[EM] thoughts on the pairwise matrix

[Paul Kislanko]

>What do you consider it?
Processed data. 
 
>what kind of information is lost when going from ballots to the matrix?
The relative positions on ballots compared to the whole field of
alternatives. Alternative A ranked first, and E ranked fifth is cancelled by
an E ranked fourth and A ranked fifth. The Condorcet methods that translate
the Pairwise Matrix into an ordered list make no distinction based upon
voter preferences as indicated by ballots, since their "raw data" is the
"pre-processed" matrix.
 
> is there anything in that data that maybe *should* be involved in
determining the winner?
Yes. The number of voters who have candidate A ranked Nth or better with
respect to the WHOLE FIELD of alternatives is just as important to me as the
pairwise results between A and {B,C,D,E}.


  _____  

From: election-methods-bounces at electorama.com
[mailto:election-methods-bounces at electorama.com] On Behalf Of rob brown
Sent: Monday, November 28, 2005 3:49 PM
To: election-methods at electorama.com
Subject: [EM] thoughts on the pairwise matrix


In a couple recent discussions, I've found myself taking almost
contradictory positions on whether the pairwise matrix is "raw data" or
"results".

In one discussion, where I advocated a more "grokkable" output format, I
argued that the pairwise matrix is effectively raw data....that is, it is
the input data prior to processing and therefore not the best thing to show
when presenting results.

In another, where Paul K indicated a dislike for methods that use the
pairwise matrix because they throw away lots of data prior to doing any
processing, I suggested that the matrix is *not* raw data, but data after
some processing has already happened, so in my opinion the complaint is
unjustified.

What do you consider it?

Another question about the matrix.....what kind of information is lost when
going from ballots to the matrix?  Obviously a lot of information is thrown
away.  My question is: 1) what interesting things are in this "lost data",
and 2) is there anything in that data that maybe *should* be involved in
determining the winner?

For 1, I'm thinking that "similarity" between candidates is lost.  For
instance, the ballots might show that people who rank C high, also tend to
rank F high.  This seems to be irrecoverably lost when going from ballots to
matrix (right?).  An interesting exercise might be to construct a
"similarity matrix" that could display this information to those who are
interested.  Is there anything else of interest in the ballots that is lost
by the time it is compressed into a matrix?

For 2, I can't come up with anything that is in this data that should be
used to determine the winner.  Similarity, while interesting, doesn't seem
to have any relevance to picking a winner.  But that's just my first
thought, so I'd be interested in what others think.

-rob


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