[EM] Displaying intermediate results in Condorcet-based elections (re: Rob Brown's original question)

[Rob Brown]

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.

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.

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?

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.

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.

-rob