There are a lot of theorems around voting. Many of them get trotted out in highly inappropriate ways. But even interpreted correctly their results sound quite disturbing: There are no fair voting systems, tactical voting is always possible, etc. Sorry. That was wrong too. There are no fair voting systems within the class of voting systems the theorems describe. The voting system I am describing is not a member of those classes, so the theorems do not apply.
I am going to propose to you a voting system you may think is impossible. It has the following properties:
- It is as easy to explain as FPTP. Possibly easier. In particular your vote is identical to that under FPTP – you cast a vote for a single candidate
- It is constituency based, with one representative per constituency, and the constituencies may be arranged however you like – geographically in particular works fine. It thus upholds our fine British traditions, unlike the PR systems which people seem to object to because they can’t have their letter ignored by their own personal MP.
- As long as the constituencies have equal populations, no voter is disenfranchised by the constituency in which they live. (Larger constituencies are inherently disenfranchising in single-representative-per-constituency models – by definition you have a larger number of people having the same number of votes as a smaller number of people)
- The results will usually be close to proportional representation. Not always, but usually (this qualification will make more sense later).
- There is no incentive to vote tactically. None. You vote for the candidate you most want to see in office. Anything else would be madness
Given the above shopping list, you probably think I’m misrepresenting the facts. It sounds too good to be true.
Well, it kindof is. There is a catch, and it’s a big one. I think it has desirable and undesirable features (in particular there’s one really major problem with it), but even with the above list I’m not sure I actually endorse it. Consider this a thought experiment more than a proposal.
So, what is this magic voting system that flagrantly disregards all the theorems that should say it’s impossible? Here it is:
- MPs run as they currently do – a smallish number of candidates stand for a single constituency
- People cast a vote as they currently do – each selects a single candidate to cast their vote for
- Once all of the votes have been cast, you pick one voter at random and use their choice
- Wait, what?
At this point you probably think I’m crazy. Well, maybe so, but I’m crazy like a – actually, no. Let’s not go there.
In order to address some of the obvious objections to this, I will take a leaf out of Scott Adams’s blog and conduct an interview with someone who knows I’m crazy. Me. Or rather my online handle.
DRMacIver: So, are you crazy?
David: Probably. But this is actually a remarkably sane idea. It goes against our intuition, but our intuition is rubbish for voting.
DRMacIver: It is? Why?
David: Beyond the scope of this. Google for “Voting Paradox”. Or read these Socratic Dialogues on voting.
DRMacIver: How did you just include a link in a spoken interview?
DRMacIver: Ok, so, some real questions. Why do the various things like Arrow’s Theorem or the Gibbard-Satterthwaite theorem not apply?
David: Because they only apply to deterministic systems. This one has a random element. It’s essentially a very specialised case of randomly selecting a dictator for each decision (which is itself a form of sortition).
DRMacIver: Is there any precedent for this?
David: For this particular one? No, not really. At least, not that I know of. Election by lottery has some precedent though. The Doges of Venice were elected by a complex system involving the drawing of lots and election by lot was a major and essential feature of Athenian Democracy
David: Quite. I genuinely don’t know why it’s not used more today.
DRMacIver: Why should it be? What’s good about it?
David: Well the advantage of the Athenian system is that decision making is not put in the hands solely of those who most want to be in politics and can convince people to elect them – which has an unfortunate tendency to result in wealthy people with too much time on their hands being the ones who actually get into power – but instead spreads the decision making process throughout the population.
DRMacIver: So why aren’t you proposing that instead?
David: Well, I’m not proposing anything. Given the choice between Athenian Democracy and what I’ve described, I genuinely don’t know which one I’d choose. What I like about my current proposal is how remarkably close it is to the current system whilst fairly resolving all sort of injustices with the current system.
DRMacIver: Like what?
David: Well, there are 650 members of the house of commons. Suppose 10% of the population supported the kitten party. How many kitten MPs do you think there should be?
DRMacIver: Well, clearly this is a proportional representation argument, but I’ll play along. Let’s see, carry the one… There should be 65 seats.
David: Right. But suppose those 10% were instead spread uniformly across the country: Each constituency only has around 10% kitten party supporters.
DRMacIver: Right. And thus no constituency elects a kitten party MP because they’re nowhere in the majority. This is classic PR stuff. But people like having their own personal MP tied to their area – it’s one of the reasons PR doesn’t get any traction.
David: Indeed. But the convenient feature here is that you get to keep that while still getting something close to PR.
DRMacIver: Huh? How is what you’re proposing close to PR? It sounds like it has exactly the same problem.
David: Ah, but this is where the magic of probability comes in! Each of those constituencies will have about a 10% chance of electing a kitten party MP. So roughly 10% of the constituencies will get a kitten, and you’ll get about 65 of them in parliament.
DRMacIver: There were a lot of weasel words in that sentence.
David: Yes, there were. And this is where the least desirable of the proposal comes in: There’s a lot of purely random variation in a party’s support. The kitten party (with their 10% of the vote) will typically have a variation of about 15 seats purely by random chance: That’s a lot of their membership. For larger parties the variation isn’t much larger – if you have 50% of the vote then you expect your seats to vary by about 25 either way. In a close race this can be a big deal.
DRMacIver: Let me see if I got that. If you have two parties with roughly the same amount of support, you’re essentially flipping a coin to see which one wins?
David: Yes. Which is of course massively different from the current system.
DRMacIver: I’m going to let that one slide… so what happens if, for example, you just randomly select all 70 people in the country who voted for the “Church of Christ the Bus” party?
David: What happens if all 70 of those people win the lottery and put their money into funding that party?
David: The chances are really really low. If you’re only expecting to get a tiny fraction of a single seat, the chances of you getting that one seat are slim and the chances of you getting more than one seat are basically negligible. Also, because minority parties tend to be geographically clustered rather than spread out everywhere the maximum number of seats they can get is basically bounded.
DRMacIver: So this can’t elect crazy minority parties?
David: Oh no, it totally can if the minority is large enough. For example the BNP have a shot at getting in under this system.
DRMacIver: Isn’t that a massive flaw?
David: No. I don’t regard it as one. The BNP have a percentage of the voters, they should get a percentage of the say. The fact that I consider someone to be utterly despicable doesn’t give me the right to disenfranchise them. Also, as Timothy Gowers so eloquently put it, WE SHOULD NOT LET THE BNP DICTATE HOW WE RUN OUR POLITICS.
DRMacIver: Ok, fine, but let me make sure I understand: It is possible for this system to elect an MP which is supported only by a tiny minority of the constituency?
David: Yes, absolutely. It’s a trade off. I don’t necessarily think that’s a bad thing though.
DRMacIver: So a staunchly Labour area could get a Conservative MP?
David: Yes, that’s right.
DRMacIver: Are you totally fucked in the head?
David: I don’t think so.
DRMacIver: How is that not completely broken?
David: Well, for starters, it’s a nice thing in that it stirs things up: If you try something different every now and then, maybe it won’t be as awful as you thought it would be. You might learn something. But more importantly it’s a trade off – in the kitten party example, 10% of the population are currently disatisfied. In the new system 10% of the constituencies will get a kitten MP, which will disastify 90% of them. that’s 9% of people disastisfied by the kitten MPs, which is 1% of the population better than before. That’s some six hundred thousand people we’ve just made happier with kittens.
DRMacIver: Hrm. It feels wrong.
David: But how can it feel wrong when the numbers are so right?
Maf: Assuming only two choices (kitten vs. non-kitten) in your proposed system, isn’t the proportion of dissatisfied voters actually 18%, i.e. 90% of the voters in the 10% of the constituencies that get a kitten MP plus 10% of the voters in the 90% of the constituencies that do not?
David: Bugger. You’re absolutely right. This scuppers a key part of my argument. I have to go away and think about this (and read more). Perhaps “number of happy people” is the wrong metric to be considering, as it should have been obvious that that was always going to be maximised by picking the candidates with the majority first-preference.
DRMacIver: So your idea is shit?
David: No, all the desirable properties I listed still hold. It’s just not a happiness maximiser.