up, declaring a pairwise winner, and then comparing all pairwise competitions to see which outcome won the most pairwise proportional competitions.  Wait.  That's more steps.  Oh well.  It is, at least, monotonic, and the direct application of the quota seems better than the use of the transferrable vote as a quota.

As for the other reply to my thread, I'm not a fan of asset either.  I have a feeling it will enforce party structures, as a candidate inside of a party is far more likely to give it to another candidate in the party than to and independent.  It also has the problem that a lot of systems do; it doesn't increase the amount of voting power per each voter to accomodate more candidates.  Therefore, it will lead probably lead to factionalization, or at least cannot handle more parties than there are seats.  I've come up with a formula, where V is the amount of voting power per a voter, and C is the amount of candidates.  The formula is, easily enough, C = V.  If the voting system keeps V stable as C increases, then vote-splitting will result.  If it adds more C then V as C increases, then teaming will result.  For instance, Plurality keeps V stable as C increases (as you always have only one vote), approval and Condercet increase V in proportion to C, and Borda increases V at a faster rate than C.  Asset seems to fall into the plurality situation, although it is a bit less vulnerable.  However, a moderate who has 20 votes as compared to the polar candidate thirty votes doesn't have much leeway to convince the other guys to send votes to him, his only choice would probably be to send his votes to the lesser of two evils.


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Abd ul-Rahman Lomax | 2 May 01:28 2006

Re: Proportional Condorcet Voting

At 05:52 PM 5/1/2006, Antonio Oneala wrote:

>As for the other reply to my thread, I'm not a fan of asset 
>either.  I have a feeling it will enforce party structures, as a 
>candidate inside of a party is far more likely to give it to another 
>candidate in the party than to and independent.

Sure. And a voter is more likely to vote for candidates who belong to 
the voter's favorite party. But the question is whether or not Asset 
would "enforce" such structures and strictures, or would it make it 
possible to move beyond them. Since Asset systems (Asset as 
effectively free proxy voting or Published List) give the power 
directly to the candidates, I strongly doubt that it will increase 
party power and factionalism. Rather, when a candidate has excess 
votes, that candidate will assign them where he or she sees will best 
advance his or her interests, which are a proxy for the interests of 
the voters who chose that candidate. If the candidate wants to 
increase his or her party's power, that's what will be done, I'd presume.

But Asset makes it possible for candidates to run *without* party 
affiliation. Normally, under every other voting system, if the 
candidate can't make the quota, that's just plain suicide for the 
voters and the candidate. Voting for the candidate effectively takes 
the votes out of the system, making them irrelevant. But with Asset, 
such votes aren't lost. They will normally be recast to create 
winners at least friendly to the interests of the transferring candidates.

What I'd see Asset as likely doing is increasing the *personal* power 
of candidates as distinct from parties. But at the same time, the 
number of active and significant candidates would likely increase greatly.

>  It also has the problem that a lot of systems do; it doesn't 
> increase the amount of voting power per each voter to accomodate 
> more candidates.

I really don't understand this. Each voter has divisible voting power 
in FAAV and in the original Asset. The number of candidates does not 
really matter. The voter's vote is not wasted if it is cast for one 
candidate, whether or not that candidate ultimately gains a seat. And 
if the voter votes for ten, none of these fractions is lost unless 
the voter votes for someone who fails to transfer them. And this 
would be an action for which a candidate can and would be held 
accountable. If I voted for Bozo, I'd really want to know why Bozo 
let my votes die without reaching a winner!

Under Asset, votes would be traceable. If a candidate transferred all 
of his or her votes to someone else, I'd have a very reasonable basis 
for considering that person *my* representative, since my vote very 
specifically brought that person toward the quota.

Ideally, under Asset, the quota can be very precisely V/N, and each 
candidate ends up being elected by exactly the quota, excepting for 
very minor roundoff error and the few votes lost. I've suggested that 
seats remain vacant if no remaining candidate reaches the quota; if 
it is allowed to be elected without the quota, if perhaps, say, the 
last seat is won by the remaining candidate with a majority of the 
vote, this would encourage intransigence by that candidate....

>   Therefore, it will lead probably lead to factionalization, or at 
> least cannot handle more parties than there are seats.

Well, duh! Asset is *non-party* PR. Of course it can't handle more 
parties than seats! It doesn't handle parties at all, not as part of 
the system. If candidates choose to recast their votes within 
parties, that's allowed. But it is not required. Party affliliation 
is irrelevant to the method.

>   I've come up with a formula, where V is the amount of voting 
> power per a voter, and C is the amount of candidates.  The formula 
> is, easily enough, C = V.

If all voters have equal voting power, then it does not matter if 
they have 1 or many votes.

>   If the voting system keeps V stable as C increases, then 
> vote-splitting will result.

So? Under Asset, votes are kept whole or split. It does not matter if 
one is splitting 10 votes or 1 vote; the only difference is that with 
the former the total vote -- and the quota -- are multiplied by ten.

I'm not sure that the terminal simplicity of FAAV has been 
understood. Every voter has 1 vote, and they may divide it among as 
many candidates as they like. By voting for a candidate, they are 
assigning a fraction of their vote to the candidate, the fraction is 
of the form 1/N, where N is the number of votes they cast.

*They have exactly what was suggested: as many "votes" as 
candidates.* But because all voters should be equal, no matter how 
many votes they cast, the votes are normalized to a *total* of one 
vote per voter.

(In standard Approval, the votes are not divided because standard 
Approval is a single-winner system and the only votes that count in 
the end are those cast for a winner. All other votes become moot. 
Standard Approval effectively discards all votes cast for other than 
the winner. They are moot; had they not been cast, the outcome would 
not change. This is why standard Approval is, in fact, "one-person, 
one-vote," in spite of charges made by some against it.)

>   If it adds more C then V as C increases, then teaming will result.

What will happen with Asset, certainly if it is free Asset, i.e., the 
original proposal, not Published List, is that candidates who do not 
reach the quota will negotiate with each other -- and with candidates 
having excess votes -- to redistribute the votes to create more 
winners. So minor parties can still gain a seat by essentially 
agreeing to share it, with a mutually acceptable winner. (I'd allow 
candidates to recast their votes outside the original candidate list, 
precisely to enable such compromises, seeking to find compromise 
winners mutually acceptable to "losers," who, since they recast votes 
to create a desired winner, are not quite losers in the same sense as today!

>   For instance, Plurality keeps V stable as C increases (as you 
> always have only one vote), approval and Condercet increase V in 
> proportion to C, and Borda increases V at a faster rate than 
> C.  Asset seems to fall into the plurality situation, although it 
> is a bit less vulnerable.

I really don't think Asset has been understood here.

>   However, a moderate who has 20 votes as compared to the polar 
> candidate thirty votes doesn't have much leeway to convince the 
> other guys to send votes to him, his only choice would probably be 
> to send his votes to the lesser of two evils.

If you are running Asset for single winner, what would you expect? 
However, even in that case you'd really need to look at the total 
election results; what was stated here is not enough to even begin to 
understand the situation. "The polar candidate"? There would 
presumably be two polar candidates, in this single-winner situation. 
And then the moderate would be able to choose, indeed, the lesser of 
two evils. But what if the rules don't allow a winner without a 
majority of votes?

And Asset would allow a far broader distribution of votes.

(I wonder why there is only one moderate.... Asset would make it 
feasible to run for office without campaigning. Campaigns are 
necessary because votes are totally wasted if they don't create a 
winner. Once one has eliminated vote-wasting, people could simply 
declare candidacies and allow those who trust them to vote for them. 
Right now, that would be simply insanity.)

But we were talking about multiwinner PR, where "moderate" does not 
carry the same meaning, and where the goal is to distribute 
representation, not to have a winner and a bunch of losers. I have 
yet to see any PR proposal that even approaches Asset in clear 
democratic function....

This is the real beauty of Asset. The voters don't have to know all 
the candidates; it is enough that they know and trust one. Presumably 
a broadly-trusted candidate will know the other candidates reasonably well.

Some don't like this concentration of power, but the fact is that the 
concentration takes place under other systems, but it is not by the 
free and direct choice of the voters, it rather takes place in the 
halls of the parties and those who fund elections.

What I'm trying to encourage, ultimately, is the concept that we can 
*choose* our representatives, which is quite distinct from trying to 
get them elected. Proxy representation is this, purely. And, beyond 
that, I'm trying to encourage the choosing of proxies who are 
personally known to the voters, who have direct communication with 
the voters. Which requires, in a large jurisdiction, delegable proxy, 
so that voters can communicate directly with their direct proxies, 
and the direct proxies can communicate directly with *their* direct 
proxies, etc.

It is a phone tree generalized into an organizational structure. 
Fractal democracy.

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Alex Small | 2 May 02:45 2006
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Re: Proportional Condorcet Voting

It's not a question of whether the method can be quickly worked out by a computer.  It's a question of whether the method is transparent enough for an average voter to look at a small set of data and quickly work out who the proper winner is.
 
 
Alex Small

Abd ul-Rahman Lomax wrote:
Date: Mon, 01 May 2006 15:56:10 -0400
From: Abd ul-Rahman Lomax
Subject: Re: [EM] Proportional Condorcet Voting
To: "Simmons, Forest" ,

Yes, the objections to Condorcet proposals based on computational
intractability are pretty silly, based only on a theoretical idea
that all possible rankings will exist in the ballot population. But
the ball ot population is a limited set, with almost certainly a high
degree of reduncancy. Systems that require all voters to rank all
candidates make it worse, to be sure, but even that will have a lot
of redundancy in it.

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Abd ul-Rahman Lomax | 2 May 03:13 2006

Re: Proportional Condorcet Voting

At 08:45 PM 5/1/2006, Alex Small wrote:
>It's not a question of whether the method can be quickly worked out 
>by a computer.  It's a question of whether the method is transparent 
>enough for an average voter to look at a small set of data and 
>quickly work out who the proper winner is.

That would seem desirable. However, I'm not sure that it is more 
valuable than the intuitive simplicity of choosing the Condorcet 
winner. It might be quite adequate, for example, that the vote 
results be available on-line, with a program that allows picking any 
two candidates and which shows the pairwise contest results for them.

Plus, of course, that shows the overall pairwise winner, assuming 
that there is one.

As long as the raw vote data is available -- quite practical -- 
anyone could write a program to analyze it, so it would be pretty 
silly for the authorities to put up a program that generated 
deceptive results. It would be caught and exposed immediately....

I've seen, among some election methods advocates, an assumption that 
"the average voter" couldn't understand something like, for example, 
a pairwise election matrix. Properly explained, I don't think the 
average voter, and, indeed, some quite below average, would have any trouble.

However, as readers must know by now, I'm not in favor of elections 
at all. I prefer that we choose representatives instead of electing 
them. As to office holders, I prefer that we hire them rather than 
electing them.... (that is, our chosen representatives -- or us 
directly -- would make hiring decisions deliberatively, as is 
routinely done in business.)

http://metaparty.beyondpolitics.org

Hey! Don't just sit there staring at your computer! DO SOMETHING!

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Matthew Welland | 3 May 07:31 2006

Re: Looking for a little voting insight...

Thanks Markus,

I don't follow the logic perfectly but looking at the example it seems that 
intuitively "A" is the choice that would leave the least number of people 
unhappy and since no-one has contradicted you I will go with that.

I think it would be interesting in a range of polls to have people rank the 
comparative results of plurality vs approval vs condorcet etc.. Maybe it has 
been done before. If anyone has pointers to such an experiment I'd be 
interested. If it hasn't been done perhaps I can build it into my site. Of 
course that begs the question - which voting system to use to measure the 
quality of the voting system!

Matt
--

On Monday 01 May 2006 02:14, Markus Schulze wrote:
> Dear Matthew Welland,
>
> you wrote (30 April 2006):
> > Rubyvote has pure condorcet and cloneproof schwartz
> > sequential available.
>
> At Wikipedia, "pure Condorcet" is called "Minimax
> Condorcet":
>
> http://en.wikipedia.org/wiki/Minimax_Condorcet
>
> At Wikipedia, "cloneproof Schwartz sequential dropping"
> is called "Schulze method":
>
> http://en.wikipedia.org/wiki/Schulze_method
>
> ******************************************
>
> You wrote (30 April 2006):
> > I want to keep things simple.
> > Does it matter which method I choose?
>
> Yes, it does matter. Minimax and Schulze are different
> methods.
>
> Example:
>
>    3   A > B > D > C
>    5   A > D > B > C
>    1   A > D > C > B
>    2   B > A > D > C
>    2   B > D > C > A
>    4   C > A > B > D
>    6   C > B > A > D
>    2   D > B > C > A
>    5   D > C > A > B
>
>    Suppose d[X,Y] is the number of voters who strictly
>    prefer candidate X to candidate Y. Then we get:
>
>    d[A,B]=18
>    d[A,C]=11
>    d[A,D]=21
>
>    d[B,A]=12
>    d[B,C]=14
>    d[B,D]=17
>
>    d[C,A]=19
>    d[C,B]=16
>    d[C,D]=10
>
>    d[D,A]=9
>    d[D,B]=13
>    d[D,C]=20
>
>    Minimax chooses candidate B.
>
>    The strongest paths are:
>
>    A-18-B
>    A-21-D-20-C
>    A-21-D
>
>    B-17-D-20-C-19-A
>    B-17-D-20-C
>    B-17-D
>
>    C-19-A
>    C-19-A-18-B
>    C-19-A-21-D
>
>    D-20-C-19-A
>    D-20-C-19-A-18-B
>    D-20-C
>
>    Schulze chooses candidate A.
>
> Markus Schulze
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