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 
understanding.

--Dan Keshet
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