[EM] "scored condorcet", etc

[Abd ul-Rahman Lomax]

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.