[EM] re: diagrams

[Bart Ingles]

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