[EM] "scored condorcet", etc

[rob brown]

On 11/30/05, Abd ul-Rahman Lomax <abd at 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
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