Paul's Internet Landfill/ lj/ Voting and pi

Voting and pi

When I die and go to Hell for being a bad person, maybe I will have to sit through bylaw amendment meetings for the rest of eternity.

In other news, voting is like pi.

Pi is an irrational mathematical constant that relates the circumference and area of a circle to its radius. Voting is the process of choosing some option from a list by having people cast ballots.

You can't actually compute numerically with pi because it is irrational. You can't get a perfect voting system because voting is hard. (I saw a good talk by Don Saari that blew my mind about this stuff. Even choosing one candidate when you have three or more choices is hard, and people are starting to understand why.)

So what do we do? When we have the radius of a circle and want to know its area, we approximate pi. People often use 3.14 as an approximation, but 3.14159 is another common choice. Some people use 3.

When we want to vote on some decision, we use a voting system. Runoff voting is one possibility, and mixed-member representation is another. Some people use first-past-the-post.

3 is an okay approximation for pi, sometimes. When I am sewing and need to approximate the amount of thread I need to cover a seam, I use something even rougher than 3. I certainly don't use 3.14159.

FPTP is an okay approximation for voting, sometimes. When your question is not so important or you need an answer right away, you can use it. Often it will give you an answer that resembles what you want.

But if you care about your circles being circular and not hexagonal, you don't use 3 as your approximation. If you care about the proportions to which your voters favour different parties and not just the overall outcome, you don't use FPTP.

It takes more work to approximate pi as 3.14 or 3.14159 than 3, but when the results matter you do the work.

My claim is that seat allocation in federal and provincial elections matter, and so it is worth doing the work to use a system that takes more calculation than FPTP. In fact, so long as the voting procedure is reasonable and the tallying procedure is well-specified and understandable by people who are smart at math, I think I am okay (speaking as somebody who used to understand math). Of course, there is no need to go overboard.

That's why I think the argument that "we should keep FPTP because it is simple to use and easy to understand" is flawed.

I don't know whether that's a good analogy (it takes upper elementary school to understand, I guess) but it seems pretty fair to me.

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Mood: flustered