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<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=602585121-28112005>><FONT face="Times New Roman" color=#000000
size=3>What do you consider it?</FONT><BR>Processed data. </SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=602585121-28112005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=602585121-28112005>><FONT face="Times New Roman" color=#000000
size=3>what kind of information is lost when going from ballots to the
matrix?</FONT></SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT><SPAN class=602585121-28112005>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.</SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT face=Arial color=#0000ff size=2><SPAN
class=602585121-28112005></SPAN></FONT><FONT face=Arial color=#0000ff
size=2><SPAN class=602585121-28112005></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT><SPAN class=602585121-28112005>> is there
anything in that data that maybe *should* be involved in determining the
winner?</SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT><SPAN class=602585121-28112005>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}.</SPAN></FONT></DIV><BR>
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<FONT face=Tahoma size=2><B>From:</B> election-methods-bounces@electorama.com
[mailto:election-methods-bounces@electorama.com] <B>On Behalf Of </B>rob
brown<BR><B>Sent:</B> Monday, November 28, 2005 3:49 PM<BR><B>To:</B>
election-methods@electorama.com<BR><B>Subject:</B> [EM] thoughts on the
pairwise matrix<BR></FONT><BR></DIV>
<DIV></DIV>In a couple recent discussions, I've found myself taking almost
contradictory positions on whether the pairwise matrix is "raw data" or
"results".<BR><BR>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.<BR><BR>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.<BR><BR>What do you consider
it?<BR><BR>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?<BR><BR>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?<BR><BR>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.<BR><BR>-rob<BR></BLOCKQUOTE></BODY></HTML>