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A “perfect” voting system (drmaciver.com)
158 points by cavedave on April 26, 2011 | hide | past | favorite | 146 comments



Random numbers in election systems are an absolute no-go.

Suppose that a court rules that one district must be re-counted, and based on the result there will be a new, random candidate.

This creates incentives for going after re-countings if your political opponent has won the lottery, not because the result will be much different, but simply because you get a second chance in the lottery.

It boils down to the thought that repeatability is import for fairness. Somebody claims that your DNA is identical to the one collected from the crime scene? You can make a second test and verify the first one. You think you have been treated unfair in court? You can repeated the trial at a higher court. All the doping tests in sports are verified by repetition.

The list is nearly endless. Even if a random experiment does treat you fair, you can't known.

The second point is that randomness only creates the appearance of fairness on the large scale, single individual still get treated unfair.


This creates incentives for going after re-countings if your political opponent has won the lottery, not because the result will be much different, but simply because you get a second chance in the lottery.

For a perfect example of this, see the presidential election in 2000. The vote totals in Florida were within the margin of error, making the election a coin flip with the pretense of counting [1]. Politicians behaved exactly as you describe.

[1] At the time I was in college, and had just learned stats. I advocated just flipping a coin in full view on TV and moving on. Everyone thought I was crazy.


In the last Washington State Governor's race, we had a similar condition, where the margin of victory was well within the margin of error. It seems that in such case, the only way to determine the actual will of the people is to do a re-vote.

Unfortunately, whatever candidate was ahead a any point in time would say "it's time to just move on".

I'm afraid that too many people don't get the concept of "margin of error" and will insist on getting a count that 100% accurate (instead of merely 99% or something).


While appealingly efficient, I don't think this is sound practice. "In the margin of error" does not mean that it's a 50/50 tossup. But you're usually pretty accurate, so what am I missing?


A coin flip is simple, decisive, and immune to political machinations. A proper probability estimate is not.

Further, if you truly believe in democracy, then a candidate with 49.9999% of the vote is probably nearly as good as one with 50.0001%, right? So the cost of an error is low as well.


OK, that seems reasonable as long as one is certain that it's 49.9999% rather than a loose standard of "pretty close". What you wouldn't want is to make possible for the clear loser in a 48% - 52% race to demand a coin toss. Or maybe you do: by the precepts of your argument, maybe that would be fine.

I'm uneasy with the random approach suggested by the article for fear that a truly crazy candidate might win the lottery, but I'd be good with having all the candidates above some large baseline (say, 30% of the vote) get a proportional shot at the win. I think I'd probably want it to be proportional to the counted share even if there is a margin of error, though.


I'd advocate calculating the statistical margin of error [1] before the election (which might, in fact, be +/-2% if the election is small enough) and doing the coin flip if it's within that margin.

[1] Technically margin_of_error(votes_cast).


As stated elsewhere in the comments, you can make a number of people (e.g. anyone who asks[1]) commit to some number[2] (e.g. by giving out SHA1(their_number)). Then calculate a random number from that (conceptually, addition modulo number of voters; actual implementation left as an exercise to the reader).

If the vote with that number was actually cast, that is the vote that is actually used. If not, try the next one until one actually was cast. Pretty repeatable, and recounting is easier.

[1] Note that "all candidates" may not be sufficient, since it allows the candidates to collectively choose the outcome by picking their numbers such that one of their own/friends' ballots is chosen. This could be used to elect a popular Labour politician in a remote district where only the major two parties are running, in exchange for electing two unknown Tories.

[2] If you're not into crypto, put tickets containing every possible ballot number in a big barrel. Have a trusted/blindfolded guy pick tickets until he finds one that corresponds to a vote that was actually cast. There are lots of solutions, of varying degrees of cleverness.

[EDITs: added two footnotes]


I'm not sure that this is enough as it is stated here and in the original comment. There may be a technical solution that allows it to be done in one go, but an alternative would be to do the count, have a window in which the count can be challenged and then do the draw in a pseudo random deterministic way with seeds coming from a number of sources (e.g. different candidates).


You know, this is a much better way of doing it.

I feel like for a complete idiot for not spotting that up front.


This does account for the repeatability, but the point still remains that it treats individuals unfair, and that the unfairness only averages out over many districts.

How would you feel if you got 80% of the votes in your district, but the lottery (even if repeatable) picked your opponent? How would those feel who gave you your vote? I'd certainly felt cheated.


Good point. You can solve this issue by electing more than one representative from ordered (per-party) lists: the first picked vote for Labour elects Labour#1, the second Labour#2, etc. Labour#4 could still be lucky or unlucky, but Labour#1 will almost certainly be picked (assuming e.g. 50% of the vote for Labour, with probability 1 - 2^-10 = 1023/1024.)

However, I'm not sure how much of a (perceived) advantage over proportional representation this gives you.


How do those who currently get 40% of the vote and 10% of the seats feel? I'm guessing pretty cheated.


Replacing a broken system with an even more broken system is not an improvement.


I agree completely, but you've not argued convincingly for this one being a more broken system. The current one is guaranteed unfair, this one is expected-fair even if the unfairness may be geographically concentrated.


It seems we've argued over different things. I picked up the "perfect" from the headline and came up with a counter-example. Comparing it with an obviously broken system doesn't make it any more perfect.

If you're looking for possible alternatives, I find Germany's model not too bad: two votes, one for per-district representatives and one for parties which is evaluated proportionally. Not perfect, but works out in practise.

I'd like one mode change though: instead of giving one vote per list, I'd like to allocate an arbitrary number of votes per list, but you can give at most one vote per candidate or party. That way you can vote for blocks of parties/candidates, or even vote against somebody by voting for everybody execpt that one party/candidate.

This would remove a lot of tactical debate if you're vasting your vote on candidates/parties who don't have huge chances for success.


> It seems we've argued over different things.

That happens with annoying regularity. I have a system for dealing with that too, but that's a different blog post. ;-)

> I picked up the "perfect" from the headline and came up with a counter-example.

Well there's a reason "perfect" is in scare quotes. If I really thought the system were perfect I'd actually be advocating it instead of going "Hey guys, here's a neat idea. I'm not really sure if I'm actually for it or not".

The meaning of perfect here was intended to be that it has a lot of the properties which many people claim are impossible to coexist and summarise under the heading "there is no perfect voting system" (it overcomes the impossibilities by being non-deterministic), whilst remaining very similar to the existing and familiar system


Can you explain why that wouldn't lead to the introduction of parties like Tories2, Tories3, ..., Tories100? One could allocate 1/#votes "points" to each party voted for, but that gets you back to strategic voting.


Every voter only gets one vote. Extra parties would change nothing.


That was my first idea, but the comment I'm replying to included

> This would remove a lot of tactical debate if you're vasting your vote on candidates/parties who don't have huge chances for success.

which doesn't work if you give each party 1/#number_of_parties_voted_for votes (voting for CoolGuy gives your vote on EstablishedAndNotTooBad less weight, after all.)


Creating a party and running it in an election is a tad more onerous than creating a Reddit account. You can't create 100 parties just to try to game the lottery.


Those of us who live in safe seats where we don't support the locally dominant party are arguably already being treated unfairly. It wouldn't be so bad if there weren't quite so many safe seats - but given that 382 out of 650 seats fall into this category I think something should change.

http://en.wikipedia.org/wiki/Safe_seat#United_Kingdom


It's worth noting that this solution utterly blows the safe seats problem out of the water. This is probably my favourite feature of it.


A related effect, of course, is that it becomes practically impossible for politicians to plan for any sort of career, or parties to make personnel plans with more than a single-parliament horizon. Even a candidate with a hefty 60% support can expect only a single term at more than even odds.

Not only would this rob the legislature of experience, it would also mean politicians towards the end of each term would be focused on securing their next job, rather than performing their current one.


> Not only would this rob the legislature of experience,

I'm not sure it does, or at least not drastically: It robs the legislature of individual experience, but on average there's no reason you'd expect each politician to be in for the first time. They could even rerun later.

> it would also mean politicians towards the end of each term would be focused on securing their next job, rather than performing their current one.

This is a really easy problem to solve: You give a recently ousted MP a paid vacation after their term is up.

(This works better of course if you stagger elections rather than electing everyone at once, but it's fine without)


Better that than the current career plan for a politician:

- Oxford PPE

- Policy researcher

- Safe seat

- Minister

- Non-exec chairman/director


Well, possibly - but the point is that while ubiquitous safe seats are obviously detrimental, so is their elimination at all costs. The problem with safe seats isn't that popular politicians are consistently elected; it's that minority voices in those constituencies are marginalised. You can certainly address the latter by preventing the former, but it's a far from ideal way of doing so.

(Edited for ghastly sentence construction, sorry)


Och yes, I don't think I'd be quite so cavalier about my advocacy of this particular voting system if there was any chance of it actually being used.

(A bit like the one time I voted for the Scottish Socialist Party - I only did so for their entertainment value, not because they would have any likely control over policies).


Just make it so recounts can only be done before the final random pick.


Here's a way to avoid it: Change the process. Do counting, re-counting, appeals, etc. first, until a final decision as to the correct count and valid votes is made (all appeals exhausted or no longer possible due to time elapsed). We have final decisions on all these matters in current systems. This way, you will "know" that the election was fair, since this depends on the ballots, not the candidate.

Then do the random step. The drawback is that there may be a month or two between casting votes and having the results, but I don't see why this is a big deal.


Not that I endorse anything but a two-step procedure can enforce a kind of repeatibility.

  * Step 1. A thousand votes are selected randomly. And counted and the counts are made public
  * Step 2. The winner vote is selected at random in public procedure.
Now step 1 can be repeated at a contestant request, but if the counts are roughly the same, step 2 doesn't happen. Actually if the counts are too different, a revote may be in order


How can you have a recount of a single vote?


Imagine that some civil servants hates, for instance, the BNP. If the proposed system is implemented carelessly, (s)he may elect to "lose" the randomly-chosen vote that would otherwise put a BNP politician in power, and hope that the "next" vote will be for a party more to his/her liking.

"Recounts" are nonsense, but I can imagine that an audit might help against the above scenario.


Just make the drawing out of the single vote a public event.


I sketched a process for how this could work in a blog comment: http://www.drmaciver.com/2011/04/a-perfect-voting-system/com...


Obviously there couldn't be recounts but since there wouldn't be "outlier" elections (where someone would win by an unusual five votes), that wouldn't matter as much. (Of course, every election could be an outlier so this might not make it pleasing)

The result clearly wouldn't be fair in our normal sense of fairness and that would indeed be a huge roadblock.

The only appeal would come if a given system looks both unfair, unprincipled and corrupt. Then "just unfair" might be better.


Electronic voting?


Some background on the problem this is trying to solve:

There are a handful of mathematical theorems that basically say "there is no perfect voting system." More rigorously, they enumerate a list of desirable properties that you would like voting systems to have, and show that NO voting system can have all of these properties, because they are actually contradictory.

Some of these properties are things that are "obvious" ones that any practical voting system should satisfy: voting matters, there is no dictator, candidates can win, determinism. Two of them are non-trivial: absence of tactical voting, and irrelevance of independent alternatives (IIA). Tactical voting basically means you have a game-theoretic incentive to vote in a way that differs from your true desires. IIA basically means that if Gore would win a 2-man election against Bush, adding Nader to the race should not make Bush the winner. These properties are related, but not the same.

All of these properties are desirable, and a "perfect" voting system would have all of them, but you can't have all of them. You have to pick at least one to give up. Tactical voting in particular is extremely hard to remove, even if you give up IIA, while systems that satisfy IIA are somewhat complicated. The article suggests that it is very easy to satisfy all of the other criteria, if we let go of one of the "obvious" criteria: determinism.

So it's basically a question of picking your poison. You can have determinism, or you can get rid of tactical voting, but you can't do both. The author is contending that determinism is the best property to give up.

Further reading: http://en.wikipedia.org/wiki/Arrows_theorem is one of the mentioned theorems, dealing with ranked-preference voting systems (vote-for-one-candidate is a special case). There are a few others for different classes of voting systems.


As a side note, this does not directly address the problem proposed by Arrow's theorem, although it could easily be made to do so, but the post isn't so interesting in that context. It's more about how it interacts with a constituency system.

If you want a randomised solution to Arrow style preferential voting, the following is the best I currently know of:

1. If you have one candidate, stop. That candidate is elected.

2. If you have more than one candidate, pick a candidate at random. Call that candidate Pivot. Every candidate who the majority thinks is worse than Pivot drops out of the race. If there is no one the majority thinks are worse than Pivot, Pivot drops out.

3. Goto 1.

Edit: Err. Correction. That's an algorithm for selecting a single winner from Arrow style preferential voting. It's based on an only slightly more complicated one for giving you the full range though.


The condition you identify as "IIA" isn't Arrow's condition. IIA in Arrow's theorem is best understood as the principle that only information on the ballot is relevant to the vote. The condition you cite is a much stronger counterfactual property: that if x beats y, then x beats y even if we introduce z. But this is not Arrow's condition (see Bordes and Tideman on this).


This is a refreshing and interesting suggestion for a voting system, and it seems like David and others here are far more knowledgeable about voting systems than I am.

I have been thinking about a voting system for a while and I really need feedback from people who know this stuff - I have a feeling there's large flaws with it. Here's the general idea:

· Each voter can delegate his/her vote to any other voter, in any number of levels. I.e., if Alice delegates her vote to Bob, and Bob delegates his vote to Carol, Carol carries three votes.

· Delegation of votes can happen at any time, so Alice can delegate her vote to Bob until further notice.

· Each voter can change their delegate at any time.

· Each voter can vote for a motion. If the voter has previously delegated his/her vote, the delegate will not carry that voters voting power in this motion. So, if Alice uses her vote in motion 1, Bob only carries one vote and Carlos 2, but only in that motion.

· Each voter can delegate his/her vote to different voters in different issues; Bob may delegate his vote to Carlos in financial issues, and to Alice in justice issues.

My hope is that this would scale to e.g. a nation state, as an alternative direct democracy. Today in Sweden, we delegate our votes to 349 MPs every four years. When introducing my system, that would be the initial state. After that, voters would start delegating their vote to other people that they trust, while using their vote in issues that they know or feel strongly about.

This is probably an old idea, and as I stated earlier, I'm guessing there are major flaws with it, so fire away!


This seems really vulnerable to vote buying, unless the person receiving the vote delegation isn't informed that they're voting for two. Otherwise, your boss will say "delegate me your vote, or else". If he doesn't straight-up fire you for refusing[1], he can write bad performance reviews for two straight quarters and then dump you. Or imagine if a church threw caution into the wind (sacrificing their tax-exempt status) and said "delegate your vote to your preacher/pastor/etc., or you're going to Hell". Unless you can lie about delegating the vote, then you may as well not have it.

In the above cases under the present system, I can just say "sure boss, I'll vote for Obama/Romney/whoever" and then walk into the booth and vote for whomever I like.

[1] - This is arguably not illegal in some "right to work" states in the US.


Hi Zach, yes, that's true. I definitely think it's a good feature to let people know their voting power though. It might be solvable by only letting them know in segments: 1-5, 6-10, and so on, or something like that.


This sounds like the Liquid Democracy system, which the Pirate Party of Germany uses to decide on party-internal policy questions. (Other organizations may have had it before them, but they're the first I heard it of)

The major point of dispute there is that this system cannot be simultaneously anonymous (nobody knows whether I voted for or against nuclear weapons for public schools) and independently verifiable (anyone can check that everybody's delegations have been computed correctly).


Right, and liquid democracy is really a specific application of proxy voting: http://en.wikipedia.org/wiki/Proxy_voting

A startup working with this idea: http://www.telegraph.co.uk/technology/social-media/8394883/J...


Thanks limmeau, indeed it does sound exactly like Liquid Democracy. I have thought about the problem you raise and it is indeed a drawback.


One interesting point about this concept is that one of the limiting factors was likely that it was too complex to keep track of who had whose vote. Traditionally, with paper and bureaucracy, it would have been a near impossible task to calculate that on the day of the vote, Carol has been delegated Bob's vote and Alice's and that neither have rescinded such delegation prior to the vote. The paper trail made it infeasible.

However, now that we have computers to do most of the figuring, things can happen in near real-time thereby removing this constraint and making this (more) possible. Certainly there are many other side issues (authentication of Alice delegating her vote to Bob, did she do so under duress?, etc.)

Very interesting idea though and, as you said, probably an old idea, but one that may have been scrapped due to these technical issues. Now that we can overcome them, seems worth revisiting.


Thank you vaporstun, that's exactly what I think as well. Delegating of votes is not a new idea, it's used in lots of societies - I got the idea from my housing cooperative. But it quickly gets out of hand after just one level of delegation, and if people are allowed to delegate their vote and then vote, well such a system has to be electronic.

As I said, I'm sure there are ways for ambitious politicians to game the system so please try!


I don't think your categories work very well (even absent politicking, is a bill to raise teachers' salaries an educational, financial or social bill?). The rest of your scheme is complicated but seems to work as designed.

That said, a big advantage of the currently popular party-based systems is that it ensures at least a minimum of coherent policy-making - a party that votes for both more spending and tax cuts can at least be called on it. I didn't follow it closely, but I've seen suggestions that California's experiments with direct democracy have at least partly caused financial troubles.


Thanks Joachim! The categories are meant as examples only, but I think that when applied to a nation state the various departments might be a good start.

It might seem complicated but I don't think it is, rather I think I am bad at explaining it. Then again, in the words of Swedish poet Esaias Tegnér, "that which is dimly said is dimly thought", so I will try to clear it up!

The main problem, I think, is how to count the votes, i.e. when Alice has delegated her vote to Bob, and Bob votes, and then Alice votes, I think there might be race conditions where people could game the system. So, it might be that you would have to have "voting windows", where people who carry the most voting power has to vote first, for instance.


Don't worry: I understood you just fine.

I'm still not convinced of your category system: if lots of people give their education vote to EducationFirst and their finance vote to NoMoreTaxes, the classification of the "increase teachers' salaries" bill becomes very important. I'm not aware of any current system to classify it under either department; you could let people elect category-sorting representatives, but that is an entirely new set of problems (the NoMoreTaxes representative may plausibly argue that every bill spending money should be in the finance department, for instance - not coincidentally a department where his/her party has lots of power.)

I don't think there's any kind of race condition: Alice just sends the voting office a note "if I don't explicitly vote, I vote the same as Bob" and the voting office can just check whether or not she did when counting the votes (there is no need for a live tally, right?)


I don't know where you get the idea that formations such as EducationFirst or NoMoreTaxes would appear in this system. I think it's more likely that we will see basically the same formations as today; liberals, conservatives, democrats, green and so on.

That said, it's an important feature of the proposed system that it encourages, or even demands, a higher level of engagement with the issues than under today's system. Voters should vote directly in issues that concern them deeply. What the system fixes is rather a problem with direct democracy, where people vote the "wrong" way, or don't vote at all, in issues they don't understand or that don't concern them.

This is done by letting people delegate their voting power to someone they trust - it might be their neighbor, their mother, a colleague or a professional politician. But to mitigate the problem with concentrating power to few, that delegated vote is not to be counted on; someone can change or even retract the vote at any time.

Calling it race condition was probably wrong, what I mean is situations like this:

· Bob delegates his vote to Alice

· Alice votes No

· Bob sees that his vote is currently on No, and he likes that to he doesn't feel the need to change his vote

· In the last minute before the voting closes, Alice changes her vote to Yes

· Alice has gamed Bob, because if Bob had known Alice would vote Yes, he would not have delegated his vote to Alice in this motion.

Of course, the above scenario might not play out simply because it hurts Alice - Bob would surely never delegate his vote to her again. But I think it's a real problem nonetheless.


NoMoreTaxes was inspired by the American Tea Party, and EducationFirst was inspired by the Dutch D66.

Re: race condition: I just assumed that votes would be secret. Are you sure you want to jettison that feature?


I think every voter needs to know where their vote lies, when it's delegated. Someone will only know where the vote of the person they delegated their vote to, currently lies. That is, Bob has delegated to Alice, Alice might have delegated to somebody and so on. Bob sees that his vote is on Yes, and so knows that Alice's vote is on Yes. Alice knows whether she voted for Yes or if she has delegated her vote.

See limmeau's comment here, it turns out that the system exists and is called Liquid Democracy: http://news.ycombinator.com/item?id=2485452


As I posted, secret / anonymous votes are essential as long as there is economic or other inequalities within the voting population. Bribery and enforcement are serious problems. For instance, it is well documented, that you can buy the national "mail votes" of Italiens living in Germany for as little as 40 Euros! One might argue, that for the voting system within a party, secrecy is not as important. However, many, many members of the Pirate Party in Germany broke up with the party, exactly because of this missing feature, when Liquid Democracy was introduced.


This isn't a different voting system; it's only a special case of the current system. Keep in mind, in your system it's got to be possible to NOT delegate your vote; it has to be possible for everyone to just vote on their own without delegation. In that case, what happens? You haven't really specified the voting system, just an additional feature that a voting system might take on.


That's true - if everyone votes on their own, it's direct democracy.


I was thinking about an essentially identical system to yours some years ago and I came up with an amendment to prevent direct democracy (if desired): nobody can vote for themselves unless they have at least X votes; if not then they must delegate.

Similarly you could try to assemble everyone who has at least X votes into a parliament (if you pick X appropriately), though I'm worried that the cutoff for getting into parliament might cause a chain of tactical redelegations which never stabilizes.


Thanks for these insights, both are interesting. I've thought about the same thing with the parliament, but I fear there are problems with that. If it turns out that there is a fairly stable selection at the top it might work and should make the voting more efficient.


The problem is not the allocation of power, but the centralization of power. Once you have a lot of power in the hands of the central government, it will be captured and misused by cliques and special interests.

The way to 'fix' democracy is to reduce its scope, to make it as localized as possible. In this way, political decisions tend to be made closer to those affected.

The idea that the various branches of government can block and check each other's power has proven quite misguided; they will always cooperate to increase their collective power.


You are familiar with the Articles of Confederation, and their abandonment?

The Federalist-Anti-Federalist debate has been going on since the Revolutionary war. It is neither a settled debate, nor is it without precedent.

The branches of government do block and check each other's powers, and to assert otherwise is just false. The fact that the Federal government doesn't do what you want isn't a sign that the US system of government is broken.

The fact that the government can't pass policies is a sign that US politics is broken (although i will grant that each branch of government has been complicit in this individually). But that's hardly collusion.


I'm guessing you're american even though this story Is about a british voting system. So you want local military, local FAA, local social security, local CDC, local EPA, local interstate highways, local FDA, local FDIC, local NASA, local weather satellites... I could go on but it seems like every little city providing all these services might be a tad wasteful.


Or maybe he's from Switzerland, which actually does have a fairly decentralized system: http://www.bhutan-switzerland.org/pdf/Kaelin_Switzerland.pdf


Why would that be wasteful? Note that having local authority does not preclude having larger organizations in place.

Changing the voting system does not change the dynamics of political power.


Why would it be wasteful: Lack of economies of scale.

If you claim that states or municipalities can get together to leverage such scale, then you've just reintroduced bureaucracy and waste. This is why centralized control is useful. The US Federal government, one of the largest employers in the US (cause there is a lot of stuff to do for citizens) can guarantee health insurance to its workers because it's big.

This is what frustrates me so much about republican/conservative free market rhetoric. They hate government because it interferes with markets, and then they try and hobble the government's ability to use market forces to save tax payers money. And then they accuse the government of being wasteful.


Did he list any of those as being what he wants localized? Did he say every "little city" should do it?

In principle, he's absolutely right. A weaker military, less intrusive FDA/EPA, no social security would be nice.


Ah, so the goal isn't some principle about democracy, it's about a desire to get rid of SS, let polluters pollute, and to have unsafe food. He should have come out and said that then.


Yep, exactly. I'm glad we're on the same page.

Or, perhaps overreaching bureaucracies should be eliminated and allow these united states to handle their own populace as they see fit, while abiding by the Constitution.


There's an interesting side effect of this system which I think means that it would have lessened impact on the policies implemented by the elected officials.

As in his example, pretend the Kitten party appeals to 10% of the electorate distributed evenly across districts. So in roughly 10% of districts, the Kitten party would earn a seat, but would only represent 10% of their constituency.

In this case, the incentives of the elected Kitten party representative shift. Instead of keeping to their Kitten party ideals, they would seek to maximize their following within their district by shifting to a median political position. This would ensure them the maximum likelihood of re-election in the following campaign.

So theoretically the actual policies coming out of each district would still represent the median view of the electorate in that district, and the Kitten party would remain disenfranchised.


Hmm. I'm not sure I believe that. I'm not sure I don't believe that either mind you. Consider the following questions:

* If they're willing to do anything to stay in power, why were they running for a minority party in the first place?

* How likely are the voters to use their single vote to vote for someone who is still running as kitten party but is acting like a watered down version of the people they actually want to vote for?


I think it fails the "easily understandable by the average voter" test. And that's kinda a big one if you actually want change.


Discussing this with colleagues someone suggested a splendid addition - give the person whose vote was used in a constituency a nice bonus (say £100,000) to encourage people to come out and vote.

[Edit - think how interesting election nights would become rather than the usual few hours of predictable tedium that I always feel compelled to watch.]


You generally do not want to know who voted for which candidate. E.g. voting should be anonymous.


I'm pretty sure voting isn't 100% anonymous in the UK - it isn't public but don't the ballot papers have a unique serial number on them?

As for collecting the cash prize - we could make people select if they want it anonymously or not (like the lottery).


The main reason for the secret ballot is to prevent vote buying. With the secret ballot, there's a low incentive to buy someone's vote, because there's no way to make sure they held up their side of the deal. Under your plan, candidates could offer a big multiple of the cash prize to the voter whose ballot was selected, if they win.


Make the offering of such cash inducements a serious criminal offense and offer a very high reward (millions) for any voter who acts as a witness for the successful prosecution of a candidate. If voters are simply doing it for the money they could take the bribe from the candidate and then dob them in and collect the reward.


Bitcoins ! :P


Or they get all the deposits of those who lost their deposits from not getting enough votes?


This needs random numbers whose randomness can be demonstrated.

You could ask every candidate to commit to his random number, publish a hash of it, and afterwards compute a hash of all candidates' random numbers to get the final random number. As long as most candidates distrust each other, this should work.


And then you need to explain how hash functions work to a bunch of people who dropped out of high school to work on the farm so that they don't feel cheated by the new electoral system.

In the long run, though, it shouldn't be so hard to get people to accept these kind of solutions.


We could use sealed envelopes made of heavy paper instead of the first hash function usage, and then have a guy in a lab coat point at a colourful picture of a fractal to demonstrate the randomness of the second hashing step.


Except that you've got people like Beck or Breitbart running around. Your election system has to be simple and transparent in order to make it as hard as possible to delegitimize in the eyes of the electorate. It's bad enough we've got a serious fraction of Americans who think Obama's not a legitimate president and/or who think that ACORN rigged the election, based on extremely spurious evidence. We can't give these factions (on either side) more ammunition.


The goal "impossible to delegitimize" is incompatible with almost all sophisticated election modes, and hard to measure. I'd settle for "impossible to delegitimize rationally once you analyse how many people who normally distrust each other would have to cooperate". Crackpot-safety is just too much of a requirement.


There's no such thing as crackpot-safe, but there is such a thing as "more crackpot-resistant" and "less crackpot-resistant".


Think of the prestige this would bring to CS... :-)


Random voting is stupid for one reason: there is little incentive for any individual to vote for a competent candidate. You have the same chance of choosing the next president whether you vote for Obama or Joe the Plumber. Yes, reasonably-minded citizens will vote for one of a handful of competent candidates, but a vast number of people will simply vote for themselves.

The equivalent in a plurality system would be if all write-in votes were counted together, and then a write-in chosen at random should the write-ins outnumber the votes for any other single candidate.

I guess the "solution" would be to require a minimum # of signatures for a candidate to be on the ballot (and votable). But that's just starting to sound like approval voting, so you might as well just go all the way with it!


I hadn't realized this, and your comment is too late to gain many upvotes, but yes - very good point.

Couldn't you solve this by requiring any randomly-elected candidate to have at least, say, 1% of the popular vote, though? (This means that you don't entirely eliminate strategic voting, unless people can specify a fallback option; but it reduces it by a lot.)


A simple way to generate random numbers:

Let's assume we have N positions that we want to elect MPs for. Each ballot contains an ID and a secret number between 1 and N (both numbers are physically on the ballot, but you can only see it by scratching an area). Next you define a hash function that takes a vote and returns an integer. For each 1 to N, you simply take all the ballots with the secret number and sum the hash of the votes. You can then use that value you choose choose a ballot ID.

The good thing about this solution is that you can easily re-count the votes and you end up with the same answer. And, you can place all the information in public so other parties can verify it.

Hm... Any randomness problems in this solution?


Have fun scratching off the tissue from millions of votes.

Even if it's statistically sound, it's not practical, because it doesn't scale.


There may be issues with the above solution, but scratching off tickets isn't one of them. Do you know how inefficient the process of counting votes can be now? You might think that it is impractical, or that it "doesn't scale", but they manage.


For some reason, I like this. However, I think that a voting system that 95% of the population can't even understand won't be very popular overall...


I don't think it's that hard to understand. Certainly as a voter it's very easy to understand what it is you should do - easier than under FPTP where you are forced to think tactically. The consequences are slightly hard to think through if you're not good at probability, but it's easy to boil those down into a set of pithy statements that will tell you most of what you need to know.


It's not hard to understand how it works. It is harder to understand how it's fair.

Of all the voting systems that will never see the light of day, I think I like this one most of all. However I would say despite its similarity to the status quo it would completely change the nature of government when parties couldn't count on who would get elected despite the safeness of their constituency.


I'm sorry, yes, this is what I meant. People will never understand how it's fair. I can see the arguments now, "What? You want us to pick representatives at random?!"...


Yes. Agreed. I suspect it would be ridiculously hard to get this through (witness how much trouble we're having with IMO the far less controversial AV), 'though with the right framing and a sufficiently disgruntled populace I could see it happening. Maybe. Not going to hold my breath though.


The cynic in me can't help but see the parties moving power out of the parliament as much as possible. The public sector would likewise also become more powerful. I can't help but think this is the chaos monkey of voting systems.

It's definitely crazy, I have a feeling it might work though, eventually as a voter I'd simply vote for whoever in my area promised some kind of sane approach to making decisions.


It is rather simple, if you compare it to e.g. the D'Hondt method used in Germany.


I find CGP Grey does an excellent job of explaining things very simply in his youtube videos. Personally, i'd like to see these run on British TV.

http://blog.cgpgrey.com/the-politics-in-the-animal-kingdom/


I was going to show that link as well. His explanation of instant runoff convinced me.


Instant runoff has some mathematical problems. Ranking your favorite candidate highly can actually work against you. http://www.rangevoting.org/IrvPathologySurvey.html

Empirically, every country with instant runoff still has two-party dominance.

A better system is range voting: http://www.rangevoting.org/

For a really great book on different voting systems and their advantages and disadvantages, see Gaming the Vote by William Poundstone.


> Empirically, every country with instant runoff still has two-party dominance.

I suspect this a property of single-member electorates. Australia has IRV, but Senators are elected proportionally within each state. The major parties have more members but do not always command a majority, and most Senates require negotiation to proceed. However because the House of Representatives almost always goes to one party or the other, it is possible to form the Executive and govern.

It's a fairly effective hybrid.


Thanks for that. I'm the creator of those videos and I'm really glad to know that the AV one actually changed minds.


Thanks. I've only just got around to watching these, and they're really very good.


I'm voting for AV because I want a chance to vote for PR. Proportional Representation is the proper/good/final solution.

I'm slightly confused about voting multiple people for a larger area. Is this PR, or something else good?

It will always be a boring night, even more so if there are coalitions formed. More election night comedy, and transparent coalition agreements.


> I'm slightly confused about voting multiple people for a larger area. Is this PR, or something else good?

It may or may not be PR. It depends on how you elect those multiple people: They may be elected under a PR system, or they may be elected under something non-proportional.

I'm for PR in general. I'm not sure how I'd feel about a PR-per-constituency approach.


This is a cool thought, but I think it's a bad idea to use it in actual elections. The author failed to really address the "crazy minority party" concern. His argument was that, while his system would give such people a chance in getting elected, it's only fair that it did since they indeed had a constituency and their chance of winning is proportional to their constituency size. He adds, "The fact that I consider someone to be utterly despicable doesn’t give me the right to disenfranchise them."

I'm not sure the point is valid. I certainly believe in freedom of speech and I accept my duty to protect the right of even the most offensive people to be heard (in fact, they should receive a greater degree of protection). However, by supporting a voting system that gives them no chance of being elected before they convince enough people for their ideas to be considered mainstream I'm not disenfranchising them since I'm not denying them the right to vote. I'm just marginalizing them, which is the proper response to all crazy claims and ideas. I offer two hypotheticals in support for those who still feel I'm infringing on someone's liberties by writing what I did:

(1) Suppose we live in a country that's a nuclear power. Suppose also there is a fascist party completely bent on nuclear war with Israel (for example) in our country and that they have a constituency that amounts to 1% of the electorate. Suppose nuclear war means total destruction on a global scale. I'll argue that giving those people a chance at forming a government is immoral and, in fact, disenfranchises everyone outside of your country since they have to control over who you elect, yet they suffer the horrible consequences.

(2) Suppose my party ran on a platform of dismantling democratic institutions (including elections of any sort) and vowed to distribute the majority of resources to my constituents, basically re-instituting feudalism. Random selection would give us the opportunity and the power to dismantle the democracy it was meant to be the engine of. It would also technically make it illegal for other countries to intervene, since our "feudal" government would be democratically elected.


It's worth noting that the consequences of random election are not "the crazy party gets into power". It's "the crazy party gets a couple of seats". The chances of someone with even 5% of the election are astronomically low (http://twitter.com/johnmyleswhite/status/62863260566827008 - the probability of someone with a 5% minority getting the majority over the course of 50 elections).

The likely scenario here is that your crazy party gets 1, maybe 2, seats at the worst and promptly demonstrate themselves to be incompetent tools, spoiling their chances of reelection.


I don't think that's what the author was describing. I think it was a case of everyone gets a vote, then we pick someones vote at random.


This is an issue with most (all?) PR systems. The author's argument was not that crazy minority's should get into power, but they should at least be represented in the political system (Parliament or whatever). They should at least have a chance to air their views on the national level.

I think this has two side-benefits: one is that such crazy minorities are often shown as incompetent when given such 'legitimate' representation; the other is that it removes their PR boost of being "downtrodden outcasts".


With regard to your first point, I don't think that's what the author is describing:

"Once all of the votes have been cast, you pick one voter at random and use their choice"

It's not a matter of representation, which would not only be OK with me, but necessary if we claim freedom of speech. The author is describing a random dictatorial mandate weighed based on constituency size. Maybe I'm completely misunderstanding this...


"Suppose ... there is a fascist party ... and that they have a constituency that amounts to 1% of the electorate"

Given a legislature of 600 representatives, a party with 1% support would have a vanishingly small chance of winning a majority.


Even if you consider running consistently over a long period of time?

Also, my hypotheticals were meant to be such that you wouldn't take even vanishingly small chances. If you are willing to, then I failed in my argument.


The chance of a party with 1% support getting 300 or more seats out of 600 is roughly on the order of 0.04^300.* This number is so small that you're probably better off worrying about a literal biological virus that turns people into fascists.

*The factor of 4 comes from the rate of growth of the central binomial coefficients.


I love it. We Brits would never go for it though. I can see the Daily Mail headlines now: "Fascists Given Seats in 'Election Lottery'".


Surely the Daily Mail would be delighted with such a result?


No, their particular brand of hateful racism is only acceptable if they can portray as despicable another group even more hatefully racist than them.


Using random factors in election is a really old practice going back to Athenian Democracy at least.. It's known as Sortition.


Both of which terms are explicitly used in the article. :)

However this is not a sortition. It's an application of random-dictator to the problem of electing a per-constituency representative. This turns into a sortition only in the degenerate case where everyone runs and votes for themself.


There is less feedback this way. Somebody could find a way to game the system, and all the statistics in the world couldn't prove he cheated.

Plus, randomness is a lot more random and a lot less uniform then people usually give it credit for.


You'll still know how many people voted for each candidate in this system, but instead of that determining who wins, you pick a random vote from the pool.


I think you might improve this scheme by doing it twice. First, a random sampling of votes cast are used to create a candidate pool. Next, one lucky voter's vote is selected to pick a candidate from the pool. The upside to this is that it helps get rid of self interest / crazy voting. If the scheme David MacIver proposed were used for determining president, I expect 25% of people would vote for themselves. (Well, he proposed starting from a small pool, so I guess I'm wondering about what would happen if you used this scheme to produce the pool in the first place)


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.

I completely disagree with that. Anyone that would deny you the right to do something should not be allowed to have that right. They wouldn't give immigrants and non-British citizens a right to vote, so why should they be allowed to have a say at all?

Democracy and freedom need to be defended. Allowing people who actively subvert it to win an election would be absurd.


Put another way: marginilization of fringe positions could be considered a desireable quality of a voting system, as long as sufficient free speech protections are in place.

In a sense, elections act as a sort of filter between ideas and actions. Freedom of speech can be used to disseminate ideas, and some truly awful ideas will disseminate rather widely. However, they won't usually gain enough adherents to get enough votes to make it past the "filter." That's why there's little harm in letting people espouse "dangerous" ideas with their speech[1]: most people will recognize bad ideas for what they are, and the proponents of the worst ideas generally will not be elected to positions where they can influence policy directly.

This "filter" is far from perfect: some bad ideas will become laws nonetheless, and some good ideas will get blocked. More of the former than the latter, though: if an idea is good enough, it will eventually garner sufficient support to become a significant factor in elections.

There have been cases in history where entire societies did adopt bad ideas (e.g. fascism). However, I think that when an entire society takes such a dramatically wrong turn, even the most perfect voting system will not save it.

[1]It's important to draw a line between espousing ideas and encouraging actions.


You're revising history a bit; when fascism was rising there were a lot of people that were fighting against it such as the socialist and the communists and the anarchists. Unfortunately, other societies were trying to contain those socialist forces and this reduced their power to counter the fascists. You can see this happen in Spain and Italy as well (there were a large number of collectives in Spain and Italy has had anarchists and communists for a long time, in the 1970s they were quite the active movements).

The "filter" shouldn't be just at the voting booths. We should be reminded before and after election day why the ideas of those fringe positions is a bad idea.

Espousing ideas in such a way as to hide the true nature of them is something that political parties are getting good at. If there are dangerous ideas, they're hidden behind nice language or buried in the back of the political party's plans. So it's harder for people to recognize those bad ideas.

I think we would do well to learn from the past and be more active in denouncing ideas such as those of the BNP and other fringe parties.


I don't see how a statement as brief as mine could be seen as a revision of history: fascism was a dangerous idea that took over entire countries (so was communism). That leaves out a lot of details, but hardly constitutes revisionism.

I also wasn't trying to suggest that we shouldn't denounce dangerous ideas, in fact such denunciation is one of the primary mechanisms which prevents bad ideas from garnering enough support to make a difference in elections. Rather, I was trying to say that censorship is not the proper way to marginilize dangerous ideas. Only after reading your post and then re-reading mine did I realize that I never specifically mentioned censorship, but that's what I was thinking about.


The most reliable way to defend against fringe politics from becoming overly influential is to make voting mandatory, as Australia does. See Hotelling's Law for why.

http://en.wikipedia.org/wiki/Hotellings_law


What do you consider fringe politics? And why would forcing people to vote keep them from becoming overly influential?


> What do you consider fringe politics?

Politics considered unendorsable by the median voter on in a "central" position in the hyperspace of all issues in play at an election.

> And why would forcing people to vote keep them from becoming overly influential?

Median voters are generally poorly motivated to turn out. Fringe voters are generally highly motivated. Consequently they become influential out of proportion to the actual preferences of the population taken as a whole.

When voting is mandatory, the better strategy is to aim your policies at the median voter (Hotelling's Law), which helps to create sustainable reforms because parties will converge on consensus policies.

When voting is voluntary, the better strategy is the motivate/demotivate approach. Motivate your followers with a shiny geegaw, demotivate the other guy's with dirt.

I'm generalising, of course. But the long-term principle holds fairly well.


In Ireland, we use PR (single transferable vote), however we do have local politicians. PR does not mean no local constituency stuff. If anything there is too much locality in ireland.


The thing that interests me about this article is that ~200 years ago, compared to the simplicity of FPTP, most other voting systems would be quite difficult to implement, because all bureaucracy/vote counting would have to have been carried out by hand.

I wonder what voting systems would have looked like, had electronic systems been around at the time of (public) democracy's inception.


Great, but I think he is 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 - and will happen.

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.


You need to make it expensive (in time or money) to run for office. Otherwise everybody would simply vote for themselves. Or people would vote for the special interest candidate of their pet special interest, and mainstream parties would vanish.


The proposal someone provided on my blog was that you should require X signatures for a nomination. e.g. if you have a constituency with 10,000 people and you want 10ish candidates require 1000 signatures for nomination.


Not to be dismissive, but this is a pretty unhelpful approach to the voting problem. The idea of picking a random person is motivated by the thought that the more support a candidate has the greater chance they have of being selected. But then why not just select the person with the highest probability of being selected? The difficulty is that even this "harmless" process is infected. The real upshot of Arrow's theorem is that you can't aggregate preferences: there is no "measure theory" underlying the concept of group will.


The NBA draft works this way (most votes = lowest finish previous year). It has not done a good job and I think this would create riots in the streets.


I'm sorry but how is this similar? I'm probably missing something but I don't see the connection.


If I understand this scheme, we put the "votes" in a box and pick a random winner from them. The NBA draft puts its "votes" (# based on finish order of bottom) and picks a random winner from them.


A particularly problematic aspect of this system is that, in close elections, it provides little incentive to the elected representative to do a particularly good job once they get there. If the pol won with 51% of the vote, then perhaps if they work their arse off they could get to 55%, and if they do jack they might only get to 45%.


http://news.ycombinator.com/item?id=2495775

Compares One Vote, Instant Runoff Voting, Acceptance Voting, Ranked Choice Voting, Condcorcet Method and various methods of Rated Voting via simulation testing for maximum voter happiness with the result.


I think no voting system is perfect till people can/will vote as per their conscience.


The entire point of this system is to produce a voting system that does not discourage people voting per their conscience. All deterministic systems so far have flaws that encourage people to vote "strategically" to improve the chances of their candidate being elected or other flaws.


Yes! Cancel the referendum and replace it with one that has this option as well!


Until voting is made mandatory, a "perfect" voting system is a non-starter, because no system could therefore truly reflect the will of the people.


Even if this is a necessary condition for a perfect voting system, it doesn't change the underlying problem. Even if everyone voted, you wouldn't consider it a system that "truly reflected the will of the people" unless that voting system satisfied a few basic principles, like you can vote for anyone you want, there's no dictator, only information on the ballots is taken into account, etc. But those principles are Arrow's, and Arrow shows that there can't be a voting system that satisfies them. So there can't be a perfect system at all. What's the point then in making everyone vote?


you can't reflect the will of the people with representative democracy. People have different value judgement, therefor it is impossible to create laws that are 100% reflective of the people.

Democratic representatives do not represent you like a lawyer or financial advisor. They have to act in your and your interest alone, or they breach ethics and possibly get sued. 1:1 vs. Many:1 relationship.


I'm referring to the result of an election, not the actions of those elected.




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