Anyway, for the statement of the theorem, I'll quote the Handbook of Social Choice and Welfare (Chap. 13, p.27):

]]>Richard McKelvey has stated a famous theorem: Suppose the alternatives lie in an n-dimensional space (n > 1), we choose between alternatives by majority voting (as is standard in legislation), and there is no Condorcet winner. Given any two proposals, a and b, there exists a sequence of proposals, {a'_i}(i = 0, ..., n) such that a'_0 = a, a'_n = b, and a'_i defeats a'_{i+1} for all i = 0, ..., n−1. That is, by a suitably chosen agenda, any proposal can defeat any other if there is no Condorcet winner.

Using some of the ideas in your construction I found a slightly smaller one on 8 nodes

cd7a0a63-764a-466c-ab71-8fa9552bf2fb-image.png

]]>I found this presentation very interesting:

One point brought up by an audience member during the Q&A was that QV seems to illuminate the relative preferences of the electorate, which show up in the presenter's data as approximate Gaussian distributions and the grouping together of different strata of right-wing and left-wing groups, which does not occur without the quadratic cost.

]]>https://psephomancy.medium.com/a-majority-of-voters-1d990a53b089

]]>I like the visual layout that you provided, and I haven't seen anything with the "indifference lines". It's similar to this: https://ncase.me/ballot/, which you're probably familiar with. I'd like to be able to start with ballot numbers and then have them displayed, rather than being limited to manipulating the image (which I think is fantastic too).

I was wondering too if your program calculates the distance between the two other options and then sets the second choice as the closest one.

Here's a link to the crude pages that I put together: https://wethepeople.ca/WTP_IRV-DEp1tester.php

I would definitely like to collaborate with you on an "evaluation framework".

]]>