How about quadratic voting

I would like to draw the attention to ‘qudratic voting’ (‘QV’) rather than the usual democratic ‘tyranny of the majority’. Firstly because quadratic voting is mathematically provably the most fair of voting methods, and secondly because I feel it goes very well hand in hand with the spirit of a meritocratic society like that of Liberland.

In QV all eligble voters can cast one or more votes on their favourite issue such that 1 vote costs 1 merit, 2 votes cost 4 merits, and N votes cost N² merits.

At the end of the voting procedure the issue with the most votes have won, and the pool of spent merits are distributed in equal shares among all who cast a vote. Remaining merits ($num_merits mod $num_voters) are kept in the pool for a later voting procedure.

Let’s say we have two issue — “aye” and ”nay” — and four voters who cast a number of votes:

  1. casts 1 vote (1 merit) on aye
  2. casts 2 votes (4 merits) on nay
  3. casts 5 votes (25 merits) on aye
  4. casts 10 votes (100 merits) on nay

Altogether 6 votes for aye, and 12 votes for nay. Since the 18 votes have been “bought” with 130 merits, the four voters will receive 32 merits each from the pool, and 2 merits will be passed on to the next voting procedure.

The fact that a voter can cast more than one vote means that people can spend more merits on issues that are close to their heart, and just cast a single vote on issues for which they don’t care so much, but still want to express their opinion.

On the other hand, the quadratic nature means that it quickly becomes expensive to buy votes (e.g., 100 votes will cost 10,000 merits that will be given back to everyone in equal shares), thereby preventing a few people from effecticely hi-jacking the election. And of course it should also be possible to impose a maximum number of votes per voter per issue (e.g., noone should be able to cast more than 10 votes on a single issue).

And because active voters receive at least the cost of 1 vote in return, eligible voters have an incentive to cast at least 1 vote, something that will likely increase the percentage of active voters to the benefit of everyone.

As far as I can tell, the use and circulation of vote tokens will lend itself well to a blockchain implementation, but that is a debate for some other time.

Quadratic voting is a procedure that a group of people can use to jointly choose a collective good for themselves. Each person can buy votes for or against a proposal by paying into a fund the square of the number of votes that he or she buys. The money is then returned to voters on a per capita basis. Weyl and Lalley prove that the collective decision rapidly approximates efficiency as the number of voters increases. By contrast, no extant voting procedure is efficient. Majority rule based on one-person-one-vote notoriously results in tyranny of the majority – a large number of people who care only a little about an outcome prevail over a minority that cares passionately, resulting in a reduction of aggregate welfare.


Mate… what a great idea!
I’ve never heard of this voting system until now and my initial quick skim research (I’m embarrassed to say was using Wikipedia) indicates that this voting system is untested. More of a theory than that of a solid use history.

My first suggestion is that we should trial this system in business, social, crypto environments or areas other than our nations decisions.

I have other suggestions but first I want to highlight that Liberland e-residents and citizens have a diverse wealth range. While I believe the overwhelming majority of us are rich in political, social and economic awareness and awake to the current Great Reset world order gyrations. But financially wise many of us are not at all rich and only e-residents so far, whereas most citizens are likely crypto millionaires or otherwise wealthy.

Second suggestion, voting including quadratic voting is often anonymous, why not make that optional, a choicel? A bifurcated voting system where anonymous votes are weighted 1 merit = 1 vote along with the usual quadratic formula. And non-anonymous (open) votes are weighted 1 merit = 2 votes along with the usual quadratic formula. This would help combat secret cabal vote rigging of the nature with EOS.IO block producer vote rorting a few years ago.

OK, so thinking this through, using the example in the initial post, if the first bifurcation is 1 merit per anonymous voter delivers 1 vote. And the second bifurcation is 1 merit per non-anonymous voter delivers 2 votes.
So, if voters 1 and 3 voted non-anonymously (openly) and voters 2 and 4 voted anonymously (secretly) then the result would be 12 nay votes cast secretly at a cost of 104 merits and 12 aye votes cast non-anonymously at a cost of 26 merits.
So the big spender secret voters pay for their secrecy and the budget spending non-anonymous (open) voters get rewarded for being being open and honest.

  1. casts 2 open votes (1 merit) on aye
  2. casts 2 secret votes (4 merits) on nay
  3. casts 10 open votes (25 merits) on aye
  4. casts 10 secret votes (100 merits) on nay

Note that big spender secret voters who are habitually repetitive lose merits in favour of budget spending open voters who would then become more financially empowered as the cycles of voting continue.

Third suggestion is to have a reset period where the agreed rules can be discarded, if necessary after say 5 years. This way we wouldn’t be trapped into a vote cartel system where, like EOS, the cartel voted them selves in and controlled all the rules that would otherwise have allowed the community to get rid of the cartels.


Thanks mate, there’s a lot of good suggestions in your elaborate reponse.

I fully agree with you that this should not be deployed in areas of national decisions from the beginning. Instead we should first try this in simulated runs and then in matters of less importance where possible mistakes are more easily forgiven, and — when refined — we can finally apply it to all matters.

I also like your idea of “Hey, you can have twice as many votes for a given amount of merits if you cast them in the open.” This should indeed help mitigating against voting cartels.

Since we are free to play, let me throw a few more ideas into the stew:

In my ideal world the number of votes that I cast should reflect how much I like or support the issue being voted on, rather than being a means of amassing power. Even if casting, say a thousand votes will cost a million merits, something probably only a few would or could do, it does give those with wealth an unfair advantage. So here’s a couple of things we could do:

First suggestion: Let’s limit the amount of votes that a voter can cast in a single voting round

If we compare the act of voting conceptually to the way a movie critic is star rating a movie, it doesn’t make much sense to give a movie 437 stars. Just how different is that, really, from 450 or 420 stars? We don’t need such a high resolution; we could easily make do with 5 or 10 stars and still get our point across.

So for the sake of the argument let’s go with a maximum of 10 votes (even in the case where we go with your idea that open votes cost less than secret votes).

Second suggestion: Let’s decouple voting costs from merits

As you say, some of us have more merits on our account than others, and just because some are able to throw an absurdly huge amount of money into buying a large number of votes (even if, as we have seen, it quickly becomes very expensive), it doesn’t follow that this is a practice we should applaud. After all, our value in society is not reflected by the amount of money that we have. The real wealth that we all have and can all contibute with in one way or another is our talents, our creativity, and the work we provide for the community.

So let’s decouple the voting costs from our individual merit pools and introduce a separate “currency” for voting: 1 vote costs 1 voting token, 2 votes cost 4 voting tokens, and so on, just like in the original proposal.

I now suggest that each eligible voter is given an extra vote token each year. This means that everybody can always afford to cast at least 1 vote, since all vote tokens used will be given back in equal shares. It also means that senior voters potentially have greater voting power, but not by a lot.

This scheme can be varied in a lot of ways:

We could differentiate between e-residents and citizens and give the former 1 extra vote token (1 vote) each, while the latter get 10 extra vote tokens (~3 votes) each annually.

We could also increase the amount of tokens your get by a factor based on your seniority, such that the first year you get 1 vote token (or 10 if you are a citizen and we go by the differentiated model), the second year you get 2 vote tokens (or 20 if you’re a citizen), to a total of 3 (or 30) vote tokens, and so on: After N years you will have received a total of N×(N+1)/2 vote tokens (possibly multiplied by an e-resident vs. citizen factor).

I’m throwing random numbers into the equation here, just to illustrate the concept. The exact numbers can always be negotiated. My point is that rather than basing our individual voting power on how rich or poor we are, we base it on how long we have been members of the society, which hopefully also reflects our level of knowledge and/or experience.

And we still keep in mind that even if some will gain more power than others, it will to a certain extent even out because the vote tokens will be redistributed equally among all active voters after a given voting session has been concluded.

And finally: vote tokens shouldn’t be tradeable. To give an extreme example: a single voter with a million vote tokens can cast a thousand votes. But if the same wealthy voter distributes their tokens between a thousand voters, giving 1,000 tokens to each on the condition that they vote in favour of the giver, the one million tokens can cast a total of 31,622 votes.


@kas Quadratic Voting is definitely an interesting idea and has the potential to solve an issue that keeps coming up when I talk to people about Liberland’s Merit System:

“How will Liberland be resistant to Jeff Bezos swooping in and buying enough Merits to give himself control of the entire political system?”

With that said, I am not personally such a big fan of redistribution of Merits. If we as a country choose to pursue a quadratic voting system of some sort where

X^2 Merits = X voting power

then I think that each voter should permanently keep the Merits which they own, regardless of how many times they use them to vote.

Of course, Quadratic Voting (as well as One-Person-One-Vote) requires that you have a robust identity management system in place. Otherwise, I guarantee that there will be hackers performing Sybil attacks and thereby destroying any benefits which those systems purport to provide.


You do not like the idea that all merits (or voting tokens) are redistributed in equal parts to all active voters when the voting sessions has been concluded?

People who choose to cast just 1 vote can never lose the merit they spent buying that vote right. In fact, unless all people choose to cast just 1 vote, chances are that people who cast one or a few votes will end up with more merits than they started with. I like that.


I totally disagree with your opinion. The usual “one person, one vote” is only ever fair to the majority. And the major flaw of said model is that minority will always have to yield to the majority. That’s neither fair, nor equal.

In comparison, the quadratic voting model has been mathematically proven to be the most fair solution to the “one person, one vote” model. Did you read the original paper on quadratic voting?

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Others here have put a lot of thought into their posts.
It seems to me that your post was a shot from the hip, without any deep consideration.
You infer that the one person one vote system doesn’t have “manipulated by money or similar assets” or is not prone to abuse. You appear to have put no thought into the failures of the vote system you prefer.
Some posts have touched on how to reduce vote manipulation and how to be fairer, to improve, indeed this is the purpose of this chat group. @McCormick had a suggestion (2nd last paragraph) on how to keep vote manipulation at bay and to make it fairer. @kass has 2 suggestions in his last post.
Maybe you can offer a better vote system.

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