I think that a simple model of perfectly proportional representation is to make a network flow problem and just simply set each voter's flow to be equal.

In this network flow model, a cardinal ballot would be represented as capacity for flow between a voter and each candidate. I'll put a link here to wikipedia just for general reference: https://en.wikipedia.org/wiki/Network_flow_problem

How is it possible to have each voter's flow equal? I am thinking there would have to be a change to the rules for the elected body. We might have to allow winners to have different weights. We might have to allow any amount of winners. The benefit is we get perfectly proportional representation.

@culi I'm interested in this caching. Is it a programming pattern?

@cfrank

Here's a simple example to show proportionality. This example works the same no matter what the measure of support. Basically, all these measures are clones of STV but without vote splitting. The measures I'm talking about are score, smallest pairwise win, and strongest beatpath. Also, I should say that I don't really know if the measures would work for sorting.

Setup:
2 parties: A, B.
2 seats.
100 voters.
quota: 50 voters.

Round 1:
The votes are A 55, B 45.
The best quotas of 50 voters give A 50 and B 45.
A gets a seat. The quota of 50 A-voters are removed.

Round 2:
Now we count the remaining voters, A 5, B 45.
B gets a seat.

What if we could sequentially take the biggest chunk of support for a candidate over a quota of voters?

Think of a voronoi cell. There is a perfect condorcet winner for each cell. However, we only have so many seats. So we can sort voters by how much they like the candidate for each candidate and add up support over however many voters are needed for a seat.

We would elect the candidate with the biggest support over a quota of voters and then consider the remaining voters. There are many options for measuring support:

• sum of scores
• minimax: smallest pairwise win
• schulze: strongest beatpath

We could use any voting method really, but I think we need a way to sort voters so we can add them one at a time starting with the most supportive. It's easy to see how a voter's support contributes to a sum. It's a little harder to see how a vote contributes to the smallest pairwise win. It's harder still to see contribution to a strongest beatpath.

Back to the motivation - The benefit is no vote splitting.

Also, we could do better by some optimization, which could either be realistic or not, instead of sequential selection.

@culi The OKLrCH is interesting. It seems to give the least amount of banding when cycling through hues, at least in my eyes. I would think it would be really good for measuring distance. Well, with one transformation. I would use the hue (H) as a polar angle in cylindrical coordinates and C as the radius. Then convert to cartesian and measure distance. I don't know how I would actually implement this, but it's an idea

... I guess color space is like a double cone with extra pointy parts. I wonder how different this double cone would be from the RGB cube on its diagonal.

This is a cool video about computer color blending: https://www.youtube.com/watch?v=LKnqECcg6Gw

I'm not sure if it applies to the problems you're trying to solve with color distance. It's just generally related.

Codesandbox

If you have a github repo, you can automatically deploy to CodeSandbox.io to give a sandbox for your creations.

Here's an example I'm working on: https://codesandbox.io/s/github/paretoman/votekit

Embeds

Also, we might be able to embed examples here: https://codesandbox.io/docs/embedding

But that is something that would have to be specifically set up somehow on NodeBB, and I don't really know about that. For now, a link is good.