[EM] Geometric example of Condorcet Cycle

[fsimmons at pcc.edu]

My recent example of four candidates in a planar geometric issue space could be interpreted as an 
election to determine which of the four towns would host the next harvest ball, or something like that.

The respective town coordinates in miles East and North of town B were  (0,2), (0,0), (1,0) and (4,2).

The respective town populations were in proportion 2:1:1:1.

This leads to the preference profiles

40%  A>B>C>D
20%  B>C>A>D
20%  C>B>A>D
20%  D>C>A>B

Which makes D a Condorcet loser and creates the cycle

A beats B beats C beats A.

I want to point out that this example has wiggle room, i.e. both the town distances and the town 
populations can be perturbed in arbitrary directions without changing the preference profiles, as long as 
the magnitude of the perturbations are not too large.

In other words, the example is not "marginal."