A “perfect” voting system
drmaciver.com
drmaciver.com
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.
"Recounts" are nonsense, but I can imagine that an audit might help against the above scenario.
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]
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.
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.
> 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.)
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
However, I'm not sure how much of a (perceived) advantage over proportional representation this gives you.
I feel like for a complete idiot for not spotting that up front.
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.
- Oxford PPE
- Policy researcher
- Safe seat
- Minister
- Non-exec chairman/director
(Edited for ghastly sentence construction, sorry)
(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).
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)
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.
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).
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.
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.
[1] Technically margin_of_error(votes_cast).
* 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.
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.
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.
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.
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.
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!
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.
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.
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?)
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.
Re: race condition: I just assumed that votes would be secret. Are you sure you want to jettison that feature?
See limmeau's comment here, it turns out that the system exists and is called Liquid Democracy: http://news.ycombinator.com/item?id=2485452
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.
As I said, I'm sure there are ways for ambitious politicians to game the system so please try!
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).
A startup working with this idea: http://www.telegraph.co.uk/technology/social-media/8394883/J...
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.
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.
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.
Changing the voting system does not change the dynamics of political power.
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.
In principle, he's absolutely right. A weaker military, less intrusive FDA/EPA, no social security would be nice.
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.
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.
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.
* 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?
[Edit - think how interesting election nights would become rather than the usual few hours of predictable tedium that I always feel compelled to watch.]
As for collecting the cash prize - we could make people select if they want it anonymously or not (like the lottery).
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.
In the long run, though, it shouldn't be so hard to get people to accept these kind of solutions.
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!
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.)
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?
Even if it's statistically sound, it's not practical, because it doesn't scale.
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.
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.
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.
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.
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.
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.
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.
Given a legislature of 600 representatives, a party with 1% support would have a vanishingly small chance of winning a majority.
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 factor of 4 comes from the rate of growth of the central binomial coefficients.
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 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".
"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...
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.
Plus, randomness is a lot more random and a lot less uniform then people usually give it credit for.
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.
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.
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 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.
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.
I wonder what voting systems would have looked like, had electronic systems been around at the time of (public) democracy's inception.
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.
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.
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.