Talk:McKelvey–Schofield chaos theorem

Example Unclear

The example provided was a little vague so I independently worked out an example of this theorem:

For Euclidean voters i, ii, and iii whose policy preferences are centered at

i: (0.125, 0.649) ii: (0.375, 0.216) iii: (-0.25, 0)

and policies A, B, C

located at

A: (0, 0.866) B: (0.5, 0) C: (-0.5, 0)

We see an example of no condor et winner. The way I found this was by placing the policies at vertices of an equilateral triangle and then placing the voters centers along different sides of the triangle, each near one of the policies. Anyone else think we should change the example? 75.25.161.74 (talk) 23:37, 27 September 2024 (UTC)

I agree that the current example is a little vague but I don't think it should be removed. I think the important part of the theorem is that the cycles are abundant, and every policy gets beaten by many other policies. The current example illustrates why every policy will be beaten by a lot of other policies (because of circles). It doesn't show that cycles are abundant though, but having an example of a Condorcet cycle doesn't really help that either. Though maybe I'm biased because I wrote the example text and made the image. Paditor (talk) 11:21, 28 September 2024 (UTC)