On 09/15/2012 09:55 AM, Juho Laatu wrote:
On 15.9.2012, at 6.05, Jeffrey O'Neill wrote:
You can also now save Condorcet results in HTML format but still
working on the best graphics to visualize Condorcet results.
One solution is to support minmax(margins). With that method you can
simply draw a histogram that indicates how many new (first preference)
votes each candidate would need to win (or tie) with the winner /
current leader.
That also works with minmax(wv), and similar approaches can work for
least reversal methods and those that use sums of victories rather than
minimum/maximum ones. However, those visualization methods are still
linked to specific voting methods, and thus don't provide a general
visualization of the pairwise results.
I suppose one could use something similar with Kemeny as well: use
integer programming to find the pairwise sum of scores for the best
transitive ordering that puts X first. That is X's score. Then do it for
Y and Z. Assuming X wins, all other scores will be lower than X's. The
relationship between additional votes and Kemeny scores might not be
obvious to the end user, though.
- I have seen 2D graphs that show all parwise wins, e.g. in Debian. They
are however quite difficult to draw automatically, and the positioning
of candidates in the drawing space (e.g. higher, lower) may not be
neutral (unless they are in one row or circle).
These can be "decluttered" by showing graphs where candidate X has an
arrow to candidate Y iff X beats Y pairwise, otherwise there is no
arrow. Then graph visualization programs can be used to arrange the
candidates in a way so that candidates with more pairwise victories (or
stronger ones, or whatnot) are closer to the top, or so that Smith set
members always appear above non-Smith set members.
If one wants to visualize Ranked Pairs, it'd be easy to simply color the
path throughout the graph to correspond with the pairwise
relations/defeats picked by Ranked Pairs.
----
Election-Methods mailing list - see http://electorama.com/em for list info
