Discussion:
"scored condorcet", etc
rob brown
2005-11-21 07:29:16 UTC
Permalink
Hi again.

You might remember me from a good while back when I did a little work on a
(web based) UI for a ranked voting system (it is still at
http://karmatics.com/voting/ ) Aside from my little question a week ago, I
haven't been around much, so let me introduce myself again and tell you
where I'm coming from. Like most here (presumably) I think that the
plurality system is seriously broken. In particular, I think it polarizes
people by causing parties to form. I like systems that tend to elect a
middle ground candidate, and that don't provide strategic advantage to
forming parties.

While I don't claim to be a math expert, I am confident that most any of the
condorcet methods -- if actually put into practice -- would solve this
problem, for all practical purposes. I can't claim to have a preference of a
particular one. To me, however, the biggest problem to be solved is that
existing condorcet methods (and IRV, for that matter) don't lend themselves
to showing results in a way that is comprehensible to "regular" people. In a
certain way, I suppose this could be considered more of a marketing issue
than anything, since I think this is standing in the way of people getting
comfortable with condorcet methods.

Therefore, my goal is to come up with a way of producing numerical scores
from a condorcet election that can be shown, for instance, as a bar graph.
When I suggested this here on the list over a year ago, the general reaction
seemed to be that numerical scores and condorcet methods were mutually
exclusive. I didn't agree, obviously, but I did accept that it is not as
simple a problem as it might appear.

I keep revisiting this problem, and each time, I seem to get closer and
closer to something that I feel would work well. My general approach has
*not* been to find a way to take existing methods (beatpath or ranked pairs
or what-have-you) and then work backwards to produce scores, but instead to
come up with a brand new method that produces scores first, with the top
scoring candidate being considered the winner. Meanwhile the system must
still meet the condorcet criterion...so if there is a condorcet winner, that
candidate must have the highest score. Of course it must do a reasonable job
of selecting a winner when there is a condorcet tie. Also it is important
that the scores do a good job of showing how the other candidates did
comparatively. For instance, if the #2 candidate's score is very close to
the #1 candidate, that would indicate that a relatively small number of
additional ballots could cause #2 to surpass #1 and win instead. Of course,
the more stable the scores, the better.

So before I start talking about the specific approaches I am looking at and
getting into the math and algorithms and such, I figured I'd first kind of
reintroduce myself (and my goals) to the list, and see if there is a
receptive audience to what I'm working towards.

Does this seem interesting (and valuable) to anyone?

-rob
Dave Ketchum
2005-11-21 09:58:04 UTC
Permalink
On Sun, 20 Nov 2005 23:29:16 -0800 rob brown wrote:

> Hi again.
>
> You might remember me from a good while back when I did a little work on
> a (web based) UI for a ranked voting system (it is still at
> http://karmatics.com/voting/ ) Aside from my little question a week
> ago, I haven't been around much, so let me introduce myself again and
> tell you where I'm coming from. Like most here (presumably) I think
> that the plurality system is seriously broken. In particular, I think
> it polarizes people by causing parties to form. I like systems that
> tend to elect a middle ground candidate, and that don't provide
> strategic advantage to forming parties.


An aside - Plurality is not broken - it does EXACTLY what it was designed
to do. Problem is that those of us who bother to think about it want
something else.

BUT, I do not understand your words about parties - Plurality pushes
toward two strong parties while Condorcet gives parties enough visibility
that more might thrive.

>
> While I don't claim to be a math expert, I am confident that most any of
> the condorcet methods -- if actually put into practice -- would solve
> this problem, for all practical purposes. I can't claim to have a
> preference of a particular one. To me, however, the biggest problem to
> be solved is that existing condorcet methods (and IRV, for that matter)
> don't lend themselves to showing results in a way that is comprehensible
> to "regular" people. In a certain way, I suppose this could be
> considered more of a marketing issue than anything, since I think this
> is standing in the way of people getting comfortable with condorcet methods.

Your mention of IRV makes me wonder what you are thinking of:
. Condorcet with something else mixed in, such as Approval - too
complex - leave this as a challenge to those wanting such.
. IRV - does not produce the array I discus below.
. Pure Condorcet - produces an array of counts (while variations inspire
debates as to which variation is better, all produce the same arrays).
>
> Therefore, my goal is to come up with a way of producing numerical
> scores from a condorcet election that can be shown, for instance, as a
> bar graph. When I suggested this here on the list over a year ago, the
> general reaction seemed to be that numerical scores and condorcet
> methods were mutually exclusive. I didn't agree, obviously, but I did
> accept that it is not as simple a problem as it might appear.

Condorcet uses an array to count the votes - 5x5 for 5 candidates. Look
at one ballot for 6 candidates - A thru F:
A>B=C>D
1 A>B
1 A>C
1 A>D
1 A>E
1 A>F
.5 B>C
.5 C>B The idea here is that 2 voters voting B=C shall have the same
effect as 1 B>C plus 1 C>B (but EM members vote this down, doing none of
this .5 counting).
1 B>D
1 B>E
1 B>F
1 C>D
1 C>E
1 C>F
1 D>E
1 D>F
0 E>F (all seem to agree to not count compares among truncated candidates).

With this formatted as a 6x6 array, comparative candidate strengths are visible.

While complete arrays have to be used to determine winner, could be an
option to print a smaller array excluding fringe candidates.
>
> I keep revisiting this problem, and each time, I seem to get closer and
> closer to something that I feel would work well. My general approach
> has *not* been to find a way to take existing methods (beatpath or
> ranked pairs or what-have-you) and then work backwards to produce
> scores, but instead to come up with a brand new method that produces
> scores first, with the top scoring candidate being considered the
> winner. Meanwhile the system must still meet the condorcet
> criterion...so if there is a condorcet winner, that candidate must have
> the highest score. Of course it must do a reasonable job of selecting a
> winner when there is a condorcet tie. Also it is important that the
> scores do a good job of showing how the other candidates did
> comparatively. For instance, if the #2 candidate's score is very close
> to the #1 candidate, that would indicate that a relatively small number
> of additional ballots could cause #2 to surpass #1 and win instead. Of
> course, the more stable the scores, the better.

If there is a Condorcet winner, the evidence WILL BE that that candidate
will have the highest score vs each other candidate.

Worth commenting when there is a cycle - which has to be resolved whether
or not doing pretty displays.

And, of course, the numbers WILL BE close on near ties.

You mention bar graphs - not clear how this could be done neatly,
considering that each pair of candidates is of possible interest.
>
> So before I start talking about the specific approaches I am looking at
> and getting into the math and algorithms and such, I figured I'd first
> kind of reintroduce myself (and my goals) to the list, and see if there
> is a receptive audience to what I'm working towards.
>
> Does this seem interesting (and valuable) to anyone?

I am responding because many do not realize that these arrays are a NORMAL
production of counting Condorcet ballots - and SHOULD be accessible to
the voters as part of the election report.
>
> -rob

--
***@clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.


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rob brown
2005-11-22 18:00:31 UTC
Permalink
On 11/21/05, Dave Ketchum <***@clarityconnect.com > wrote:
>
> An aside - Plurality is not broken - it does EXACTLY what it was designed
> to do. Problem is that those of us who bother to think about it want
> something else.


I suppose if what you say it was designed to do is "select the plurality
winner", well yeah, it does what it was designed to do. But that is rather
obvious and redundant.

If you say it was designed to, say, "select a reasonable candidate", I stand
by my statement that it is broken.

BUT, I do not understand your words about parties - Plurality pushes
> toward two strong parties while Condorcet gives parties enough visibility
> that more might thrive.


In some ways I think the term "party" is not a very good term. Of course,
people will always gather together to advance various causes or candidates,
and that is great.

I am referring to a more specific thing, which is the phenomena whereby
people incur strategic advantage by gathering together prior to an election
and deciding among themselves which candidate they wish to advance, so as to
avoid splitting the vote.

I think this is the number one reason for parties in the US. Parties would
still exist in the absense of a system susceptible to vote splitting, but I
don't think they would be highly polarized in the way they are today, nor
would they be as powerful and so dominate government. Also, I think they
would tend to concentrate more on specific causes (for instance, a
"pro-choice" party or what have you), rather than on choosing and then
advancing candidates.

> Your mention of IRV makes me wonder what you are thinking of:


My mention of IRV simply was saying that IRV, like condorcet, does not
produce output that is easy to grasp by average joes. I don't in any way
propose mixing IRV in.

Condorcet with something else mixed in, such as Approval - too
> complex - leave this as a challenge to those wanting such.


Yeah. Yuk.

The rest of your post seemed to be explaining to me what the pairwise matrix
is all about, and I already know all that. I think you kind of missed the
point of what I am after. I want something that gives a single score per
candidate. The pairwise matrix would still exist, but somewhere between the
pairwise matrix and the final selection of a single candidate, I want an
intermediate result with one score per candidate. Apparantly MinMax does
this, but it might not be as good a method as others, as well as producing
scores that would need some normalization prior to displaying as, say, a bar
graph (i.e. the best score is zero or possibly a negative number, with no
clear "theoretical worst score"). Still, it is in the direction I am going.

-rob
Dave Ketchum
2005-11-23 06:46:59 UTC
Permalink
On Tue, 22 Nov 2005 10:00:31 -0800 rob brown wrote:

> On 11/21/05, Dave Ketchum <***@clarityconnect.com
> <mailto:***@clarityconnect.com>> wrote:
>
> An aside - Plurality is not broken - it does EXACTLY what it was
> designed
> to do. Problem is that those of us who bother to think about it want
> something else.
>
>
> I suppose if what you say it was designed to do is "select the plurality
> winner", well yeah, it does what it was designed to do. But that is
> rather obvious and redundant.
>
> If you say it was designed to, say, "select a reasonable candidate", I
> stand by my statement that it is broken.
>
> BUT, I do not understand your words about parties - Plurality pushes
> toward two strong parties while Condorcet gives parties enough
> visibility
> that more might thrive.
>
>
> In some ways I think the term "party" is not a very good term. Of
> course, people will always gather together to advance various causes or
> candidates, and that is great.


I see three definitions here:
A group intending and getting recognition as a "party" by the state
- with associated privileges and responsibilities. In NY we have half a
dozen, based on their candidates getting about 1% of the votes for governor.
A group trying for the above, but failing to get the votes.
A group fitting within the definition of your next paragraph, but
NOT in the above more restrictive definitions. I do not like calling
these parties.

I was thinking within the first two, though the third can also do
nominating, etc.

ANYWAY, I was responding to and disagreeing with your previous lead
paragraph. I see:
Plurality promoting two parties being strong, since fringe parties
get lost in the noise.
Condorcet friendly to fringe parties since they can be voted for
while voting preferences among the major parties, and these vote counts
tell more about strength waxing and waning.

Note that I LIKE the details being visible, and understood, better than
your desire to hide them within a single number for each candidate.

>
> I am referring to a more specific thing, which is the phenomena whereby
> people incur strategic advantage by gathering together prior to an
> election and deciding among themselves which candidate they wish to
> advance, so as to avoid splitting the vote.
>
> I think this is the number one reason for parties in the US. Parties
> would still exist in the absense of a system susceptible to vote
> splitting, but I don't think they would be highly polarized in the way
> they are today, nor would they be as powerful and so dominate
> government. Also, I think they would tend to concentrate more on
> specific causes (for instance, a "pro-choice" party or what have you),
> rather than on choosing and then advancing candidates.
>
>
> Your mention of IRV makes me wonder what you are thinking of:
>
>
> My mention of IRV simply was saying that IRV, like condorcet, does not
> produce output that is easy to grasp by average joes. I don't in any
> way propose mixing IRV in.
>
> Condorcet with something else mixed in, such as Approval - too
> complex - leave this as a challenge to those wanting such.
>
>
> Yeah. Yuk.
>
> The rest of your post seemed to be explaining to me what the pairwise
> matrix is all about, and I already know all that. I think you kind of
> missed the point of what I am after. I want something that gives a
> single score per candidate. The pairwise matrix would still exist, but
> somewhere between the pairwise matrix and the final selection of a
> single candidate, I want an intermediate result with one score per
> candidate. Apparantly MinMax does this, but it might not be as good a
> method as others, as well as producing scores that would need some
> normalization prior to displaying as, say, a bar graph (i.e. the best
> score is zero or possibly a negative number, with no clear "theoretical
> worst score"). Still, it is in the direction I am going.


Clearly I see more value in the Condorcet arrays than you do. They
provide comparisons between each candidate and each opposition. I went
into that for you seemed not to.

>
> -rob

--
***@clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.


----
election-methods mailing list - see http://electorama.com/em for list info
rob brown
2005-11-23 07:43:08 UTC
Permalink
On 11/22/05, Dave Ketchum <***@clarityconnect.com> wrote:
>
> > In some ways I think the term "party" is not a very good term. Of
> > course, people will always gather together to advance various causes or
> > candidates, and that is great.
>
> I see three definitions here:
> A group intending and getting recognition as a "party" by the state
> - with associated privileges and responsibilities. In NY we have half a
> dozen, based on their candidates getting about 1% of the votes for
> governor.
> A group trying for the above, but failing to get the votes.
> A group fitting within the definition of your next paragraph, but
> NOT in the above more restrictive definitions. I do not like calling
> these parties.


I think you're definition of party is ....well, narrow. Parties would exist
whether or not the state recognizes them. They are a natural phenomena of
plurality voting. If you don't like the name "party", can you provide
another name? "Strategic clusters"?

Some time ago I wrote this fanciful little article trying to explain how
parties form:
http://www.karmatics.com/voting/moose-example.html
You would probably not call what I refer to in the article "parties" since
they are obviously not recognized by the state.

Note that I LIKE the details being visible, and understood, better than
> your desire to hide them within a single number for each candidate.


I have no desire to make it impossible, or even difficult, to view the
pairwise matrix. I just think that most regular folks would like something
in between the pairwise matrix (too much information to take in all at
once), and the simple declaration of the winner (too little information).

The matrix may contain more information than a simple array of scores, but I
don't think it *communicates* more information to most people (especially if
the scores are displayed as a bar graph). While I have a better
understanding of how the pairwise matrix works than 99.9% of the population,
I can't look at a pairwise matrix and quickly derive important information,
while I can if I look at a bar graph. For instance, looking at a bar graph
I might be able to instantly see that candidate C and candidate F were about
equally far from winning, while D did much better. Looking at a matrix it
might take me a minute or more to be able to figure that out. In fact, in
many cases I can't even tell who won by looking at the matrix (unless it
says "winner: candidate A" at the top). You talk about "hiding"....in my
opinion, that sort of information is hidden in a pairwise matrix.

I believe strongly in the ability of graphics to communicate things that are
very hard to communicate otherwise. Pairwise matrices don't lend themselves
to graphical display.

Clearly I see more value in the Condorcet arrays than you do. They
> provide comparisons between each candidate and each opposition. I went
> into that for you seemed not to.


Like I said, I don't want to prevent people from seeing them.

Let me make an analogy. Imagine you have a small condorcet election, where
there are, say, 100 voters. Someone suggests that all ballots be made
visible to all (anonymously). You say "I think we should show the pairwise
matrix too, for people who don't really want to dig through 100 ballots and
try to somehow tally them up in their head". The other person accuses you
of wanting to "hide" the ballots. You say "I'm not trying to hide anything,
I just want to show the pairwise matrix because its easier to grasp than
looking at 100 ballots....if they really want to look at all the ballots,
let them"

See where I'm coming from?

-rob
Abd ul-Rahman Lomax
2005-11-23 18:44:16 UTC
Permalink
At 02:43 AM 11/23/2005, rob brown wrote:
I believe strongly in the ability of graphics to communicate things
that are very hard to communicate otherwise. Pairwise matrices don't
lend themselves to graphical display.

Color (even gray scale) can instantly show the Condorcet winner in a
pairwise matrix. I'll use gray scale. When the candidate naming the
row wins, leave the background color of the cell white. When the
column candidate wins, gray it. The winner is the only candidate with
a white row all the way across. (Color the cell with the same name
row and column white also.)

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Rob Brown
2005-11-24 00:11:17 UTC
Permalink
Abd ul-Rahman Lomax <abd <at> lomaxdesign.com> writes:
> Color (even gray scale) can instantly show the Condorcet winner in a
> pairwise matrix. I'll use gray scale. When the candidate naming the
> row wins, leave the background color of the cell white. When the
> column candidate wins, gray it. The winner is the only candidate with
> a white row all the way across. (Color the cell with the same name
> row and column white also.)

Yes, but all it shows is the winner, and only if that candidate is the condorcet
winner. What if the winner is not a condorcet winner? The matrix gives no hint
of how the winner was arrived at, short of "here's all the numbers, get out your
calculator and have fun!" Nor does it show anything about how non-winners did
in comparison. The color hints that "number of pairwise wins" is the
determining factor, but it's not.

Basically, it just doesn't communicate what a bar graph does.

Here is something I did some time ago that shows a matrix (and yes, with color),
and some bar graph stuff. I was experimenting with trying to show some
additional information in the bar graph ("relative scores" between candidates),
in a more graphical way than is shown in the matrix. It's by no means complete
(and some of the text is incorrect, such as how the relative scores are
calculated), but basically I was trying to hint at how the information in a
matrix might be presented in a more graphical way that is easier to take in than
just a big table of numbers you throw at people and expect them to make sense
of. It goes with the "progressive disclosure" idea, which is that initially you
see the most important information (the candidate "composite" scores as a bar
graph) and only by "digging in" (in this case, mousing over various things) do
you get the additional information.

Progressive disclosure:
http://www.usabilityfirst.com/glossary/main.cgi?function=display_term&term_id=401


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Paul Kislanko
2005-11-24 04:21:30 UTC
Permalink
> Rob Brown wrote:
>
> Abd ul-Rahman Lomax <abd <at> lomaxdesign.com> writes:
> > Color (even gray scale) can instantly show the Condorcet
> winner in a
> > pairwise matrix. I'll use gray scale. When the candidate naming the
> > row wins, leave the background color of the cell white. When the
> > column candidate wins, gray it. The winner is the only
> candidate with
> > a white row all the way across. (Color the cell with the same name
> > row and column white also.)
>
> Yes, but all it shows is the winner, and only if that
> candidate is the condorcet
> winner. What if the winner is not a condorcet winner? The
> matrix gives no hint
> of how the winner was arrived at, short of "here's all the
> numbers, get out your
> calculator and have fun!" Nor does it show anything about
> how non-winners did
> in comparison. The color hints that "number of pairwise wins" is the
> determining factor, but it's not.
>

As I see it, there are two problems here. First, a Condorcet method is a
process that translates a 3-dimensional input (ballots, alternatives, ranks)
into a two-dimensional represemtation of the result of the process. I played
around with a graphic to show how ranked ballots look when turned into a
bar-graph and it looks like http://www.kislanko.com/poll.jpg, which I didn't
find helpful enough to use.

> Basically, it just doesn't communicate what a bar graph does.

Well, the second problem is that a bar graph sometimes isn't able to
communicate enough. The closest I can come to translating ranked ballots
(NOT a pairwise matrix) into a bar graph along the lines of your example
would be something that has a row for each candidate that shows the
percentage of votes for each rank in different colors in the same bar.


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Abd ul-Rahman Lomax
2005-12-01 04:36:38 UTC
Permalink
At 01:51 PM 11/27/2005, Abd ul-Rahman Lomax wrote:
>At 07:11 PM 11/23/2005, Rob Brown wrote:
>>Abd ul-Rahman Lomax <abd <at> lomaxdesign.com> writes:
>> > Color (even gray scale) can instantly show the Condorcet winner in a
>> > pairwise matrix. I'll use gray scale. When the candidate naming the
>> > row wins, leave the background color of the cell white. When the
>> > column candidate wins, gray it. The winner is the only candidate with
>> > a white row all the way across. (Color the cell with the same name
>> > row and column white also.)
>>
>>Yes, but all it shows is the winner, and only if that candidate is
>>the condorcet winner. What if the winner is not a condorcet winner?

Then the matrix also shows that. Now, my suggestion was only about a
way to make a Condorcet matrix easier to read. (And, by the way, my
intention was indeed that the color overlay the numerical matrix. The
contents of each cell would be the pairwise vote results.)

>> The matrix gives no hint
>>of how the winner was arrived at, short of "here's all the numbers,
>>get out your
>>calculator and have fun!"

What I described would show the Condorcet winner from the raw vote data.

>> Nor does it show anything about how non-winners did
>>in comparison. The color hints that "number of pairwise wins" is the
>>determining factor, but it's not.

This isn't exactly correct. If there is a Condorcet winner, then the
number of pairwise wins *is* the determining factor. I.e., N
candidates, N-1 wins indicates the Condorcet winner.

There is an additional way in which the data can be presented that
would quickly show more information. The candidates can be sorted
according to some criterion or other. Redundant information can be
removed from the matrix, so that it looks like one of those highway
mileage charts.

So the rows could be sorted by the number of pairwise wins (which
puts any Condorcet winner at the top, as well as the Copeland
winner), or by some other criterion, but the winner should be at the top.

It might also be interesting to sort the rows by Cordorcet sequence,
which I would define as

>>Basically, it just doesn't communicate what a bar graph does.

It *is* a bar graph. The Condorcet winner has a visible bar across
the entire matrix.

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rob brown
2005-12-01 10:50:25 UTC
Permalink
On 11/30/05, Abd ul-Rahman Lomax <***@lomaxdesign.com> wrote:
>
> At 01:51 PM 11/27/2005, Abd ul-Rahman Lomax wrote:
> >At 07:11 PM 11/23/2005, Rob Brown wrote:
> >>Yes, but all it shows is the winner, and only if that candidate is
> >>the condorcet winner. What if the winner is not a condorcet winner?
>
> Then the matrix also shows that. Now, my suggestion was only about a
> way to make a Condorcet matrix easier to read. (And, by the way, my
> intention was indeed that the color overlay the numerical matrix. The
> contents of each cell would be the pairwise vote results.)


I don't disagree that color makes the matrix easier to read, but I don't
think color can replace bar charts.

Take a look at my experimental matrix/bar chart display at
http://karmatics.com/voting/testharness.html
(try clicking on the "sample 1", "sample 2" etc). I tried hard to make the
matrix convey as much information as possible with color, but I am convinced
the bar charts still convey information that is not readily discernable from
the matrix by itself.

Of course there is the question of "exactly what is the information the bar
charts convey?" Hopefully, they show "how well each candidate did relative
to the others" but that is quite a fuzzy definition. I'd be glad to
elaborate on what I think they should show, but for now suffice to say that
it is possible to have them display something meaningful, and something
consistant with the method used to find the winner, regardless of which
condorcet method we are using.

>> The matrix gives no hint

> >>of how the winner was arrived at, short of "here's all the numbers,
> >>get out your
> >>calculator and have fun!"
>
> What I described would show the Condorcet winner from the raw vote data.


If there is a condorcet winner. You kind of split my quote above....I had
preceded that with the question "what if there is no condorcet winner?"
Yes, as you say above, the matrix will show that there is no condorcet
winner. But it doesn't show who IS the non-condorcet winner. You have to
accompany the matrix with something like "since you can't tell just by
looking, candidate D wins". If I may be a tad blunt, that's lame. :)

>> Nor does it show anything about how non-winners did
> >>in comparison. The color hints that "number of pairwise wins" is the
> >>determining factor, but it's not.
>
> This isn't exactly correct. If there is a Condorcet winner, then the
> number of pairwise wins *is* the determining factor. I.e., N
> candidates, N-1 wins indicates the Condorcet winner.


Pairwise wins is a very crude measure of how well people do relative to each
other. There are large discrete "steps", since the numbers are small
integers (i.e. less than the number of candidates), And, the candidate with
the most pairwise wins is not necessarily going to be the winner. Nor is a
candidate who has more pairwise wins necessarily "closer to winning" than
another candidate.

There is an additional way in which the data can be presented that
> would quickly show more information. The candidates can be sorted
> according to some criterion or other. Redundant information can be
> removed from the matrix, so that it looks like one of those highway
> mileage charts.
>
> So the rows could be sorted by the number of pairwise wins (which
> puts any Condorcet winner at the top, as well as the Copeland
> winner), or by some other criterion, but the winner should be at the top.


Well, if you sort by pairwise wins, you don't necessarily have the winner at
top (unless you choose the winner with Copeland, which I think we all agree
is a bad idea). And of course there will likely be a lot of ties. But if
you sort by "some criterion or other" as you say.....well, that's exactly
what I'm calling a "score"! Not only do I have something to sort by, but
people can look at the bar chart and see the "shape", which is significant.

It might also be interesting to sort the rows by Cordorcet sequence,
> which I would define as
>
> >>Basically, it just doesn't communicate what a bar graph does.
>
> It *is* a bar graph. The Condorcet winner has a visible bar across
> the entire matrix.


I think my web page clearly demonstrates that the matrix alone, if trying to
use it as a bar chart, is only a crude, low resolution approximation, and
hides subtleties that a true bar chart reveals. I suggest you spend some
time playing with it, modifying the numbers in the matrix and seeing how the
scores change.

And don't get me wrong, I want to keep the matrix available to anyone who
wants to see it. Obviously it provides information the bar chart doesn't
that some people will be interested in. But everyone already knows how to
look at a bar chart and derive useful information out of it....not so with a
matrix. I am quite confident that any sort of usability testing would make
this exceptionally clear.

-rob
Dave Ketchum
2005-11-23 23:36:24 UTC
Permalink
On Wed, 23 Nov 2005 13:44:16 -0500 Abd ul-Rahman Lomax wrote:

> At 02:43 AM 11/23/2005, rob brown wrote:
> I believe strongly in the ability of graphics to communicate things
> that are very hard to communicate otherwise. Pairwise matrices don't
> lend themselves to graphical display.
>
> Color (even gray scale) can instantly show the Condorcet winner in a
> pairwise matrix. I'll use gray scale. When the candidate naming the
> row wins, leave the background color of the cell white. When the
> column candidate wins, gray it. The winner is the only candidate with
> a white row all the way across. (Color the cell with the same name
> row and column white also.)
>
Let's combine the two ideas:

Above I see the matrix with coloring to point to the winner - fine.
But overlay that on the matrix with all the counts.

This keeps the counts that I consider important, with colors over winning
column and row.

To clarify - all of winning row and column get marked "winning".

--
***@clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.


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Rob Brown
2005-11-24 00:30:24 UTC
Permalink
Oops silly me forgot the link!

http://karmatics.com/voting/bargraphs.html

-rob

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Kevin Venzke
2005-11-21 14:26:24 UTC
Permalink
Rob,

--- rob brown <***@karmatics.com> a écrit :
> I keep revisiting this problem, and each time, I seem to get closer and
> closer to something that I feel would work well. My general approach has
> *not* been to find a way to take existing methods (beatpath or ranked pairs
> or what-have-you) and then work backwards to produce scores, but instead to
> come up with a brand new method that produces scores first, with the top
> scoring candidate being considered the winner. Meanwhile the system must
> still meet the condorcet criterion...so if there is a condorcet winner, that
> candidate must have the highest score. Of course it must do a reasonable job
> of selecting a winner when there is a condorcet tie.
> Also it is important
> that the scores do a good job of showing how the other candidates did
> comparatively. For instance, if the #2 candidate's score is very close to
> the #1 candidate, that would indicate that a relatively small number of
> additional ballots could cause #2 to surpass #1 and win instead. Of course,
> the more stable the scores, the better.

I'd just use the beatpath ordering (that is, candidate A has a
stronger beatpath to every other candidate than vice versa and so
wins; candidate B has a stronger beatpath to everyone but A, etc.).

But you seem to not want this because it doesn't consider any
specific contests.

Additional ballots aren't a bad idea. Say that the beatpath(wv)
winner has a score of 0. Everyone else's score is the number of
bullet votes they'd neat to become the Condorcet winner. (You
could also say "to become the beatpath winner," but that would be
harder to calculate.) That gives a good idea of how close everyone
was, and still picks a good winner.

Some examples:

7 A>B
5 B
8 C

Scores are B 0, A 2, C 5.

If A gets those two votes:

2 A
7 A>B
5 B
8 C

Scores are A 0, B 5, C 5. (Tie for second.)

49 A
24 B
27 C>B

Scores are B 0, A 2, C 23.

40 A>B>C
35 B>C>A
25 C>A>B

Scores are A 0, B 31, C 50.

I think that's a decent method.

Kevin Venzke







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Rob Brown
2005-11-21 21:03:48 UTC
Permalink
Kevin Venzke <stepjak <at> yahoo.fr> writes:

> I'd just use the beatpath ordering (that is, candidate A has a
> stronger beatpath to every other candidate than vice versa and so
> wins; candidate B has a stronger beatpath to everyone but A, etc.).
>
> But you seem to not want this because it doesn't consider any
> specific contests.

I don't want to use beatpath unless there is a way to derive scores from
it....not just ordering.

> Additional ballots aren't a bad idea. Say that the beatpath(wv)
> winner has a score of 0. Everyone else's score is the number of
> bullet votes they'd neat to become the Condorcet winner. (You
> could also say "to become the beatpath winner," but that would be
> harder to calculate.) That gives a good idea of how close everyone
> was, and still picks a good winner.

I think you have described Minmax (margins) as the way of assigning scores. I
don't particularly like the inconsistancy of using beatpath to determine the
winner (and arbitrarily giving the winner a score of 0), then using minmax to
determine the score.

Still, interesting....

-rob

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Kevin Venzke
2005-11-21 21:49:38 UTC
Permalink
Rob,

--- Rob Brown <***@karmatics.com> a écrit :
> > Additional ballots aren't a bad idea. Say that the beatpath(wv)
> > winner has a score of 0. Everyone else's score is the number of
> > bullet votes they'd neat to become the Condorcet winner. (You
> > could also say "to become the beatpath winner," but that would be
> > harder to calculate.) That gives a good idea of how close everyone
> > was, and still picks a good winner.
>
> I think you have described Minmax (margins) as the way of assigning scores. I
> don't particularly like the inconsistancy of using beatpath to determine the
> winner (and arbitrarily giving the winner a score of 0), then using minmax to
> determine the score.
>
> Still, interesting....

The problem I see is that the best Condorcet rankings-only methods seem
to have already been invented. So unless your method is going to be sub-par,
you have to agree with one of them for the first position.

If you don't like the inconsistency of mixing methods, you could go with
my other suggestion, to score based on the number of bullet votes needed
to make a given candidate into the beatpath(wv) winner. This is just
potentially a lot harder to calculate.

Using this rule, the winner could be assigned a negative score, if you
wanted, since it's likely that the winner could sacrifice some bullet
votes (assuming some actually exist) and still win.

Kevin Venzke







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Rob Brown
2005-11-21 22:33:34 UTC
Permalink
Kevin Venzke <stepjak <at> yahoo.fr> writes:

> The problem I see is that the best Condorcet rankings-only
> methods seem to have already been invented. So unless your
> method is going to be sub-par, you have to agree with one
> of them for the first position.

Hmmm. Well from my point of view, not producing scores makes a
method sub-par. So beatpath etc. are sub-par in that respect....

But I'm curious....what makes you say that all the best have been
invented? I sorta figured that if you come at it with a different
approach (that scores are a required feature), it may provide new
insights into better methods. To me, scored methods are also
inherently more "tunable". For instance, you can easily mix two
scored methods together to "smooth out" their problems.

> If you don't like the inconsistency of mixing methods, you
> could go with my other suggestion, to score based on the number
> of bullet votes needed to make a given candidate into the
> beatpath(wv) winner. This is just potentially a lot harder to
> calculate.

Hmmmm.....not sure I want to go there. :)

> Using this rule, the winner could be assigned a negative score,
> if yo wanted, since it's likely that the winner could sacrifice
> some bullet votes (assuming some actually exist) and still win.

Yeah, I thought about that and would certainly want to do that.

-rob

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Kevin Venzke
2005-11-22 15:29:08 UTC
Permalink
Rob,

--- Rob Brown <***@karmatics.com> a écrit :
>Wow no one?
>
>I'll try to reword since my first explanation was rather rambly >and not
all that clear.
>
>The candidate with the smallest sum of all losing margins is the winner.

It's not clone-independent. I'm fairly confident that this fails
plurality and minimal defense, as well (which is the reason I suggest
not to use margins to pick the winner). I doubt it satisfies Condorcet
Loser or Schwartz.

> Kevin Venzke <stepjak <at> yahoo.fr> writes:
> > The problem I see is that the best Condorcet rankings-only
> > methods seem to have already been invented. So unless your
> > method is going to be sub-par, you have to agree with one
> > of them for the first position.
>
> Hmmm. Well from my point of view, not producing scores makes a
> method sub-par. So beatpath etc. are sub-par in that respect....

Ok.

> But I'm curious....what makes you say that all the best have been
> invented? I sorta figured that if you come at it with a different
> approach (that scores are a required feature), it may provide new
> insights into better methods. To me, scored methods are also
> inherently more "tunable". For instance, you can easily mix two
> scored methods together to "smooth out" their problems.

Beatpath(wv) satisfies clone independence, monotonicity, plurality,
minimal defense, Condorcet Loser, Local IIA, always elects from Schwartz,
always elects from the CDTT...

It'll be very hard to meet the same properties if you design the method
from scratch.

You can value different properties (FBC, LNHarm...) of course, but the
tradeoff should be worth it. I'm not so convinced that it's valuable
for a method to be tunable. I can't imagine how you could really use
this to fix a perceived problem.

Kevin Venzke







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Rob Brown
2005-11-22 20:34:27 UTC
Permalink
Kevin Venzke <stepjak <at> yahoo.fr> writes:
> Beatpath(wv) satisfies clone independence, monotonicity,
> plurality, minimal defense, Condorcet Loser, Local IIA,
> always elects from Schwartz, always elects from the CDTT..
> It'll be very hard to meet the same properties if you
> design method from scratch.

Fair enough. The biggest problem I have with beatpath is that I CAN'T ACTUALLY
ELECT ANYONE WITH IT. (sorry if that looks like shouting, but I can't
emphasize that point enough)

No one is using beatpath in the real world. I actually *can* elect people with
IRV (since I am lucky enough to live in San Francisco), even though most
election methods geeks know it's inferior to condorcet methods. Why is that?
(and more importantly, why is plurality still so much more common than any
ranked system?)

I don't question that meeting lots of criteria is good, but sometimes I question
whether some of the people on this list tend to see things in such black and
white terms that they are really missing some important points. For instance,
with regard to, say, the "clone independence" criterion: is it possible that
two methods both technically fail this criterion, but that one does a whole lot
better than the other on it? For instance, plurality utterly fails this.
Minmax....seems to me that it would only affected by clone candidates in the
most contrived situations. I think that saying that something "fails", without
saying "how badly it fails", is misleading.

So if MinMax (or the "MinSum" method I proposed) fails some criteria, but "only
by a little bit", while having other desirable properties that can make it more
"marketable" (i.e. you can actually explain how it is tabulated to regular
people in a way they will understand, and show the results in a way they will
understand), I think that could far outweigh its technical imperfections.

> I'm not so convinced that it's valuable
> for a method to be tunable. I can't imagine how you could really use
> this to fix a perceived problem.

Well, let me give an example of tunability that currently exists in the real
world: the "two-thirds majority" required to, for instance, ammend the US
constition.

Why two-thirds? It's not a magic number. It could have been three-fourths (as
it is for final adoption of any constitutional amendment in state legistatures),
or three-fifths, or 70 percent, or whatever. Such a thing is inherently
tunable, by simply adjusting a variable, rather than by selecting a completely
different system. Typically the value is not going to be adjusted for each
election but it will be selected when framing a new constution or by-laws,
allowing the framers to select whatever value they want to strike the right
balance (in this case between flexibility and stability).

Now, with electing a single candidate, things are different, but tunabilily
could still be valuable. Here is an example:

Say one election method tends to pick a non-controversial, middle ground
candidate. Someone that doesn't offend anyone but isn't necessarily loved by
many people either.

Say another method tends to favor a candidate that is strongly favored by many,
disregarding whether that candidate is despised by a few.

Now, wouldn't it be nice if you could, when writing a new constitution or
by-laws, decide the exact balance that is desired, to encourage harmony while
also allowing for healthy debate? Rather than having to say "should we use
beatpath or minmax or approval or IRV or plurality?", they could say "we'll use
the Tun-o-matic system with the harmony factor set to .7".

-rob

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Rob Lanphier
2005-11-22 21:29:13 UTC
Permalink
On Tue, 2005-11-22 at 20:34 +0000, Rob Brown wrote:
> Kevin Venzke <stepjak <at> yahoo.fr> writes:
> > Beatpath(wv) satisfies clone independence, monotonicity,
> > plurality, minimal defense, Condorcet Loser, Local IIA,
> > always elects from Schwartz, always elects from the CDTT..
> > It'll be very hard to meet the same properties if you
> > design method from scratch.

[...]
> I don't question that meeting lots of criteria is good, but sometimes I question
> whether some of the people on this list tend to see things in such black and
> white terms that they are really missing some important points.

In my experience, when Kevin rattles off a list of failed criteria, it's
only a matter of time before he comes up with an example that shows you
why at least one of them is really, really important.

If all you're looking for is something better than IRV that can be
boiled down to a single score, you're better off going with Approval or
Range. My sense is that by insisting on shoehorning a Condorcet winner
method into a single score, you're treating the Condorcet winner
criterion as an absolute priority, while ignoring all of the others.
There are good reasons to believe that the other criteria are at least
as important as the Condorcet winner criterion.

Rob


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rob brown
2005-11-22 23:19:17 UTC
Permalink
On 11/22/05, Rob Lanphier <***@robla.net> wrote:
>
> If all you're looking for is something better than IRV that can be
> boiled down to a single score, you're better off going with Approval or
> Range. My sense is that by insisting on shoehorning a Condorcet winner
> method into a single score, you're treating the Condorcet winner
> criterion as an absolute priority, while ignoring all of the others.
> There are good reasons to believe that the other criteria are at least
> as important as the Condorcet winner criterion.


Hi Rob,

I'm not really all that set on the Condorcet criterion. However, I do *much*
prefer ranked systems than those employed by range or approval. The
advantage of ranked is that it is easy to explain to people what to do,
completely independent of strategy. Just put them in order of preference.
With approval, it is very ambiguous whether to approve or not approve a
non-favorite candidate, as that is all strategy. I think preferences are by
nature relative, but approval implies they are absolute. Range has similar
issues. I wouldn't know what valus to give the various candidates, and I
would find that frustrating (and expect that those with less knowledge of
the process would as well, likely more so).

I also have problems with approval in that, whether or not it is true, it
*feels* like someone who is approving more candidates than another voter is
having more say. I think people have a problem with that, and will never
accept it for that reason.

Obviously, I'm a lot more into the psychology of it all than most people
here. I hate the word marketing, because I tend not to be a fan of marketing
people, but still....having a system that is comfortable to regular people
counts for a lot, and I think existing systems (other than plurality, sadly)
fail miserably on this.

Regarding your comment about "shoehorning" scores onto condorcet: since
MinMax *is* condorcet, and does produce scores....that isn't really
shoehorning, is it?

Is MinMax really that bad? You said yourself that not having a Condorcet
winner is rare, so, that being the case, it seems that in most cases MinMax
is just as good as other Condorcet methods. My guess is that even rarer is
the case where the MinMax winner would differ from the Beatpath winner.

You mentioned priorities, here are my main priorites (none of which is
"meeting the Condorcet criterion"):

1) Reducing or eliminating the strategic advantage that clustering into two
parties gives (due to vote splitting). I think this is the most destructive
force in US politics, resulting in a polarized government that spends a
ridiculous amount of effort trying to "bring down the other side", rather
than actually running the government and solving real problems.

2) having a user interface to voting that is something that people can
easily use, and that gives the voter the feeling that they expressed their
true preferences, and that doing so did not compromise their interests.

3) having results that the public can easily view and feel that they
understand the main gist of what happened. (this also applies to
pre-election polling results)

4) having no strategic advantage to voting late, after you have seen how
others have voted. This could allow real elections (as opposed to just
things like web based polls) to happen over a longer period of time than a
single day, which could make them far less costly and far more convenient to
voters.

5) having the tabulation method easily explainable to average people who are
not necessarily great at math and logic.

Reasons 2, 3 and 5 have to do as much with marketing as anything. I think if
you can get people to understand the system (and to understand the results
of elections carried out using the system), you are more likely to get the
system put into place for real government elections.

Reason #1, however, is the main reason I care about all this. My gut feeling
is -- and feel free to dispute this if you disagree -- that a minmax system
would address the destructive partisanship in government pretty much as well
as something like beatpath.

-rob
Paul Kislanko
2005-11-22 23:32:40 UTC
Permalink
This is a more eloquent description of what I've always been saying. Voters
understand "list the candidates you like in order". Approval makes us uneasy
because "list any candidate that isn't one you don't like" causes is to
worry that which we do like better might get an advantage depeding upon
where we decide to stop holding our nose and give up.

On the voter side I am confortable with ranking all and only candidates of
which I approve. (That means truncation allowed on the collection side).
Don't make it harder than that.

The ranked ballot form of approval is Bucklin with = rankings and truncation
allowed (assuming the counting-method handles = rankings correctly). Even if
it's not the METHOD, it is a useful tool for analyzing ranked ballots.


_____

From: election-methods-***@electorama.com
[mailto:election-methods-***@electorama.com] On Behalf Of rob brown
Sent: Tuesday, November 22, 2005 5:19 PM
To: Rob Lanphier; election-***@electorama.com
Subject: Re: [EM] "scored condorcet", etc


On 11/22/05, Rob Lanphier <***@robla.net> wrote:


If all you're looking for is something better than IRV that can be
boiled down to a single score, you're better off going with Approval or
Range. My sense is that by insisting on shoehorning a Condorcet winner
method into a single score, you're treating the Condorcet winner
criterion as an absolute priority, while ignoring all of the others.
There are good reasons to believe that the other criteria are at least
as important as the Condorcet winner criterion.


Hi Rob,

I'm not really all that set on the Condorcet criterion. However, I do
*much* prefer ranked systems than those employed by range or approval. The
advantage of ranked is that it is easy to explain to people what to do,
completely independent of strategy. Just put them in order of preference.
With approval, it is very ambiguous whether to approve or not approve a
non-favorite candidate, as that is all strategy. I think preferences are by
nature relative, but approval implies they are absolute. Range has similar
issues. I wouldn't know what valus to give the various candidates, and I
would find that frustrating (and expect that those with less knowledge of
the process would as well, likely more so).

I also have problems with approval in that, whether or not it is true, it
*feels* like someone who is approving more candidates than another voter is
having more say. I think people have a problem with that, and will never
accept it for that reason.

Obviously, I'm a lot more into the psychology of it all than most people
here. I hate the word marketing, because I tend not to be a fan of
marketing people, but still....having a system that is comfortable to
regular people counts for a lot, and I think existing systems (other than
plurality, sadly) fail miserably on this.

Regarding your comment about "shoehorning" scores onto condorcet: since
MinMax *is* condorcet, and does produce scores....that isn't really
shoehorning, is it?

Is MinMax really that bad? You said yourself that not having a Condorcet
winner is rare, so, that being the case, it seems that in most cases MinMax
is just as good as other Condorcet methods. My guess is that even rarer is
the case where the MinMax winner would differ from the Beatpath winner.

You mentioned priorities, here are my main priorites (none of which is
"meeting the Condorcet criterion"):

1) Reducing or eliminating the strategic advantage that clustering into two
parties gives (due to vote splitting). I think this is the most destructive
force in US politics, resulting in a polarized government that spends a
ridiculous amount of effort trying to "bring down the other side", rather
than actually running the government and solving real problems.

2) having a user interface to voting that is something that people can
easily use, and that gives the voter the feeling that they expressed their
true preferences, and that doing so did not compromise their interests.

3) having results that the public can easily view and feel that they
understand the main gist of what happened. (this also applies to
pre-election polling results)

4) having no strategic advantage to voting late, after you have seen how
others have voted. This could allow real elections (as opposed to just
things like web based polls) to happen over a longer period of time than a
single day, which could make them far less costly and far more convenient to
voters.

5) having the tabulation method easily explainable to average people who are
not necessarily great at math and logic.

Reasons 2, 3 and 5 have to do as much with marketing as anything. I think
if you can get people to understand the system (and to understand the
results of elections carried out using the system), you are more likely to
get the system put into place for real government elections.

Reason #1, however, is the main reason I care about all this. My gut
feeling is -- and feel free to dispute this if you disagree -- that a minmax
system would address the destructive partisanship in government pretty much
as well as something like beatpath.

-rob
Kevin Venzke
2005-11-22 22:38:06 UTC
Permalink
Rob,

--- Rob Brown <***@karmatics.com> a écrit :
> I don't question that meeting lots of criteria is good, but sometimes I
> question
> whether some of the people on this list tend to see things in such black
> and
> white terms that they are really missing some important points. For
> instance,
> with regard to, say, the "clone independence" criterion: is it possible
> that
> two methods both technically fail this criterion, but that one does a
> whole lot
> better than the other on it? For instance, plurality utterly fails this.

Actually plurality only fails half of it. Plurality isn't sensitive to
cloning losers.

> Minmax....seems to me that it would only affected by clone candidates in
> the
> most contrived situations. I think that saying that something "fails",
> without
> saying "how badly it fails", is misleading.

Ok. MinSum fails clone independence "badly."

MinMax is halfway decent on clone independence because 1. It is completely
insensitive to cloning losers, and 2. Only regarding the greatest loss
means the number of losses (and the number of candidates) is not so
important.

In MinSum, if A defeats B, cloning A always hurts B's score. I don't
think this will be acceptable.

> So if MinMax (or the "MinSum" method I proposed) fails some criteria, but
> "only
> by a little bit",

MinSum is identical to MinMax(margins) when there are only three
candidates.
In my opinion, MinMax(margins) isn't usable. I don't find that it fails
criteria "only by a little bit."

>while having other desirable properties that can make
> it more
> "marketable" (i.e. you can actually explain how it is tabulated to
> regular
> people in a way they will understand, and show the results in a way they
> will
> understand), I think that could far outweigh its technical imperfections.

I understand that marketability/explicability is important. But is MinSum
really that great here? I think it would be easier to explain MinMax(wv)
(which satisfies plurality and fails minimal defense "only a little").

> Now, with electing a single candidate, things are different, but
> tunabilily
> could still be valuable. Here is an example:
>
> Say one election method tends to pick a non-controversial, middle ground
> candidate. Someone that doesn't offend anyone but isn't necessarily
> loved by
> many people either.
>
> Say another method tends to favor a candidate that is strongly favored by
> many,
> disregarding whether that candidate is despised by a few.

I don't think this kind of method really exists.

> Now, wouldn't it be nice if you could, when writing a new constitution or
> by-laws, decide the exact balance that is desired, to encourage harmony
> while
> also allowing for healthy debate? Rather than having to say "should we
> use
> beatpath or minmax or approval or IRV or plurality?", they could say
> "we'll use
> the Tun-o-matic system with the harmony factor set to .7".

Well, if we're going to use something so complicated as a tun-o-matic
system with harmony factors, it should make little difference whether
MinSum (for example) is easy to understand on its own.

Kevin Venzke







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Rob Brown
2005-11-23 00:16:16 UTC
Permalink
Kevin Venzke <stepjak <at> yahoo.fr> writes:
> Actually plurality only fails half of it. Plurality isn't sensitive to
> cloning losers.

Ok, well what plurality does with cloning winners is so bad that it results in
the partisan stuff that we have today in Washington and elsewhere.

> > Minmax....seems to me that it would only affected by clone candidates in
> > the
> > most contrived situations. I think that saying that something "fails",
> > without
> > saying "how badly it fails", is misleading.
>
> Ok. MinSum fails clone independence "badly."

Ok, I can see your point, and I appreciate your satisfying my need to a see
qualifier. :)

However, I'm still unable to picture the real world consequenses of
minsum/dodgson's problems. Similar candidates would help each other, as opposed
to hurting each other as they do in plurality. Since it requires a
non-condorcet winner for this to even have an effect, how much of a real effect
would this have?

The biggest question for me is whether a method would reduce (or eliminate) the
ugly and destructive partisanship we see in government (at least in the US). I
don't claim to know how dodgson would compare to minmax or beatpath in that
respect. But that's what I'm more interested in knowing.

> I understand that marketability/explicability is important. But is MinSum
> really that great here? I think it would be easier to explain MinMax(wv)
> (which satisfies plurality and fails minimal defense "only a little").

I have no problem with MinMax, I only explored MinSum, which I now see is called
Dodgson, because I hadn't seen it discussed. Minmax is fine.

> Well, if we're going to use something so complicated as a tun-o-matic
> system with harmony factors, it should make little difference whether
> MinSum (for example) is easy to understand on its own.

Maybe my description was a bit fanciful, but I still think there is potential
value in the idea of tunability. What I think helps people understand things is
graphical output. If you could look at the output of an election (or fictional
election) as a bar graph, then drag little sliders to explore "what-if"
scenarios with different settings and watch the bar graph adjust in real
time...well... I think you'd be surprised at what people can grasp.

In any case, it is the graphical output (and hence scores), not the tunability,
that is my main concern.

-rob

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Kevin Venzke
2005-11-23 16:11:39 UTC
Permalink
Rob,

--- Rob Brown <***@karmatics.com> a écrit :
> Kevin Venzke <stepjak <at> yahoo.fr> writes:
> > Actually plurality only fails half of it. Plurality isn't sensitive to
> > cloning losers.
>
> Ok, well what plurality does with cloning winners is so bad that it
> results in
> the partisan stuff that we have today in Washington and elsewhere.

I don't think I would blame this on failing clone independence. If
plurality could detect compromise candidates, I think that would be
enough. (There are a number of methods that satisfy clone independence
which do not seem to me to be better than plurality here. Also, my own
favorite method is a "little bit" sensitive to cloning winners, but I
don't think it makes any difference in this area.)

> However, I'm still unable to picture the real world consequenses of
> minsum/dodgson's problems. Similar candidates would help each other,

But this means that factions can deliberately nominate multiple candidates
solely because it may help, and can't hurt, assuming other voters ignore
the clones (rather than trying to do something strategic with them).

> as opposed
> to hurting each other as they do in plurality. Since it requires a
> non-condorcet winner for this to even have an effect, how much of a real
> effect
> would this have?

Hard to say. But I don't think it's ever safe to expect that cycles
will be rare.

My bigger complaints are that MinSum fails the plurality criterion (i.e.
MinSum can elect a candidate who has fewer votes in any position than
some other candidate has in first place) and minimal defense (i.e., if
more than half of the voters rank A, and leave B out of their ranking
entirely, MinSum can still elect B).

> The biggest question for me is whether a method would reduce (or
> eliminate) the
> ugly and destructive partisanship we see in government (at least in the
> US). I
> don't claim to know how dodgson would compare to minmax or beatpath in
> that
> respect. But that's what I'm more interested in knowing.

You have to decide what causes this partisanship, and then you can identify
criteria which address the problem. I'd say the problem is caused in
large part by the fact that only the two candidates most perceived to
be viable can expect to receive votes.

The "favorite betrayal criterion" addresses this in that a voter is assured
that he can rank any number of candidates in the top position without fear
that his vote would be more effective in electing one of these candidates
if he had not included some of those candidates (i.e., less viable
candidates) at the top.

None of the methods you listed satisfy FBC, but beatpath(wv) was quite
good when I included it in some simulations.

> I have no problem with MinMax, I only explored MinSum, which I now see is
> called
> Dodgson, because I hadn't seen it discussed. Minmax is fine.

(Just to say it again, I don't think MinSum should be called "Dodgson."
You can't find the Dodgson winner just from the pairwise matrix. You
have to count movement on the actual ballots. Summing the defeat margins
is just an approximation of this.)

Kevin Venzke







___________________________________________________________________________
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Rob Brown
2005-11-23 18:00:06 UTC
Permalink
Kevin Venzke <stepjak <at> yahoo.fr> writes:
> > However, I'm still unable to picture the real world consequenses of
> > minsum/dodgson's problems. Similar candidates would help each other,
>
> But this means that factions can deliberately nominate multiple candidates
> solely because it may help, and can't hurt, assuming other voters ignore
> the clones (rather than trying to do something strategic with them).

Well, I suppose in theory they could, but I don't see that it would be wise for
them to do it. Whatever slight advantage it may give them to, say, put another
candidate out there would probably be far outweighed by the effort they have to
go to (i.e. money they must spend) to promote another candidate.

Regardless, I'm not pushing for MinSum. MinMax is groovy.

Can you give me a real world scenario where having minmax could cause problems?
I don't think it's a hugely horrible thing to have a slightly "less
preferred" candidate elected. What is a problem is when the whole structure of
politics centers around a strategy for manipulating the voting system, which is
what I see in the US today. It's about priorities to me.

> You have to decide what causes this partisanship, and then you can identify
> criteria which address the problem. I'd say the problem is caused in
> large part by the fact that only the two candidates most perceived to
> be viable can expect to receive votes.

Well, I think it's obvious what causes partisanship in plurality. Eliminating
similar candidates prior to the election has MASSIVE strategic advantage. This
should be common sense to anyone who has ever had a group of people who vote on
which movie to see: "Hey, sci fi buffs.....let's decide between us whether we
all vote for 'Serenity' or for "Hitchhiker's Guide", or we're gonna be outvoted
by the ones who want to watch the lame chick flick".

Almost ANY semi-reasonable election system would eliminate this effect in a
simple situation like that: beatpath, minmax, minsum, copeland, irv, approval,
range, hell probably even borda.

In another post I mentioned my goofy little article on the Moose Lodge, which I
think does a pretty good job of showing how easy it is for parties (or
"strategic clusters") form.

http://www.karmatics.com/voting/moose-example.html

> > I have no problem with MinMax, I only explored MinSum, which I now see is
> > called
> > Dodgson, because I hadn't seen it discussed. Minmax is fine.
>
> (Just to say it again, I don't think MinSum should be called "Dodgson."
> You can't find the Dodgson winner just from the pairwise matrix. You
> have to count movement on the actual ballots. Summing the defeat margins
> is just an approximation of this.)

Ok, I'll call it MinSum. Is that actually what others call it? I just made up
the name. But I probably won't talk about it any more because you've convinced
me MinMax is better. So no more using it as a straw man, ok? ;)

-rob

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Dave Ketchum
2005-11-23 01:57:11 UTC
Permalink
On Tue, 22 Nov 2005 20:34:27 +0000 (UTC) Rob Brown wrote:

> Kevin Venzke <stepjak <at> yahoo.fr> writes:
>
>>Beatpath(wv) satisfies clone independence, monotonicity,
>>plurality, minimal defense, Condorcet Loser, Local IIA,
>>always elects from Schwartz, always elects from the CDTT..
>>It'll be very hard to meet the same properties if you
>> design method from scratch.
>>
>
> Fair enough. The biggest problem I have with beatpath is that I CAN'T ACTUALLY
> ELECT ANYONE WITH IT. (sorry if that looks like shouting, but I can't
> emphasize that point enough)
>
> No one is using beatpath in the real world. I actually *can* elect people with
> IRV (since I am lucky enough to live in San Francisco), even though most
> election methods geeks know it's inferior to condorcet methods. Why is that?
> (and more importantly, why is plurality still so much more common than any
> ranked system?)


Try an electorate with a popular leader, A, and candidates B, C, and D
each VERY popular with a fraction, such that a possible vote with IRV or
Condorcet could be:
40 B>A
35 C>A
25 D>A

For Plurality A gets no votes so B wins - or perhaps a rerun between B and C.

For IRV discard D as smallest stack - creating a new smallest stack for A
- so this gets discarded and B wins.

For Condorcet 60 like A better than B; 65 like A better than C; and 75
like A better than D; so A wins.

Plurality is simple, people are used to it, and it is, usually, good
enough - stack up the ballots in a stack per candidate, biggest stack
wins, DONE.

Condorcet lets voters rank the candidates, looks at ALL that the voters
say, and compares each pair of candidates. Doing all the counting is easy
enough by computer, but a strain by hand. When there are near ties they
can get called cycles and resolution takes thought.

IRV uses the same ballots and, usually, chooses the same winner, though
without looking at all that the voters say. Back to doable by hand -
stacking ballots per choice ala Priority. Then removing top candidate
from smallest stack, moving these to next candidate they vote for, and
repeating until there is a majority winner.
As in the example, not looking at all that the voters say can pick a
less-than-best winner.
When Condorcet sees a cycle, it is only luck whether IRV picks the
same winner (really no complaints proper if picked among those tied -
different variations of Condorcet disagree that much).

>
> I don't question that meeting lots of criteria is good, but sometimes I question
> whether some of the people on this list tend to see things in such black and
> white terms that they are really missing some important points. For instance,
> with regard to, say, the "clone independence" criterion: is it possible that
> two methods both technically fail this criterion, but that one does a whole lot
> better than the other on it? For instance, plurality utterly fails this.
> Minmax....seems to me that it would only affected by clone candidates in the
> most contrived situations. I think that saying that something "fails", without
> saying "how badly it fails", is misleading.
>
> So if MinMax (or the "MinSum" method I proposed) fails some criteria, but "only
> by a little bit", while having other desirable properties that can make it more
> "marketable" (i.e. you can actually explain how it is tabulated to regular
> people in a way they will understand, and show the results in a way they will
> understand), I think that could far outweigh its technical imperfections.
>
>
>>I'm not so convinced that it's valuable
>>for a method to be tunable. I can't imagine how you could really use
>>this to fix a perceived problem.
>>
>
> Well, let me give an example of tunability that currently exists in the real
> world: the "two-thirds majority" required to, for instance, ammend the US
> constition.
>
> Why two-thirds? It's not a magic number. It could have been three-fourths (as
> it is for final adoption of any constitutional amendment in state legistatures),
> or three-fifths, or 70 percent, or whatever. Such a thing is inherently
> tunable, by simply adjusting a variable, rather than by selecting a completely
> different system. Typically the value is not going to be adjusted for each
> election but it will be selected when framing a new constution or by-laws,
> allowing the framers to select whatever value they want to strike the right
> balance (in this case between flexibility and stability).


After ratifying the 18th amendment, it took only 14 years for Congress to
propose ending it with the 21st - and then a few months to ratify the
21st. Do not want ratifying to be too easy or we would be changing every
time the wind blows - nor too hard when a true majority are agreed. My
example is a true exception - having the 18th made people think more
seriously on the subject.

>
> Now, with electing a single candidate, things are different, but tunabilily
> could still be valuable. Here is an example:
>
> Say one election method tends to pick a non-controversial, middle ground
> candidate. Someone that doesn't offend anyone but isn't necessarily loved by
> many people either.
>
> Say another method tends to favor a candidate that is strongly favored by many,
> disregarding whether that candidate is despised by a few.
>
> Now, wouldn't it be nice if you could, when writing a new constitution or
> by-laws, decide the exact balance that is desired, to encourage harmony while
> also allowing for healthy debate? Rather than having to say "should we use
> beatpath or minmax or approval or IRV or plurality?", they could say "we'll use
> the Tun-o-matic system with the harmony factor set to .7".


Need for tunability varies with election method.

With Plurality and multiple candidates, many voters cannot completely
express their wishes - so want a rerun when there is reason to suspect
this may be a problem.

With Plurality and two candidates, a majority may be enough.

Can allow a win on less than 50% with Condorcet, for voters have expressed
their wishes more completely, so 30% might be enough with 25% for
strongest runner-up.

IRV claims getting a majority - but this is of the ballots that made it
thru the last rerun.

>
> -rob

--
***@clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.


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Paul Kislanko
2005-11-23 02:15:11 UTC
Permalink
"Condorcet lets voters rank the candidates, looks at ALL that the voters
say, and compares each pair of candidates. Doing all the counting is easy
enough by computer, but a strain by hand. When there are near ties they
can get called cycles and resolution takes thought."

Defend the statement that "Condorcet looks at ALL that the voters say". No
method that begins counting from a pairwise matrix can do that. Furthermore,
there are numerous "Condorcet" methods because there are numerous ways to
distinguish between the cycles created when ONLY the pairwise matrix is
used.

There isn't even A "Condorcet method". Choose one, and that you have to
proves that there are many "Condorcet" ways to process "ALL that the voters
say", though none really do.

> -----Original Message-----
> From: election-methods-***@electorama.com
> [mailto:election-methods-***@electorama.com] On Behalf Of
> Dave Ketchum
> Sent: Tuesday, November 22, 2005 7:57 PM
> To: Rob Brown
> Cc: election-***@electorama.com
> Subject: Re: [EM] "scored condorcet", etc
>
> On Tue, 22 Nov 2005 20:34:27 +0000 (UTC) Rob Brown wrote:
>
> > Kevin Venzke <stepjak <at> yahoo.fr> writes:
> >
> >>Beatpath(wv) satisfies clone independence, monotonicity,
> >>plurality, minimal defense, Condorcet Loser, Local IIA,
> >>always elects from Schwartz, always elects from the CDTT..
> >>It'll be very hard to meet the same properties if you
> >> design method from scratch.
> >>
> >
> > Fair enough. The biggest problem I have with beatpath is
> that I CAN'T ACTUALLY
> > ELECT ANYONE WITH IT. (sorry if that looks like shouting,
> but I can't
> > emphasize that point enough)
> >
> > No one is using beatpath in the real world. I actually
> *can* elect people with
> > IRV (since I am lucky enough to live in San Francisco),
> even though most
> > election methods geeks know it's inferior to condorcet
> methods. Why is that?
> > (and more importantly, why is plurality still so much more
> common than any
> > ranked system?)
>
>
> Try an electorate with a popular leader, A, and candidates B,
> C, and D
> each VERY popular with a fraction, such that a possible vote
> with IRV or
> Condorcet could be:
> 40 B>A
> 35 C>A
> 25 D>A
>
> For Plurality A gets no votes so B wins - or perhaps a rerun
> between B and C.
>
> For IRV discard D as smallest stack - creating a new smallest
> stack for A
> - so this gets discarded and B wins.
>
> For Condorcet 60 like A better than B; 65 like A better than
> C; and 75
> like A better than D; so A wins.
>
> Plurality is simple, people are used to it, and it is, usually, good
> enough - stack up the ballots in a stack per candidate, biggest stack
> wins, DONE.
>
> Condorcet lets voters rank the candidates, looks at ALL that
> the voters
> say, and compares each pair of candidates. Doing all the
> counting is easy
> enough by computer, but a strain by hand. When there are
> near ties they
> can get called cycles and resolution takes thought.
>
> IRV uses the same ballots and, usually, chooses the same
> winner, though
> without looking at all that the voters say. Back to doable by hand -
> stacking ballots per choice ala Priority. Then removing top
> candidate
> from smallest stack, moving these to next candidate they vote
> for, and
> repeating until there is a majority winner.
> As in the example, not looking at all that the voters
> say can pick a
> less-than-best winner.
> When Condorcet sees a cycle, it is only luck whether
> IRV picks the
> same winner (really no complaints proper if picked among those tied -
> different variations of Condorcet disagree that much).
>
> >
> > I don't question that meeting lots of criteria is good, but
> sometimes I question
> > whether some of the people on this list tend to see things
> in such black and
> > white terms that they are really missing some important
> points. For instance,
> > with regard to, say, the "clone independence" criterion:
> is it possible that
> > two methods both technically fail this criterion, but that
> one does a whole lot
> > better than the other on it? For instance, plurality
> utterly fails this.
> > Minmax....seems to me that it would only affected by clone
> candidates in the
> > most contrived situations. I think that saying that
> something "fails", without
> > saying "how badly it fails", is misleading.
> >
> > So if MinMax (or the "MinSum" method I proposed) fails some
> criteria, but "only
> > by a little bit", while having other desirable properties
> that can make it more
> > "marketable" (i.e. you can actually explain how it is
> tabulated to regular
> > people in a way they will understand, and show the results
> in a way they will
> > understand), I think that could far outweigh its technical
> imperfections.
> >
> >
> >>I'm not so convinced that it's valuable
> >>for a method to be tunable. I can't imagine how you could really use
> >>this to fix a perceived problem.
> >>
> >
> > Well, let me give an example of tunability that currently
> exists in the real
> > world: the "two-thirds majority" required to, for instance,
> ammend the US
> > constition.
> >
> > Why two-thirds? It's not a magic number. It could have
> been three-fourths (as
> > it is for final adoption of any constitutional amendment in
> state legistatures),
> > or three-fifths, or 70 percent, or whatever. Such a thing
> is inherently
> > tunable, by simply adjusting a variable, rather than by
> selecting a completely
> > different system. Typically the value is not going to be
> adjusted for each
> > election but it will be selected when framing a new
> constution or by-laws,
> > allowing the framers to select whatever value they want to
> strike the right
> > balance (in this case between flexibility and stability).
>
>
> After ratifying the 18th amendment, it took only 14 years for
> Congress to
> propose ending it with the 21st - and then a few months to ratify the
> 21st. Do not want ratifying to be too easy or we would be
> changing every
> time the wind blows - nor too hard when a true majority are
> agreed. My
> example is a true exception - having the 18th made people think more
> seriously on the subject.
>
> >
> > Now, with electing a single candidate, things are
> different, but tunabilily
> > could still be valuable. Here is an example:
> >
> > Say one election method tends to pick a non-controversial,
> middle ground
> > candidate. Someone that doesn't offend anyone but isn't
> necessarily loved by
> > many people either.
> >
> > Say another method tends to favor a candidate that is
> strongly favored by many,
> > disregarding whether that candidate is despised by a few.
> >
> > Now, wouldn't it be nice if you could, when writing a new
> constitution or
> > by-laws, decide the exact balance that is desired, to
> encourage harmony while
> > also allowing for healthy debate? Rather than having to
> say "should we use
> > beatpath or minmax or approval or IRV or plurality?", they
> could say "we'll use
> > the Tun-o-matic system with the harmony factor set to .7".
>
>
> Need for tunability varies with election method.
>
> With Plurality and multiple candidates, many voters cannot completely
> express their wishes - so want a rerun when there is reason
> to suspect
> this may be a problem.
>
> With Plurality and two candidates, a majority may be enough.
>
> Can allow a win on less than 50% with Condorcet, for voters
> have expressed
> their wishes more completely, so 30% might be enough with 25% for
> strongest runner-up.
>
> IRV claims getting a majority - but this is of the ballots
> that made it
> thru the last rerun.
>
> >
> > -rob
>
> --
> ***@clarityconnect.com
> people.clarityconnect.com/webpages3/davek
> Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708
> 607-687-5026
> Do to no one what you would not want done to you.
> If you want peace, work for justice.
>
>
> ----
> election-methods mailing list - see http://electorama.com/em
> for list info
>


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Dave Ketchum
2005-11-23 03:17:10 UTC
Permalink
On Tue, 22 Nov 2005 20:15:11 -0600 Paul Kislanko wrote:

> "Condorcet lets voters rank the candidates, looks at ALL that the voters
> say, and compares each pair of candidates. Doing all the counting is easy
> enough by computer, but a strain by hand. When there are near ties they
> can get called cycles and resolution takes thought."
>
> Defend the statement that "Condorcet looks at ALL that the voters say". No
> method that begins counting from a pairwise matrix can do that. Furthermore,
> there are numerous "Condorcet" methods because there are numerous ways to
> distinguish between the cycles created when ONLY the pairwise matrix is
> used.


ALL that the voters have said is to offer lists of candidates in
preference order.

Condorcet DOES LOOK at all of that, though the significance is that IRV,
looking at the same lists, often pays no attention to ends of the lists.

>
> There isn't even A "Condorcet method". Choose one, and that you have to
> proves that there are many "Condorcet" ways to process "ALL that the voters
> say", though none really do.


Agreed that there are variations in how the data is processed. I say
little about that - just that the pairs get compared. What claims to be a
Condorcet method that does not agree on that much?

>
>
>>-----Original Message-----
>>From: election-methods-***@electorama.com
>>[mailto:election-methods-***@electorama.com] On Behalf Of
>>Dave Ketchum
>>Sent: Tuesday, November 22, 2005 7:57 PM
>>To: Rob Brown
>>Cc: election-***@electorama.com
>>Subject: Re: [EM] "scored condorcet", etc
>>
>>On Tue, 22 Nov 2005 20:34:27 +0000 (UTC) Rob Brown wrote:
>>
>>
>>>Kevin Venzke <stepjak <at> yahoo.fr> writes:
>>>
>>>
>>>>Beatpath(wv) satisfies clone independence, monotonicity,
>>>>plurality, minimal defense, Condorcet Loser, Local IIA,
>>>>always elects from Schwartz, always elects from the CDTT..
>>>>It'll be very hard to meet the same properties if you
>>>>design method from scratch.
>>>>
>>>>
>>>Fair enough. The biggest problem I have with beatpath is
>>>
>>that I CAN'T ACTUALLY
>>
>>>ELECT ANYONE WITH IT. (sorry if that looks like shouting,
>>>
>>but I can't
>>
>>>emphasize that point enough)
>>>
>>>No one is using beatpath in the real world. I actually
>>>
>>*can* elect people with
>>
>>>IRV (since I am lucky enough to live in San Francisco),
>>>
>>even though most
>>
>>>election methods geeks know it's inferior to condorcet
>>>
>>methods. Why is that?
>>
>>>(and more importantly, why is plurality still so much more
>>>
>>common than any
>>
>>>ranked system?)
>>>
>>
>>Try an electorate with a popular leader, A, and candidates B,
>>C, and D
>>each VERY popular with a fraction, such that a possible vote
>>with IRV or
>>Condorcet could be:
>>40 B>A
>>35 C>A
>>25 D>A
>>
>>For Plurality A gets no votes so B wins - or perhaps a rerun
>>between B and C.
>>
>>For IRV discard D as smallest stack - creating a new smallest
>>stack for A
>>- so this gets discarded and B wins.
>>
>>For Condorcet 60 like A better than B; 65 like A better than
>>C; and 75
>>like A better than D; so A wins.
>>
>>Plurality is simple, people are used to it, and it is, usually, good
>>enough - stack up the ballots in a stack per candidate, biggest stack
>>wins, DONE.
>>
>>Condorcet lets voters rank the candidates, looks at ALL that
>>the voters
>>say, and compares each pair of candidates. Doing all the
>>counting is easy
>>enough by computer, but a strain by hand. When there are
>>near ties they
>>can get called cycles and resolution takes thought.
>>
>>IRV uses the same ballots and, usually, chooses the same
>>winner, though
>>without looking at all that the voters say. Back to doable by hand -
>>stacking ballots per choice ala Priority. Then removing top
>>candidate
>>from smallest stack, moving these to next candidate they vote
>>for, and
>>repeating until there is a majority winner.
>> As in the example, not looking at all that the voters
>>say can pick a
>>less-than-best winner.
>> When Condorcet sees a cycle, it is only luck whether
>>IRV picks the
>>same winner (really no complaints proper if picked among those tied -
>>different variations of Condorcet disagree that much).
>>
>>
>>>I don't question that meeting lots of criteria is good, but
>>>
>>sometimes I question
>>
>>>whether some of the people on this list tend to see things
>>>
>>in such black and
>>
>>>white terms that they are really missing some important
>>>
>>points. For instance,
>>
>>>with regard to, say, the "clone independence" criterion:
>>>
>>is it possible that
>>
>>>two methods both technically fail this criterion, but that
>>>
>>one does a whole lot
>>
>>>better than the other on it? For instance, plurality
>>>
>>utterly fails this.
>>
>>>Minmax....seems to me that it would only affected by clone
>>>
>>candidates in the
>>
>>>most contrived situations. I think that saying that
>>>
>>something "fails", without
>>
>>>saying "how badly it fails", is misleading.
>>>
>>>So if MinMax (or the "MinSum" method I proposed) fails some
>>>
>>criteria, but "only
>>
>>>by a little bit", while having other desirable properties
>>>
>>that can make it more
>>
>>>"marketable" (i.e. you can actually explain how it is
>>>
>>tabulated to regular
>>
>>>people in a way they will understand, and show the results
>>>
>>in a way they will
>>
>>>understand), I think that could far outweigh its technical
>>>
>>imperfections.
>>
>>>
>>>
>>>>I'm not so convinced that it's valuable
>>>>for a method to be tunable. I can't imagine how you could really use
>>>>this to fix a perceived problem.
>>>>
>>>>
>>>Well, let me give an example of tunability that currently
>>>
>>exists in the real
>>
>>>world: the "two-thirds majority" required to, for instance,
>>>
>>ammend the US
>>
>>>constition.
>>>
>>>Why two-thirds? It's not a magic number. It could have
>>>
>>been three-fourths (as
>>
>>>it is for final adoption of any constitutional amendment in
>>>
>>state legistatures),
>>
>>>or three-fifths, or 70 percent, or whatever. Such a thing
>>>
>>is inherently
>>
>>>tunable, by simply adjusting a variable, rather than by
>>>
>>selecting a completely
>>
>>>different system. Typically the value is not going to be
>>>
>>adjusted for each
>>
>>>election but it will be selected when framing a new
>>>
>>constution or by-laws,
>>
>>>allowing the framers to select whatever value they want to
>>>
>>strike the right
>>
>>>balance (in this case between flexibility and stability).
>>>
>>
>>After ratifying the 18th amendment, it took only 14 years for
>>Congress to
>>propose ending it with the 21st - and then a few months to ratify the
>>21st. Do not want ratifying to be too easy or we would be
>>changing every
>>time the wind blows - nor too hard when a true majority are
>>agreed. My
>>example is a true exception - having the 18th made people think more
>>seriously on the subject.
>>
>>
>>>Now, with electing a single candidate, things are
>>>
>>different, but tunabilily
>>
>>>could still be valuable. Here is an example:
>>>
>>>Say one election method tends to pick a non-controversial,
>>>
>>middle ground
>>
>>>candidate. Someone that doesn't offend anyone but isn't
>>>
>>necessarily loved by
>>
>>>many people either.
>>>
>>>Say another method tends to favor a candidate that is
>>>
>>strongly favored by many,
>>
>>>disregarding whether that candidate is despised by a few.
>>>
>>>Now, wouldn't it be nice if you could, when writing a new
>>>
>>constitution or
>>
>>>by-laws, decide the exact balance that is desired, to
>>>
>>encourage harmony while
>>
>>>also allowing for healthy debate? Rather than having to
>>>
>>say "should we use
>>
>>>beatpath or minmax or approval or IRV or plurality?", they
>>>
>>could say "we'll use
>>
>>>the Tun-o-matic system with the harmony factor set to .7".
>>>
>>
>>Need for tunability varies with election method.
>>
>>With Plurality and multiple candidates, many voters cannot completely
>>express their wishes - so want a rerun when there is reason
>>to suspect
>>this may be a problem.
>>
>>With Plurality and two candidates, a majority may be enough.
>>
>>Can allow a win on less than 50% with Condorcet, for voters
>>have expressed
>>their wishes more completely, so 30% might be enough with 25% for
>>strongest runner-up.
>>
>>IRV claims getting a majority - but this is of the ballots
>>that made it
>>thru the last rerun.
>>
>>
>>>-rob

--
***@clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.


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rob brown
2005-11-23 03:20:01 UTC
Permalink
On 11/22/05, Paul Kislanko <***@airmail.net> wrote:
>
> Defend the statement that "Condorcet looks at ALL that the voters say". No
> method that begins counting from a pairwise matrix can do that.
> Furthermore,
> there are numerous "Condorcet" methods because there are numerous ways to
> distinguish between the cycles created when ONLY the pairwise matrix is
> used.


If I may jump in -- I have to take issue that Condorcet "doesn't look at all
the voters have to say" because it "begins counting" with the pairwise
matrix.

It begins counting with the ballots. By the time it gets to the pairwise
matrix, it has certainly eliminated a lot of data, having distilled possibly
several megabytes of data into a few kilobytes or less (depending on how
many candidates and how many ballots). But then, it has to distill it
further, into maybe a single byte of data (assuming there are less than 256
candidates).

Somewhere along the line, information has to be pared down and eliminated.
The pairwise matrix is an intermediate step between having several megs (all
the ballots) and 1 byte (a winner). I'm not sure I understand why having an
intermediate step is such a problem.

-rob
Rob Brown
2005-11-23 02:47:11 UTC
Permalink
Dave Ketchum <davek <at> clarityconnect.com> writes:

> Plurality is simple, people are used to it, and it is, usually, good
> enough

Yes, agree with your first two points, STRONGLY disagree that plurality is
"usually good enough".

I hear plenty of complaining about how partisan our government is, I personally
can't even watch politics because it is just....sad. I think very few people
have any clue that this is plain and simple CAUSED by plurality voting.
Plurality causes people who cluster into opposing groups to have a massive
strategic advantage...which in fact forces people into opposition rather than
toward the center. I don't see how that could be considered "good enough" by
anyone who understands what is going on.

BTW, my question of "why is plurality more popular" was intended rhetorically.
I think I know many of the reasons why....like you say, understandability and
simplicity. I do, however, think that better systems could be put into
practice, if only those who advocated them had as much of a feel for psychology,
user interface, and marketability as they do for the math.

And as an aside, I think it is sad that if someone wants to learn more about
better ways of voting and types "election methods" into Google, the first hit
they get.....well let's just say it doesn't create a positive impression of the
election methods community.

-rob

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Gervase Lam
2005-11-21 21:36:41 UTC
Permalink
> Date: Sun, 20 Nov 2005 23:29:16 -0800
> From: rob brown
> Subject: [EM] "scored condorcet", etc

> Therefore, my goal is to come up with a way of producing numerical scores
> from a condorcet election that can be shown, for instance, as a bar graph.

If I remember rightly, Forest and then I came up with MinMax(wv) or
other MinMax Condorcet method. This is probably the easiest way to get
scores from a Condorcet method.

With MinMax, it is very easy to get the scores of the other candidates.
You don't even need to drop the winning candidate and re-run the method
again in order to work out the score of the runner up.

Is MinMax good enough?

Thanks,
Gervase.


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Paul Kislanko
2005-11-21 22:00:50 UTC
Permalink
If I'm not getting too senile, somewhere I read that the definition of an
"election method" was a mapping of ranked ballots into an ordered list. That
would make "scoring" a Condorcet method a legitimate question.

I have a personal distrust of methods that "score" by looking at only the
contents of the pairwise matrix, but there should surely be a mapping from
the CW back to the ballots that contributed to the CW being the CW. Take
those ballots and remove all winners, moving up all alternatives ranked
lower than the winner. Then form a new pairwise matrix from the revised
ballots, etc.

> -----Original Message-----
> From: election-methods-***@electorama.com
> [mailto:election-methods-***@electorama.com] On Behalf Of
> Gervase Lam
> Sent: Monday, November 21, 2005 3:37 PM
> To: election-***@electorama.com
> Subject: Re: [EM] "scored condorcet", etc
>
> > Date: Sun, 20 Nov 2005 23:29:16 -0800
> > From: rob brown
> > Subject: [EM] "scored condorcet", etc
>
> > Therefore, my goal is to come up with a way of producing
> numerical scores
> > from a condorcet election that can be shown, for instance,
> as a bar graph.
>
> If I remember rightly, Forest and then I came up with MinMax(wv) or
> other MinMax Condorcet method. This is probably the easiest
> way to get
> scores from a Condorcet method.
>
> With MinMax, it is very easy to get the scores of the other
> candidates.
> You don't even need to drop the winning candidate and re-run
> the method
> again in order to work out the score of the runner up.
>
> Is MinMax good enough?
>
> Thanks,
> Gervase.
>
>
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> election-methods mailing list - see http://electorama.com/em
> for list info
>


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Gervase Lam
2005-11-23 00:06:35 UTC
Permalink
On Mon, 2005-11-21 at 16:00 -0600, Paul Kislanko wrote:
> I have a personal distrust of methods that "score" by looking at only the
> contents of the pairwise matrix, but there should surely be a mapping from
> the CW back to the ballots that contributed to the CW being the CW. Take
> those ballots and remove all winners, moving up all alternatives ranked
> lower than the winner. Then form a new pairwise matrix from the revised
> ballots, etc.

Suppose there are candidates A, B, C and D. B is the Condorcet winner
and has the following pairwise results:

45-5 B:A
37-13 B:C
29-21 B:D

Now, the B v. D result is the pivotal result as it is the closest result
of the three. Therefore, it is the most critical one in contributing B
to be the Condorcet Winner (I hope I got the gist of your post correct
here). So, let's convert the results to margins:

+40 B:A
+24 B:C
+8 B:D

Now, it could be argued that we are heading towards a MinMax(Margins)
type method here. And MinMax methods look directly at the pairwise
matrix.

Carrying this further, we then need to remove the ballots that
contributed to B being the Condorcet Winner. That is, of the ballots
that ranked B>D, 8 need to be removed (or 9, depending on your point of
view). But which 8 (or 9)? That is at best non-trivial.

Thinking more about the "mapping" idea, the pairwise matrix is really
only a way of "mapping" ballots into a convenient form so as to
determine an election result. I don't think somebody throwing a load of
ballots at me and them asking me to give a result "just like that" is
reasonable. That is unless the person doesn't mind me using the Random
Ballot method.

The only alternative "mappings" I can think of are methods that are
Condorcet compliant. Is Borda a Condorcet compliant method? From my
vague recollections, I think there are other methods that are Condorcet
compliant but don't use a pairwise matrix.

Thanks,
Gervase.


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Rob Brown
2005-11-21 22:22:00 UTC
Permalink
Gervase Lam <gervase.lam <at> group.force9.co.uk> writes:
> If I remember rightly, Forest and then I came up with MinMax(wv) or
> other MinMax Condorcet method. This is probably the easiest way to get
> scores from a Condorcet method.
>
> ...
>
> Is MinMax good enough?

Yeah, I just realized (see my reply to Kevin) that MinMax probably does
what I need.

Whether its good enough or not I don't know. I think the ability to show
scores would far outweigh its imperfections.

I would probably want to do some normalization with the scores so that
higher scores are better, and so that the score of the lowest candidate
is not zero unless he really got zero votes....but that is fairly trivial.

-rob

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Gervase Lam
2005-11-23 00:06:42 UTC
Permalink
> Date: Mon, 21 Nov 2005 22:22:00 +0000 (UTC)
> From: Rob Brown
> Subject: Re: [EM] "scored condorcet", etc

> I would probably want to do some normalization with the scores so that
> higher scores are better, and so that the score of the lowest
> candidate
> is not zero unless he really got zero votes....but that is fairly
> trivial.

I don't know what you mean by normalisation here, but it usually means
some scaling up or down (i.e. multiplication or division). What I would
do is probably apply the following formula to get each candidate's
score.

Candidate's Score = Total No. of Ballots - Max wv against Candidate

If there is a Condorcet Winner, then I think it would be easiest to make
that candidate's "Max wv against" equal 0. This means that it is best
to assume that a pairwise result of 0-0 between two candidates is a loss
for both candidates. Therefore, it would be best if any tie between two
candidates is a loss for both the candidates.

If you think that this is a bit kludgy, then I suppose you could use
MMPO (MinMax Pairwise Opposition). This is basically the same as MinMax
(wv) except that you "ignore" whether a pairwise result is a win or
loss. You just look at the number of pairwise 'votes' that oppose a
candidate.

As discussed quite recently, MMPO is FBC compliant and basically elects
the candidate who the voters oppose the least. On the other hand, it
can elect a candidate who the voters support the least. (I hope I got
this paragraph right).

Thanks,
Gervase.


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Rob Brown
2005-11-23 00:30:35 UTC
Permalink
Gervase Lam <gervase.lam <at> group.force9.co.uk> writes:
> I don't know what you mean by normalisation here, but it usually means
> some scaling up or down (i.e. multiplication or division). What I would
> do is probably apply the following formula to get each candidate's
> score.
>
> Candidate's Score = Total No. of Ballots - Max wv against Candidate

That's close to what I was thinking. I probably would, rather than using "total
number of ballots", use something that can be derived from the pairwise matrix,
which the total number of ballots isn't.

It would be nice if the score could be represented in a way that compares to
percentage, so that all scores add up to 100. Then again, you could treat
"condorcet winner" as a score of 100, and any extra votes would push it above
100. Non condorcet winners' scores might be "percentage of the votes necessary
to be the condorcet winner".

> If there is a Condorcet Winner, then I think it would be easiest to make
> that candidate's "Max wv against" equal 0. This means that it is best
> to assume that a pairwise result of 0-0 between two candidates is a loss
> for both candidates. Therefore, it would be best if any tie between two
> candidates is a loss for both the candidates.

Hmmmm, that doesn't sound right to me.

> If you think that this is a bit kludgy, then I suppose you could use
> MMPO (MinMax Pairwise Opposition). This is basically the same as MinMax
> (wv) except that you "ignore" whether a pairwise result is a win or
> loss. You just look at the number of pairwise 'votes' that oppose a
> candidate.

Yeah, I understand that there are advantages to that, but again, something
doesn't feel right about it to me. It seems like you are throwing out valuable
information. (I know throwing out valueable information is a necessity at times
to avoid worse effects, but still....something seems wrong with your description
to me.



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Gervase Lam
2005-11-23 00:38:07 UTC
Permalink
Some quick replies here before I go to bed.

> Date: Tue, 22 Nov 2005 15:19:17 -0800
> From: rob brown <***@karmatics.com>
> Subject: Re: [EM] "scored condorcet", etc

> I also have problems with approval in that, whether or not it is true,
> it
> *feels* like someone who is approving more candidates than another
> voter is
> having more say. I think people have a problem with that, and will
> never
> accept it for that reason.

Well, there have been proposals on this list of methods where the input
are ranked ballots and the output is an approval score. Because really,
in order to determine what a voter's best approval strategy is, the
voter at the very least needs to have a ranking of the candidates in
mind if not cardinal ratings for the candidates.

> 3) having results that the public can easily view and feel that they
> understand the main gist of what happened. (this also applies to
> pre-election polling results)

> 5) having the tabulation method easily explainable to average people
> who are
> not necessarily great at math and logic.

Well, apart from Borda, which I basically knew of before I started
reading this mailing list, the first ranking method(s) I first
understood was Condorcet, though this took me a while because I had to
work out how it worked not knowing where I could find a definition for
it.

For similar reasons, it took me longer still to understand IRV. To me,
the way IRV results are tabulated are more complicated than the way
pairwise results are tabulated.

> 4) having no strategic advantage to voting late, after you have seen
> how
> others have voted. This could allow real elections (as opposed to just
> things like web based polls) to happen over a longer period of time
> than a
> single day, which could make them far less costly and far more
> convenient to
> voters.

Well, the relatively recent elections in India took over a month to do.
As security was a problem and India is a big and highly populous
country, each group of regions in the country had their voting stations
open on different days. And India uses plurality. So I think this is
not a problem.

However, I think India keeps the result of each region under lock and
key until all the regions have finished voting. Therefore, you won't
get the situation of being able to use strategic voting as a result of
voting late.

I'm sure there are other countries in the world where the election is
spread over many days with each region in the country voting on
different days.

Thanks,
Gervase.


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Gervase Lam
2005-11-23 23:21:11 UTC
Permalink
> Date: Wed, 23 Nov 2005 00:30:35 +0000 (UTC)
> From: Rob Brown
> Subject: Re: [EM] "scored condorcet", etc

> > Candidate's Score = Total No. of Ballots - Max wv against Candidate
>
> That's close to what I was thinking. I probably would, rather than
> using "total
> number of ballots", use something that can be derived from the
> pairwise matrix,
> which the total number of ballots isn't.

In a similar vein to Forest's O/D (Offense/Defense) method, which is a
variation of MMPO, you could do the following:

Candidate's Score = Min votes FOR Candidate - Max votes AGAINST
Candidate

The Candidate with the highest score is the winner. This is the same as
MMPO except that "Min votes for Candidate" has been included in the
formula. The problem with adding the "Min votes FOR Candidate" is that
I think it makes the method not satisfy FBC.

In Forest's O/D method, the minus is turned into a divide and for each
pair of candidates, if both candidates are ranked equal first (or last),
they are counted as votes for (or against) the candidate in the pairwise
matrix. I think O/D (with the said first/last rankings handling)
satisfies FBC.

> It would be nice if the score could be represented in a way that
> compares to
> percentage, so that all scores add up to 100.

This just requires a bit school pupil mathematics to do this.

Thanks,
Gervase.


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