Interesting, the diagram can be viewed as either a two-dimensional diagram or 3-D object (in which the triangle is an intersection of a plane with three Cartesian axes). The diagram works either way, but taken as 3-D, it shows that cycles are a natural and predictable outcome when there are three candidates and three policy dimensions (or presumably n-candidates and n-dimensions where n > 2).
Dan Keshet wrote:
For what it's worth, I drew up a pretty simplistic diagram to make demonstrations of how a cycle can happen in election results:
http://www.channel1.com/users/dkesh/green/voting/condorcetparadox.png (available in SVG format as well)
It's a simple triangle with a bunch of dots around it. A majority of the dots are closer to B than A, C than B, and A than C.
I have also used even simpler diagrams (not online) with dots bunched around three points on a line, heavier on the edges than in the middle, to demonstrate a situation where IRV fails.
I find that for some visual thinkers the diagrams really help their
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