A “perfect” voting system

AN UPDATE FROM THE FUTURE: I come to you from the year 2013 to tell you that there is a new version of this post. This is one of my popular posts ever, but I have since updated my beliefs around it somewhat and I’m a little embarrassed by some of the writing in this one. It will remain around for posterity, but as a persuasive and descriptive piece you should really be reading and referencing my later piece “Towards a more perfect democracy

No, seriously, go read that one instead of this. Shoo.


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:

  1. MPs run as they currently do – a smallish number of candidates stand for a single constituency
  2. People cast a vote as they currently do – each selects a single candidate to cast their vote for
  3. Once all of the votes have been cast, you pick one voter at random and use their choice
  4. 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 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?
David: Magic.
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
DRMacIver: Huh
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?
DRMacIver: What?
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.

This entry was posted in voting on by .

77 thoughts on “A “perfect” voting system

  1. iamreddave

    Is it naive to assume that this will not increase the number of candidates? In this system if everyone put themselves forward you would have a Sortition system. So you would have to have a high cost of entry deposit to discourage sortition. Also you would have all the costs of counting votes as otherwise you could not have refundable deposits based on vote number.

    So essentially is this a sortition system with an entry fee to be in the running? And the level of entry fee is picked by who? Too high and you will only have one party. To low and everyone will join. At the current deposit amount i predict many people would enter the election race.

    1. david Post author

      Yes, absolutely that could happen. I don’t know where the equilibrium would settle, but I’m sure it would be larger than it is currently. I’m not sure that’s a major problem. It might even be a good thing.

      But even then it’s not a sortition: The candidates still have to convince the populace to vote for them, same as they currently do. They don’t have to win the majority vote to do so, but their probability of getting in is still directly proportional to how many people they can get to vote for them.

      1. iamreddave

        Sorry I wasn’t clear. I meant imagine a situation where it cost nothing to go for election. Further imagine that everyone then went for election. And that everyone voted for themselves. Then your system would be a sortition system as every person would be equally likely to be elected.

        But that would require three things to happen that would not happen so the danger of this system become sortition is minimal.

      2. david Post author

        Yes, I can imagine that happening, but I don’t think it happens inevitably, and even as a degenerate case it’s not that bad – sortition is a perfectly valid way of electing a representative! (Indeed it’s very close or even identical to Athenian Democracy).

    2. Antonio Cangiano

      Require a given number of signatures to be considered as a candidate (e.g., 10%). For example, if your town has 30,000 eligible voters, require 3000 signatures to run. This would lead to just a few candidates, all with proven support of some of the local populace.

      1. Simon Rigelsford

        Problem with that is that people will be reluctant to sign for parties which it is not socially acceptable to support, e.g. the “extremists.” While this may seem tempting, we have secret ballots for a reason.

  2. Achllies

    This system does not violate all the theorems. It is well known that dictatorship is the one voting system that satisfies all the nice properties you would want. The system you describe is a called a randomized dictator ( cause you randomly select the one dictator ) and hence has all the nice properties. Of course, its not desirable cause it would be rather unpopular to enact one !

    1. david Post author

      Sorry, I’m fully aware that it does not violate the theorems – it works because it doesn’t satisfy the hypothesis of the theorems that they only apply to deterministic systems. I have modified the post accordingly.

      It’s true that this is a randomized dictator system. However it is a randomized dictator system which avoids many of the associated social problems whilst retaining the mathematical benefits: You’re electing a representative, and you are not given foreknowledge of whether you are the dictator, so there’s no danger of the power going to your head or you being bribed. Further, because you’re doing this 650 times (or whatever) you have the weight of statistics on your side to guarantee that things don’t go too badly wrong.

  3. beza1e1

    “you pick one voter at random”

    Who is “you” and how is “at random” done?

    Paper votes can be counted again and again and yield the same deterministic result. This means the election process can be checked for fraud. How would you check randomness?

    1. david Post author

      I’m pretty sure the technical problems are surmountable, if possibly expensive to do so. Here is a possibly overengineered solution for how I would do it off the top of my head:

      * Every ballot paper is given a unique number (these will be allocated contiguously – so a region will have all its ballots lying in [0, n]. The papers are shuffled in such a way as to ensure your number does not correspond to when you arrived at the polling station.
      * The ballot papers are sorted roughly into piles (say sorted by the 100s and higher digits)
      * The random number generator is a shielded black box device into which you simply enter the maximum number and get out an LCD screen. The number is generated before you look at the votes, so even if it is biased it is hard to bias it usefullly. Additionally the designed are an open standard subject to independent review and manufacturers are subject to random oversight.
      * When the number is generated it is done by several witnesses and ecorded somewhere.
      * You then look for the ballot paper with that number. If it has been scratched, or was otherwise unused, you repeat the previous step.
      * All proceedings are recorded and uploaded to the internet to be publicly visible for oversight.

      1. Paul Crowley

        You don’t need a black box, just a good hash function H

        – Each candidate is numbered
        – All candidates make up a random bitstring R_c (say 256 bits)
        – All candidates publish H(R_c)
        – Ballots are sorted into counted piles so they can be numbered. No effort need be made to shuffle them, so long as we can arrange to have a public bijective map between ballots and integers 0…N-1.
        – The PRNG used to pick the ballot is seeded with H(R_1 | R_2 | … | R_n)
        – The PRNG generates i in 0…N-1 in a fair, deterministic way based on the seed.
        – i is used to select the ballot that determines the election

      2. Ian Walker

        You don’t even need an electronic device. Divide the ballot papers into six piles, number them one to six, roll a dice. Repeat until done – even with 100,000 papers it will take no more than seven rounds (since 6^7 = 279936) You could even have the candidates take turns to roll the dice

      3. david Post author

        That’s a neat solution, thanks. I had previously been thinking that you needed a machine for doing this. Not needing one is a nice feature.

    2. Paul Keeble

      In any one consituency you couldn’t detect fraud. On the other hand you could check for fraud across a range of votes. Proving fraud would be tricky, but detecting it is easy enough.

      Interesting idea, bonkers of course! But what it does is put determinism up as being a property of a voting system, which opens up a host of possibilities to play with the level of determinism.

    1. david Post author

      Thanks for the links. I’m not surprised this idea isn’t novel – it would have frankly been surprising if it were.

  4. Michael Chermside

    I realize you are not suggesting immediately implementing this system, just point out it’s interesting properties. However, I think that there is a significant flaw in this system: it fails to discourage extremism.

    With the randomized election system you describe, people with extreme views are welcome to vote for extreme candidates. On the other hand, with some other systems (including FPTP which is used today) rational voters, realizing that an extremist candidate has no chance of success, are encouraged to find a more moderate candidate who is acceptable to a larger percentage of the population. And while that does a poor job of exactly reflecting the wishes of the voters, I think it is good for society as a whole because it encourages people to find compromises that are acceptable.

    1. david Post author

      I don’t agree that this is a problem. In fact I think this is a desirable feature. The problem is that by discouraging extremism and encouraging “compromises” what you are actually encouraging is polarisation of views. By allowing minorities to have a say that reflects their actual opinions you are enabling the whole spectrum of political discourse instead of a two party system. Sure, this may get extremists into power, but it will also get more moderate minorities into power. You should discourage extremists by discouraging extremists in voice and in deed, not by crippling your political system to exclude votes you don’t like.

      1. tomcpp

        I see a bit of a problem. You would seriously allow this : http://www.youtube.com/watch?v=UzguXsBYReI if a minority desired it ?

        The random voting system has the problem in what you might call “terminal” candidates. Historical examples might include people like Hitler and Khomeini (there are lots more examples of this in the middle east, and I’m sure elsewhere too). The issue is that if these people are elected you will get a situation 99.9% of the population finds utterly repulsive and yet the elected officials prevent further elections, keeping themselves in power.

        The only way to prevent these terminal candidates would be to have “super political actors”, people who have both the means and the duty to safeguard the next election. In order to do this they would obviously need the ability to use more violence than all other factions *combined* (e.g. they would need a blanket permission to fire at the police if the police was under political control), and they themselves would have to be utterly unaccountable (since you can’t let one of these terminal candidates judge them, the system would fail).

        I think this system is utterly incompatible with what might perhaps best be called “evil”. One bad fish can and will crash the whole system, and it’s a matter of time until such a fish is elected.

      2. david Post author

        Tom, one of us is misunderstanding the other..

        The proposed system absolutely and fundamentally does not randomly select a single leader for the country. It randomly selects a single representative for each constituency. There are the a large enough number of constituencies that the chances of a minority with even 5% of the vote achieving a majority are so close to negligible that they’d be better off pursuing alternative strategies like vote rigging and violent revolution.

        Speaking of violent revolution: No, I absolutely would not allow that if a minority desired it. I wouldn’t allow it if a majority desired it. There is always the possibility that a government (democratically elected or not) will go sour. That’s what revolutions are for.

  5. Brian Hurt

    The biggest problem with your proposal is one of simply psychology. We not only have to select a government that is (more or less) representative- we also have to get people to accept it’s decisions whether they support those decisions or not. Especially when people don’t support the decision, and are then looking for a reason, any reason, to invalidate the decision. This is especially true when the population is more or less evenly decided on an issue, and that thus small differences in the electoral outcome- a few officials here or there switched one way or the other- changes the outcome of the decision.

    Take a long hard look at what’s going on in the US. This is what you get when a significant fraction of the population stops believing that the government is representative. Mathematical proofs are irrelevant- people suck at math (especially people inclined to believe that any decision that they don’t like implies the government is not representative).

  6. maf.

    “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.”

    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?

    1. david Post author

      Bugger. You’re absolutely right.

      In retrospect that should have been obvious: It’s not surprising that the optimal strategy for maximising the number of happy people is to assign everyone to the most popular group.

      1. Ben

        The national dissatisfaction would average, not add. It would be 10% nationally. You’re just moving the dissatisfied into large pockets. For this to work you have to convince people to care about the national parties, not local candidates. In which case their local constituencies don’t matter that much.
        In actuality the dissatisfied population nationwide would be the average combined percentage of all the loosing parties in each constituency.

    2. knowtheory

      Only if your satisfaction is determined by your direct representation. The key feature of Proportional Representation, and this… Frequentist Representation model is that your constituency is still represented in parliament, even if your individual district/riding/whatever isn’t represented by the party of your choice. And that addresses the problem that First Past the Post systems have is that there is global underrepresentation of certain view points.

      If voters are still satisfied by having *someone* represent their POV in parliament, even if they’re not directly beholden to your vote, the voting system still works. However, what is necessary then is some sort of party structure through which ideological groups have some sort of say (election of party leaders and the like).

  7. Jon

    I think the problem here is the fashion for simple mathematical models of electoral systems that capture the election process, but do not even attempt to capture the nature of actual democratic system in question.

    The lack of certain foreknowledge does not prevent a candidate from having delusions of grandeur. They may be in a statistically safe seat for their ideology; they may simply be delusional. Nor does it stop them quickly developing the tendency to be bribed once that temptation is made available to them. With no basis given for filtering out poor candidates, the quality of candidate would likely fall.

    In the individual constituency, you are only doing it once, not 650 times. So to the voter, the weight of statistics is only on their side for national issues. In a random, multi-party election, the odds are that each MP is neither the best one nor the most popular one in the constituency. You make a passing comment about being ignored by your MP; a more substantial case needs to be made that MPs have no local impact before this becomes a serious thought experiment.

    This system might statistically balance out in terms of winning party. The price could be a Parliament of MPs that tend to be less ethical, less popular, and less capable. That might not be the case, but does capture the fundamental, fatal flaw in the thought experiment: it assumes that the inputs and consequences of elections are captured in such a simple mathematical model.

    Bear in mind Athenian Democracy most of the population was disenfranchised. Voting was for adult males with military training. Restricting votes and candidacy to some definition of “right kind of people” is a feature of most lottery based systems, including the Doges of Venice. Where lotteries are used, the lottery itself is perhaps the least significant mechanism in the system.

    Someone mentions getting 3,000 signatures to stand as a candidate. However, the average ward is only something like 6,000 voters in size. I am not sure a random system for national government but a deterministic one at the local level would produce healthy political discourse. Imagine being a citizen with a problem, and one port of call is a random individual, and the other selected by a process not considered good enough to be used nationally.

    All that said, I think there would be one very useful consequence: having some number of representatives with viewpoints are against mainstream opinion. Meta-heuristic algorithms to solve difficult problems usually involve a random element; the suppression of unpredictability is unhealthy. Forget top up lists, let’s have a top up lottery!

    1. david Post author

      Jon, just to say: This comment is full of good points which I fully intend to respond to properly. Unfortunately I accidentally trashed a half-written one and am really supposed to be working right now, so I will have to do so later!

    2. david Post author

      The promised response (apologies if I’ve left anything out. Feel free to chastise me if I have and I will correct):

      > I think the problem here is the fashion for simple mathematical models of electoral systems that capture the election process, but do not even attempt to capture the nature of actual democratic system in question.

      Be fair. This is actually extremely close to the existing actual democratic system: It’s basically the current system + randomization. It’s hardly an abstract mathematical model at all.

      > With no basis given for filtering out poor candidates, the quality of candidate would likely fall.

      I don’t understand. How is the basis different? The candidate selection system is identical.

      > In the individual constituency, you are only doing it once, not 650 times. So to the voter, the weight of statistics is only on their side for national issues.

      This is true. However the odds are weighted fairly heavily in favour of the candidates people are actually voting for. Also while people want to be represented by their MP, I feel that they also want (possibly want more) to be represented by the government as a whole.

      > You make a passing comment about being ignored by your MP; a more substantial case needs to be made that MPs have no local impact before this becomes a serious thought experiment.

      Apologies. Throw-away sarcasm rather than seriously intended point. Feel free to ignore it.

      > Bear in mind Athenian Democracy most of the population was disenfranchised. Voting was for adult males with military training. Restricting votes and candidacy to some definition of “right kind of people” is a feature of most lottery based systems, including the Doges of Venice.

      It’s a feature of this one too.

      > Where lotteries are used, the lottery itself is perhaps the least significant mechanism in the system.

      In some ways that’s true here. The lottery is only the most significant mechanism here because it’s the only one that differs from the current mechanism.

      > Someone mentions getting 3,000 signatures to stand as a candidate. However, the average ward is only something like 6,000 voters in size.

      I think 3000 was specifically mentioned in the context of the size of the constituency. A smaller constituency would definitely need a smaller number of signatures in such a model.

      > All that said, I think there would be one very useful consequence: having some number of representatives with viewpoints are against mainstream opinion. Meta-heuristic algorithms to solve difficult problems usually involve a random element; the suppression of unpredictability is unhealthy. Forget top up lists, let’s have a top up lottery!

      Agreed. I’m much more strongly in favour of a sortition based system to add some smallish number of randomly selected individuals to the house of commons than I am of this particular system. It has many of the advantages and few of the drawbacks.

  8. A

    So Surrey Heath or Richmond could be stuck with a Communist MP for 5 years. That’s alright I suppose, but he’s going to get some nasty letters and his constituents will feel unrepresented.

    1. david Post author

      Yes, it may sometimes lead to an area being very unhappy. OTOH they might find that actually their communist MP does a great job and they feel a little less polarized next time it comes around to vote. Shaking things up a little isn’t always bad.

      (I’m also inclined to think that this system would benefit from more frequent and possibly staggered elections, but that’s beyond the scope of this comment)

  9. Bruce Stephens

    Doesn’t this system make the problem (presuming it is one) of “wasted votes” even worse than FPTP? I think you could be more radical: choose the voter before anybody votes (but choose randomly since we don’t know how to do what Asimov’s story suggests).

    Or hedge your bets a bit: choose 12 people at random (for some value of 12) and have them consider the question in some depth. Since there’s a small number they could be secluded and paid in some suitable way much as juries are. And (best of all) the rest of the population could be spared listening to the arguments.

    1. david Post author

      > Doesn’t this system make the problem (presuming it is one) of “wasted votes” even worse than FPTP?

      I don’t think so. It seems to me it makes every vote count equally – the benefit derived from your vote is completely independent of what everyone else is voting. Could you clarify what you mean?

  10. Tonio Loewald

    There’s an even simpler system than this, and it’s the logical end-result of your proposed system:

    Select your house of representatives by lottery.

    It’s easy to demonstrate that 400 randomly selected people will be more likely to reflect the will of the overall population than any elected group. If you wrap your randomly selected assembly with a supporting bureaucracy (who can explain the implications of issues to them, etc.) you could have a pretty fine system.

    And this would undercut the power of political parties too.

    I can’t take credit for the idea — I first encountered it in a science fiction novel by Jack Vance (where the random selection process had been corrupted).

  11. Mark M. Fredrickson

    In “A modest proposal for election reform” (Public Choice, Vol 28, Issue 37, 1974), Abrams and Settle argue for a similar system, but instead of having ballots first cast then randomly selected, the electors are randomly selected from the population and then cast ballots. Their argument is that this saves people the trouble (cost) of voting when similar outcomes could be achieved with far fewer votes cast and tabulated. Conceivably, you could pick a single individual to be the sole elector and get the same results with less effort from the public.

    1. Dubi

      The one suggested above, at the very least, removes from the lottery those citizens who have no actual opinion, or don’t care enough to go and vote. By adding those to the mix, you’re significantly increasing “Silly Candidate” election.

  12. Bruce Stephens

    I think an opponent of this scheme could argue that since only one vote is counted, all the rest were pointless. (I entirely agree that that’s not a particularly convincing argument, but it seems at least as valid as many arguments being made in the FPTP/AV campaigns.)

    1. david Post author

      Yes, I’m sure they would. But the political rhetoric around voting systems is distressingly dishonest enough without making it up for campaigns that aren’t being run.

  13. Dubi

    I haven’t read all the comments, so I apologize if this was already raised, but why not use a mixed-member proportional system, similar to the German one? You get to keep your own MP who can ignore you individually, you get a largely-proportional system, you eliminate rouge elements like those introduced by your randomized system, and finally – you don’t have to teach people about probability and why this isn’t bonkers (this last point, by the way, shows that your “easy to explain” point is false).

    And the main argument against sortition, in my view, is that when representatives cannot seek re-election, there is a serious problem of accountability.

    1. david Post author

      No reason at all. Although I don’t know the German system myself, but in reality I’m more in favour of some sort of deterministic proportional representation system which it sounds like an instance of. That being said, this system does have some compelling features the German one almost certainly lacks – in particular the fact that it’s completely impossible to vote tactically in this one is quite nice.

      RE a sortition and accountability: Pay members tolerably well (worse than ours currently are, but enough to be comfortable), but run an approval poll of some sort on exit – the candidates with the highest approval get a large cash bonus.

      Ok, maybe that doesn’t work. But it’s worth thinking about. :-)

      1. Dubi

        The German system, broadly speaking (actually, this is the old one, they changed it since in a way I’ll discuss below):

        You get one vote, for your single-member district, which goes by FPTP. Districts represent approx. half of the seats in parliament. After all votes are tallied, the remainder of the seats are distributed between the parties so as to achieve results that are closest as possible to full proportionality. The number of seats in the house can fluctuate a bit to accommodate best proportionality.
        End of story. Very little room for tactical voting.

        The new version has two votes – one for the district and one for the PR pool. They did the change because they wanted local reps to be more accountable, which turned out to be a problem with the one vote.

        BTW, you’re wrong in claiming there’s no room for tactical voting in your system. Tactical voting can also relate to the entire system (I’d rather increase the Labour’s chances at a majority than vote in a single-seat party which will stay outside of the government anyway, for example).

      2. david Post author

        Hmm. That’s a good point: It still makes sense to perform party-level tactical decisions (which is going to be true in any party-affiliation representative system). I was thinking purely in terms of tactical voting for electing individual candidates – there is no possibly choice other than “vote for this candidate” you can use to ensure your chosen candidate gets into power.

        Thanks for the explanation of the German system.

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  15. Peter

    Can’t remember who told me about this system, but it’s my favourite:

    Anyone can vote for themselves at any time and in so doing instantly becomes prime minister / president / supreme dictator.

    However, in doing so, the person who previously held the title is instantly decapitated by remote-controlled impossible-to-remove necklace of plastic explosives.

    You are free to reign and your word is law so long as –
    -> you do not remove the collar
    -> you do not prevent voting

    I think we’d end up with a pretty stable government!

  16. Frieder Wittmann

    Great, but I think you’re missing one more big requirement. Your vote must be secret.
    That is, there must be no way for YOU to prove others how you voted. If not, bribery and enforcement become possible.

    To make things even more complicated, it would also be good if you can be sure and CHECK at any point that you vote was counted the way you intended. I don’t know if there is a solution to this, but I’m imagining something like a hash code, that you see the moment you vote, together with feedback. That is, you can actually see, that your vote got counted the moment you vote and then later you can use the hash code to see, that the data base was not corrupted. Of course you should not be able to prove how you voted.

    1. david Post author

      Yes, I was definitely considering secret voting as read.

      one thing that was suggested is that this works much better if you actually just count the votes and then use that count to work out the result – you still do everything as I described, but you don’t *actually* pick a vote, you just run a process logically equivalent to it based on the aggregate counts.

      1. david Post author

        It depends what you’re trying to explain. What to do is easy. How it works is easy. Why it’s fair isn’t so easy, but I’d rather have a hard proof of fairness than an easy proof of unfairness

  17. Dale Sheldon-Hess

    The random selections for Venetian elections were to pick the electors, NOT to pick the winner.

    But the electors, after deliberating, actually voted by using a form of approval voting; a method which also side-steps Arrow and G-S (which, in addition to only applying to deterministic methods (which approval is), also apply only to ranking-based methods of which approval is not.)

    Also, “random ballot” has a Bayesian regret (a measure of voter dis-satisfaction with the results of the election) about twice as high as FPTP, while approval has a regret three times lower.


    1. david Post author

      I’m suspicious of approval voting. Fundamentally as a voter it lets me give a strict subset of a ranked system which includes RON (reopen nominations), and it doesn’t actually let me express my desires much better than simple plurality (ie not very at all).

      Since my prior error was pointed out I’m not surprised random ballot doesn’t minimise regret. The appeal of this idea is the combination of constituencies, PR and no tactical voting at the candidate level.

  18. Warren D Smith

    This “random ballot” voting system was invented previously. Gibbard, in a famous paper in (I think) the late 1970s, proved it is one of the few voting systems in which honest voting is best strategy. Another is “random pair” where the votes are rank-orderings of the candidates, a random pair of candidates is then chosen, and the ballots are used to elect the winner within that pair, via simple majority vote. Both random ballot
    and random pair are generally regarded (and Gibbard regarded them as) very bad voting systems despite this honesty-property.

    For more info, see this webpage:

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  21. gowers

    One compromise that might deal with the problem (or perceived problem) of candidates getting elected with only a very small proportion of the vote would be to make the probabilities proportional to the square of the percentage of votes instead. Then the chances of a candidate getting elected with 5% of the vote would be more like 1/400 than 1/20. (I say “more like” because the squares of the proportions of votes do not add up to 1, but they will typically add up to at least 1/2.)

    Of course, in the eyes of the general public this would be heaping craziness upon craziness, so I’m not expecting to see it implemented any time soon …

    1. david Post author

      Hmm. I’m not sure that’s a good idea – it loses the appealing expected proportionality of using straight random ballot.

      The solution for this that someone suggested and I liked was to use just a straight cutoff – if the vote is under some fraction reject any draws for that candidate. It causes a mild incentive for minority voters to vote tactically, but it also helps keep the number of candidates under control

      1. gowers

        I’m not too bothered by the proportionality — that’s what makes it a compromise. However, it has a worse defect that I hadn’t thought of, which is that it doesn’t even give the same expected reward to two parties with an equal share of the vote: the reward depends on how geographically concentrated the support for a party is.

        In general I don’t like sharp cutoffs for anything, though perhaps here one could argue that if the discontinuity is just in the probability rather than in the outcome then it is less serious.

        I forgot to say in my previous comment that I very much like the idea of using probability in politics, though I think it would be impossible to sell it. I would go further and have it for votes in the House of Commons. I don’t see why a party with 60% of seats should get 100% of the power, and probability can help in this respect. (Of course, this would be completely unworkable unless policies were bundled together into broad programmes, but I don’t think that it would be impossible to do that.)

      2. david Post author

        I’m not sure, but I think the two issues (proportionality and geographical distribution) may be inextricably linked in this model.

        Suppose your probability of winning in a constituency where you have a fraction p of the vote is f(p). Let p_1, …, p_n be your representation in constituencies 1 to n. Then your expected number of candidates is sum f(p_i). In order for the voting mechanism to not be geographically sensitive, this has to be be constant as you vary the p_i whilst holding sum p_i constant (avg(p_i) being the proportion of the population you get, assuming same-population constituencies). So you’ve got sum f(p_i) = g(sum p_i). I’ve not thought through the details, but with continuity assumptions on f and possibly assumptions that f is not dependent on the number of constituencies I’m pretty sure this implies f is linear (and because it should map 0 to 0 and 1 to 1 this assumes f(x) = x).

        I agree about the dislike of sharp cutoffs. but at least there is an obvious cutoff point here: If you do not expect to be able to elect at least one candidate based on your fraction of this constituency (if that fraction were represented elsewhere) then you don’t qualify. e.g. you need 1/650th of the vote in the UK.

        I agree completely with what you said about probability in politics: Both the good features and the near impossibility of selling it.

  22. Norwegian Guy

    I see one additional problem with this system that as far as I can see has not been mentioned. Since chance plays such a large role in this election process, it will be significantly harder – an much more random – for a politician to be reelected. Now, this is not always a bad thing, but it is not entirely unproblematic either. Even if 2/3 of the the people in your constituency vote for you, there is still 1/3 chance that you will lose. This means that a popular, experienced and capable MP or even cabinet member could very well end up losing his or her seat just by being a bit unlucky.

    1. david Post author

      I think this was mentioned somewhere. I must admit I don’t consider it wholly bad. Last general election I was voting against someone who had been in that seat longer than I’ve been alive.

      It is a bit too fickle perhaps, but that might create a useful social pressure. If it’s a bit harder to be a career politician that might mix things up in a useful way

      Or it might be a disaster. Hard to say

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  24. Paul in Canada

    Fascinating concept – thanks for the analysis.
    Having lived under preferential voting (Australia) and now under FPTP (Canada) I can honestly say that FPTP sucks!
    But I really like this system. I think the cutoff of 1/n seats would be good enough to eliminate the UFO spotter parties from the game.
    As time goes on, i think more and more people tend to vote the party of their choice rather than the local candidate, and this reflects that.
    That said, a really good local candidate would garner a large % of the votes, and have a good chance of getting in.
    The six piles and dice selection system is brilliant – watching the candidates roll the dice would make for great tv.
    Perhaps the best feature is that it eliminates the concept of a “safe” seat. Some parties tend to “parachute”candidates into safe electorates, where they are guaranteed to be elected – this system leaves a non trivial chance they won’t – it keeps everyone on their toes as no result can be taken for granted.

    One last comment – i did not know Britain had 650 MP’s – there is your first problem. 300 is plenty.

    1. david Post author

      I’m not sure it plays out this way in practice, but I tend to think that when you’ve got a geographical constituency system, the more MPs the better – otherwise you end up with a really crude cross-section of the country.

      On the other hand, I think that’s more a problem with geographical constituency systems than the number of MPs per se.

      RE Safe Seats: There are arguments about whether this is a good or a bad feature of the system. I’m inclined to agree with you that it’s good, but some seats at least are safe because they’ve got a single, fairly good, MP in them. It’s something of a shame to kick them out with the roll of the dice. On balance though I think that’s a tradeoff I’m willing to make.

      It’s absolutely the case that people vote parties instead of candidates. I think the logic basically goes “I will vote for my party unless I have some specific reason to consider this candidate an utter tool”. As a side-note, one thing I like about this system is that there’s no penalty for a party running multiple candidates (as long as the party is significantly above the cutoff threshold if there is one): Even if the vote splits between the two, the total probability of the party getting in doesn’t change.

      Oh, and I completely agree that FPTP sucks. It’s just about the worst possible system we could be using.

      1. Paul in Canada

        Thx David,

        I think the biggest objection would be regarding the safe seats – the MacIver System would be seen as punishing them, and giving more chance to poor performers – tending to lessen incentives to do a good job.
        Given that we agree most people vote party rather than candidate, I agree it’s a tradeoff I am willing to take.

        It does then raise the question about the party leaders – as the leader voted by the party caucus has a random chance of losing their seat – more than they do today. You could exempt the leaders from the process – i.e. the leader does not not have a constituency – but then you run into “some are more equal than others”.
        Another way would be that you have 5% more MP’s than there are constituencies – and each party has to nominate, before the election, who those people are and in what order. so the party that wins 200 seats actually gets 210 MPs. It allows continuity, but at the cost of some accountability/elitism.

        Overall, its a fascinating concept – but if you can’t get them to abandon FPTP for anything else, I can’t see them going for this, either. But I would vote for it.

      2. david Post author

        I think the restriction that the party leader has to be an MP is a bit of a dumb one, personally. How well do we really think the PM represents his particular constituency? Hell, most of the time (in England at least) the party leader isn’t even from their constituency – they just get allocated a “safe” seat. This is, frankly, utterly ludicrous.

        As an alternative, a fairer / more interesting setup would be to do away with the idea that the PM is whomever leads the party with a majority. Why not run a general election and *then* elect the PM and cabinet from amongst those who got into power?

        But yes, the very idea of trying to get this system voted in fills me with dread. I think violent revolution to impose it is the way forward.

  25. Paul in Canada

    Agreed that the PM just doesn’t have time to represent their constituency.
    But the idea of a second election seems to make the first one kinda redundant – because, if you are voting for the party of your choice, but have no idea who it’s PM will, what is the point?
    Maybe have it that the party gets to nominate their leader/PM candidate, who is the only one that does not have a constituency.
    As long as the party gets “official party status”, meaning more than 10% of the seats available, then their leader is in. Less than that, and they were never a chance at forming government anyway.

    This whole thing would have made for a great episode of “Yes, Prime Minister”.

    Good luck with the revolution – I will support you because I cannot think of a cause more worth dying for than to have the MP selected by a drawing out of a hat of ballots!

    At the very least, the gov. should employ you to turn this into a serious study. Actually, since the gov has an interest in maintaining the status quo, maybe you should take this directly to the Queen – she is probably bored with the current system. The Monarchs have been known to impose new voting systems from time to time. If she doesn’t it could be the big change that Charles enacts to make his mark – at least then he would achieve something. You might even get a knighthood for it – drawn out of hat, of course.

    1. david Post author

      Hmm. Yeah, that’s a convincing point: Voting for a party without knowing its leader is essentially a non-starter. It doesn’t necessarily invalidate my idea if the PM has to be elected from amongst the party leaders though.

      I’m not necessarily sure it’s an essential feature for the PM to have a vote in parliament. Maybe it’s even more appropriate if they don’t?

      Hm. I wonder what happens at the moment if a party forms a majority but their PM loses their seat?

      As to turning this into a formal study, I’m not really sure I’d be up for that. :-) It sounds like an awful lot of quite fruitless work. I have been thinking about doing some experiments with direct democracy as a social site though.

      1. Paul in Canada

        I agree it is not necessary for the party leader to vote – their job is to lead.

        My suggestion – each party gets one freerider – a non- elected MP – which would logically be their leader. As long as they get 1-+% of seats, their leader is in.
        But the quid pro quo is that the leader doesn’t get to vote – that is what the elected MP’s are for.

        Now, within a party, to be the leader and not have to worry about winning a seat is a great bonus – would make the job highly prized, so I think the leaders would be keep on their tow by their party. You could still have mid term leadership challenges – an elected MP can take over the leadership, and the leader is either out, or takes over their successors constituency – but I think out is better – what constituency that was represented by the now leader, wants to be represented by the losing one. The new leader’s constituency would have a by-election – decided by random vote, of course – what a television event that would be!

        As I understand it at present, if the leader loses their seat, they are obviously out and the party has to choose someone else. It is the party (or even a coalition) that the Queen asks to form a government, not the leader. I have no idea if this has ever happened though.

        As for turning it into a study, you could always turn it into an online open source experiment, and run a “shadow election” – no better way to verify it than have real people do it. It doesn’t matter who the voters or the “parties”, or constituencies are, you just need an actual run through to validate your model – which it would.

        It might also be an interesting way to determine the winners of something like a tv “talent” show – like one with inventors (as that might actually produce something useful). The public gets to vote one which of the six inventions they like best (one of them could be someone with a new voting system!), and then, on the finale show, there is a “pile” of votes, and the six inventors pull out a chunk to make six piles, and one rolls the dice to eliminate a pile, they divide again etc. I don;t know if you would want to reveal the actual voting pattern though. This also represents just one constituency, of course, so you don;t have enough to take out the “randomness”, but it would make for good tv.

        In any case, it is a great concept, and deserves to get formalised in some way, so it can be placed alongside all the other systems, duly evaluated and then not be implemented – same as all the other systems except FPTP!

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