[EM] Tiebreaker graphs for Condorcet and other methods
mrouse1 at mrouse.com
mrouse1 at mrouse.com
Fri Jan 26 20:10:00 PST 2007
I was looking at the Yee diagrams again, and I was wondering if anyone had
created tiebreaker diagrams. By that I mean remove the part of the image
where no tiebreaker is necessary, leaving just the part where there is
some type of tie, since this is typically the area you get voting
paradoxes.
Also, I was wondering if anyone (Warren Smith? :D ) had looked into the
Bayesian regret of just those portions of the graph where there is a
definitive winner without going to a tiebreaker method, since this would
set a lower bound for this number even if a perfect tiebreaker were found.
For example, looking at Condorcet only in the areas where there are no
ties (circular or otherwise), what is the lowest Bayesian regret possible?
In addition, if the graph of minimum Bayesian regret were plotted, would
it simply be a Voronoi diagram, and would it be possible to plot this on
the Yee diagrams to see where voting methods diverge from it? And is there
a way to display the difference in two voting systems' results?
(And, as a completely separate side note, I've been playing around with
the system I originally called IFNOP, and have come up with sixteen
variations so far, which is kind of giving me a headache, especially
trying to come up with any semblance of usable pseudocode. What really
makes it sad is that it's easy enough to do by hand.)
Michael Rouse
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