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<DIV><FONT size=2><BR><FONT size=3>-----Original Message-----<BR>From: Rob Brown
<</FONT><A href="mailto:rob@hypermatch.com"><FONT
size=3>rob@hypermatch.com</FONT></A><FONT size=3>><BR>To: </FONT><A
href="mailto:election-methods@electorama.com"><FONT
size=3>election-methods@electorama.com</FONT></A><FONT size=3> <</FONT><A
href="mailto:election-methods@electorama.com"><FONT
size=3>election-methods@electorama.com</FONT></A><FONT size=3>><BR>Date:
Wednesday, October 29, 2003 3:05 PM<BR>Subject: Re: [EM] Displaying intermediate
results in Condorcet-based<BR>elections (re: Rob Brown's original
question)<BR><BR><BR>>At 09:00 AM 10/28/2003, Paul Kislanko
wrote:<BR>>>If I were going to display intermediate results in a Condorcet
election I<BR>>>think this is how I would do it. It presents all the
information the<BR>>>voters need to see how their candidate is doing
compared to all of the<BR>>>others. (I usually convert all of the count:
A>B>C style examples on this<BR>>>list to this format anyway,
because it is easier for me to spot the<BR>>>patterns of blocks of
like-minded voters).<BR>><BR>>Well, its interesting, but I do not think
that showing a pairwise matrix,<BR>>and especially a list of all ballot
combinations, is going to be the<BR>>appropriate output for most
people.<BR><BR>Here I have a philosophical problem. If you want to show
intermediate<BR>results, and you are insistent on using a pairwise matrix to
determine the<BR>winner, if you DON'T show the pairwise matrix you are
misleading the voters.<BR><BR>>I think they want something more distilled and
that instantly communicates,<BR>>as does a bar graph of scores. If I
take a quick look at a vote matrix, it<BR>>doesn't really communicate very
much to me. This is not because I am<BR>>stupid or don't understand
what the matrix represents (obviously I do), its<BR>>just that a table of
numbers is not very easy to take in in any meaningful<BR>>way to visually
oriented people. If I have trouble instantly digesting a<BR>>matrix, I
expect that mainstream uses will have *much* more trouble.<BR><BR>Agree. They
want Borda. You want Condorcet.<BR><BR>>Many people on the list have
questioned whether there is any way to<BR>>simplify the output to a set of
scores, and whether such a thing is<BR>>useful. On the first question,
I understand that finding a reasonable way<BR>>of assigning a 1-d set of
scores from a 2-d matrix is a difficult problem,<BR>>but then again, isn't
picking a single winner from a 2-d matrix a similar,<BR>>and equally
difficult, problem?<BR><BR>This is why I suggested you display the 1-d list of
votes by ballot<BR>configuration. There is no ambiguity, and no information is
lost. If you<BR>display this then you don't need to display the pairwise matrix
that you're<BR>going to finally use to determine the winner, since anyone who
cares can<BR>construct it for themselves.<BR><BR>>As I think we all agree, if
you can pick a single winner, you should by<BR>>straightforward extension be
able to rank all the candidates. In ranking<BR>>the candidates we have,
then, linearized the matrix. If it can be<BR>>linearized in a
reasonable way, I believe it can be done such that each<BR>>candidate has not
only an order, but a scalar dimension, i.e. a score -- in<BR>>an equally
reasonable way, that does not conflict with the ordering.
Maybe<BR>>this is a naive leap of logic (or maybe intuition) on my part, but
I have<BR>>yet to see an argument which leads me to believe
otherwise.<BR><BR>This is really disturbing to me. What Arrow got his Nobel
prize for was the<BR>proof that you CANNOT create a linear ranking from a
pairwise matrix. Not<BR>only can it be linearized in "a reasonable way", it can
be linearized in an<BR>infinite number of "reasonable" ways. But at the end of
the day whatever<BR>linearization you chose has to match up with your election
method, and I<BR>don't believe it is possible to do so for Condorcet-based
methods. (That is<BR>not in itself a bad thing, it is just that that the
requirement to display<BR>intermediate results is incompatible with an election
method that only<BR>selects a winner after all results are in).<BR><BR>>As
for the utility of a graph of scores: such a graph has less
information<BR>>than a pairwise matrix, but that doesn't mean it is
useless. I tend to<BR>>look at the various "outputs" like
this:<BR>><BR>>Full set of ballots -- all information<BR>>Pairwise
matrix -- lots of information<BR>>One score per candidate -- some
information<BR>>Ranking -- little information<BR>>Single winner -- least
information<BR>><BR>>Looking at a matrix, you cannot tell, for instance,
whether Nader voters<BR>>were likely to prefer Gore over Bush, as you would
see if you looked at a<BR>>count of all ballot combinations. Likewise,
looking at a set of linear<BR>>scores, you can't be tell whether McCain beat
Bradley in a pairwise<BR>>election. But it's a matter of finding the
right amount of information to<BR>>display. I say that a matrix is too
much information for most people, and<BR>>a simple ranking of candidates is
too little.<BR><BR>The matrix is LESS information than the the counts per ballot
combination,<BR>not more. But if you're going to use the matrix to determine the
winner and<BR>also want to display intermediate results, then you should display
the<BR>matrix (nobody has to look at it if they don't want to). If "a
simple<BR>ranking of candidates is to little." I am very confused, because as
I<BR>understood it was the original request was for us to help come up with
a<BR>simple ranking of
candidates....<BR><BR><BR></FONT></FONT></DIV></BODY></HTML>