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

[Adam Haas Tarr]

>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.

I agree.  I think the limit of what I can digest quickly and visually would be a 
directed graph.  This could be a very nice way to display scores - you could 
arrange things so that defeats point down whenever possible, so that the Smith 
set would be at the top, and the Condorcet losers would be at the bottom.

That said, I still think this is probably too much detail for the average 
CNN.com user.  There could be a link to "verbose results" that displayed things 
this way, and perhaps a link to "even more verbose results" that displayed the 
pairwise 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.

Well, finding a set of scores that reflect the way the election was decided is 
not hard.  For example, using beatpath scores of each loser against the winner 
works.  The real trick is finding a set of scores that convey information you 
actually care about.

I maintain that the best such score would be each candidate's pairwise vote 
total against the winner, and the winner's pairwise vote total against the 
losing candidate with the highest score.  If such an approach led to a losing 
candidate having a higher score than the winner, then I would fall back on 
beatpaths, as I (eventually) explained in my other post(s).

-Adam