[EM] Continuing: Displaying intermediate results for a Condorcet-based election

[Paul Kislanko]

-----Original Message-----
From: Rob Brown <rob at hypermatch.com>
To: election-methods at electorama.com <election-methods at electorama.com>
Date: Wednesday, October 29, 2003 3:05 PM
Subject: Re: [EM] Displaying intermediate results in Condorcet-based
elections (re: Rob Brown's original question)


>At 09:00 AM 10/28/2003, Paul Kislanko wrote:
>>If I were going to display intermediate results in a Condorcet election I
>>think this is how I would do it. It presents all the information the
>>voters need to see how their candidate is doing compared to all of the
>>others. (I usually convert all of the count: A>B>C style examples on this
>>list to this format anyway, because it is easier for me to spot the
>>patterns of blocks of like-minded voters).
>
>Well, its interesting, but I do not think that showing a pairwise matrix,
>and especially a list of all ballot combinations, is going to be the
>appropriate output for most people.

Here I have a philosophical problem. If you want to show intermediate
results, and you are insistent on using a pairwise matrix to determine the
winner, if you DON'T show the pairwise matrix you are misleading the voters.

>I think they want something more distilled and that instantly communicates,
>as does a bar graph of scores.  If I take a quick look at a vote matrix, it
>doesn't really communicate very much to me.  This is not because I am
>stupid or don't understand what the matrix represents (obviously I do), its
>just that a table of numbers is not very easy to take in in any meaningful
>way to visually oriented people.  If I have trouble instantly digesting a
>matrix, I expect that mainstream uses will have *much* more trouble.

Agree. They want Borda. You want Condorcet.

>Many people on the list have questioned whether there is any way to
>simplify the output to a set of scores, and whether such a thing is
>useful.  On the first question, I understand that finding a reasonable way
>of assigning a 1-d set of scores from a 2-d matrix is a difficult problem,
>but then again, isn't picking a single winner from a 2-d matrix a similar,
>and equally difficult, problem?

This is why I suggested you display the 1-d list of votes by ballot
configuration. There is no ambiguity, and no information is lost. If you
display this then you don't need to display the pairwise matrix that you're
going to finally use to determine the winner, since anyone who cares can
construct it for themselves.

>As I think we all agree, if you can pick a single winner, you should by
>straightforward extension be able to rank all the candidates.  In ranking
>the candidates we have, then, linearized the matrix.  If it can be
>linearized in a reasonable way, I believe it can be done such that each
>candidate has not only an order, but a scalar dimension, i.e. a score -- in
>an equally reasonable way, that does not conflict with the ordering.  Maybe
>this is a naive leap of logic (or maybe intuition) on my part, but I have
>yet to see an argument which leads me to believe otherwise.

This is really disturbing to me. What Arrow got his Nobel prize for was the
proof that you CANNOT create a linear ranking from a pairwise matrix. Not
only can it be linearized in "a reasonable way", it can be linearized in an
infinite number of "reasonable" ways. But at the end of the day whatever
linearization you chose has to match up with your election method, and I
don't believe it is possible to do so for Condorcet-based methods. (That is
not in itself a bad thing, it is just that that the requirement to display
intermediate results is incompatible with an election method that only
selects a winner after all results are in).

>As for the utility of a graph of scores: such a graph has less information
>than a pairwise matrix,  but that doesn't mean it is useless.  I tend to
>look at the various "outputs" like this:
>
>Full set of ballots -- all information
>Pairwise matrix -- lots of information
>One score per candidate -- some information
>Ranking -- little information
>Single winner -- least information
>
>Looking at a matrix, you cannot tell, for instance, whether Nader voters
>were likely to prefer Gore over Bush, as you would see if you looked at a
>count of all ballot combinations.  Likewise, looking at a set of linear
>scores, you can't be tell whether McCain beat Bradley in a pairwise
>election.  But it's a matter of finding the right amount of information to
>display.  I say that a matrix is too much information for most people, and
>a simple ranking of candidates is too little.

The matrix is LESS information than the the counts per ballot combination,
not more. But if you're going to use the matrix to determine the winner and
also want to display intermediate results, then you should display the
matrix (nobody has to look at it if they don't want to). If "a simple
ranking of candidates is to little." I am very confused, because as I
understood it was the original request was for us to help come up with a
simple ranking of candidates....


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