Democracy 2.1: when maths reinvent politics

Photo Karel Janeček / Mathematician, entrepreneur, and anti-corruption campaigner / September 29th, 2015

Mathematics and technology are increasingly used in decision-making. The current trend is even to replace human decisions by machine decisions. But in some experiences, technological innovation helps to reinvigorate the most human of all decision process: democracy. This is the purpose of the Democracy 2.1 experiment, launched by the Czech mathematician Karel Janeček: a radical innovation of the voting system, based on mathematical intuitions derived from game theory.

ParisTech Review – How did you shift from mathematics to entrepreneurship and eventually, to the reform of institutions?

Karel Janeček – My approach is basically the same, but I apply it to other areas now. At first, I was a mathematician, but also a player. I started to deviate a little from my main field when I developed a Blackjack software in the early 1990s. In 1995, I founded RSJ, a firm of trading algorithms. Mathematics remained at the heart of these activities. The first real change came with the launch of the Fund Against Corruption, which had nothing to do with my training but reflected a civic concern. Democracy 2.1 brings together both aspects, by introducing mathematical solutions to problems affecting the heart of our democratic system.

According to you, what are the biggest defects of our current systems?

The possibility of voting is at the heart of modern democracy and universal suffrage is a fundamental step. The challenge is to achieve both richer deliberation, allowing more informed decisions, and to choose among representatives those that are most consistent with the preferences of voters. Initially, this model kept its promises: the system was difficult to divert from its purposes. But over time, it became clear that politicians less concerned about the public good could easily use this system to manipulate voters and democracy for their own greed of power or money. Today, this deviation has reached the extremes and the system no longer selects the best, most honest candidates: it rewards the most cunning and loudest. The entry of media moguls in politics does not improve the situation, far from it! It seems to me that although citizens were perhaps more naive in the past, they were, in a sense, more difficult to manipulate.

One aspect of this problem is that people with the worst moral qualities have a systematic advantage. This is not only seen in politics, but also in big companies. Selfish, brutal individuals, those who do not bother about the consequences of their actions, have a systematic advantage. Psychological studies have shown this very clearly: within a group of individuals, a psychopath (i.e. a person who suffers from an ethical or emotional defect that impedes them from feeling empathy) it perfectly capable of keeping others away and seizing power. This is one of the major flaws of democracy.

One can be tempted to say that the voters’ equality is the issue. But it would taking a slippery slope: I think it is absolutely impossible to restrict voting rights in any manner whatsoever. In a modern democracy, we can not decide that only those who pay taxes or have certain qualifications will vote. We must resolve the problem differently.

This is precisely the challenge that Democracy 2.1 tries to tackle: preserving the equality of votes, while ensuring that voters with knowledge and ethical values have a greater impact on the result.

This seems insolvable!

Yes, that’s what I thought two years ago. But there are solutions, therefore we are trying to think “outside the box.” After a debate on electoral systems, I began to reflect on the effects of the possibility of having more votes instead of fewer voters. The result of the effect of multiple votes is that even if we maintain the absolute equality of voting and even if the rules are the same for everyone, those who are most committed, those who devote more time to a problem, will have a greater part in its resolution that those who are ignorant, extremist or do not accept consensus.

Let’s go back in time for a moment. Before developing this idea, I created the Fund against corruption in 2011, to support whistleblowers in the Czech Republic. After one year, I realized that the main problem in my country – like in many others – was not corruption, but the consequences of decisions. In other words, the problem was the inconsistency of policy makers, their chronic inability to seriously consider the impact of their own decisions.

This is where mathematics come into play: many algorithms for taking better decisions have been developed in numerous fields. Was it possible to redesign the electoral system and modify the  algorithm for choosing politicians in the Czech Republic? This was the first draft of what would become Democracy 2.1. The electoral system I imagined was based on two innovations. The first is negative voice: people can say not only “yes” but also “no.” They can specify who is not desirable. The second idea is that we can bestow two mandates at once: as opposed to the classic majority system, with the opposition of two candidates, and only one elected, each voter has two positive votes and one negative vote. They choose between three persons and designate two.

These ideas were discussed and in May 2013, during a discussion in a faculty of law, a critic of my proposal referred to the fact that some people voted exclusively for one political party. That made me think. Why not give more votes to people? Each voter could for example be given four votes. Whoever wishes to use all their votes will therefore vote outside “their” political party. Or else, they will give up the remaining votes. Consequently, the elected candidate will be forced to seek consensus. This is how the project Democracy 2.1 was born.

What is remarkable about this system is that it gives more power to people who are informed, interested and who accept a form of pluralism. But it’s a fair system: everybody has the same opportunities. Whoever isn’t interested in politics will choose one or two candidates. Whoever is committed can take advantage of a real electoral power, without concentrating that power under the form of a plebiscite, on one sole party. From a political point of view, this formula seems to me very important in so far that it helps support the consensus, that is to say, what we have in common.

Let’s consider, for example, the case of an extremist political party. The extremist party voter wants to support his political party and all other parties in his eyes are bad, according to the old saying “All rotten!” used and abused by populists. In the standard electoral system, extremist political parties have a great advantage. Why? Because most of the time, they do not compete with one another. We can have an extremist party on the right side, a fascist party for example, and an extremist party on the left, say communists, but it is rare to have two communist parties or two fascist parties that compete with one another. Whereas the spectrum of democratic parties, which caters to the majority of voters, is much more competitive. This puts moderate Democrats at a disadvantage.

I do not think that extremist parties should be banned. A number of voters supports them and it’s fine that they express their opinions. But it is important not to offer them benefits and yet this is what happens in a standard electoral system. The Democracy 2.1 project is precisely meant to correct this disadvantage of democratic parties. By giving voters four votes for four seats, a voter with a democratic and pluralistic sensitivity can get the best out their four votes. An extremist voter will give one to voice to his extremist party and will probably not have any other option.

This is the most important aspect of the project. The “negative” vote, which was crucial in the original version, eventually plays a less important role. The key element is the effect of multiple votes.

Where can this voting system be implemented?

Generally speaking, in any election with multiple options. Of course, in types of decisions that don’t necessarily fall in the field of politics. At the moment, we are focusing on three possible uses: smart cities, smart schools and smart companies. Politics is not the only field where decision-making processes can be improved!

Political democracy is, of course, the most important issue to me, because it determines everything else. But Paris was not built in a day. Not surprisingly, those in power today are not very supportive of the implementation of D21. We are building on the success of “apolitical” applications to help the system take root in politics. When its advantages will be better known to the public, political parties will no longer be able to ignore it. I am fairly optimistic: this could be a faster process than expected. D21 has been used in several countries, mainly in a framework of local democracy. The media coverage of certain projects, such as the participatory budget of the city of New York, for which we closely collaborated, allows to move faster.


What kind of feedback are you receiving?

Most of it is very positive, both for “apolitical” applications and the few tests we made in the political field. Democracy 2.1 is a tool for effective decision making, but not only: it is also a means of communication that allows for richer interactions with citizens. Take the example of smart cities, which isn’t all about technology:  when the City Council asks for the opinion of citizens on a project, they look at the one that was most successful, but also, among those that were selected, to the ones that raised controversy (i.e. with enough positive votes but also many negative votes). If a project is controversial, it may be that it wasn’t well explained enough: the Council can focus on the best approach to the project and try to understand more precisely the reasons for the rejection among some voters: the project, even after being selected, can be improved. The communication tool is also a management tool.

We currently receive many demands from cities and companies. One of the biggest Czech banks is actively using our tool. Two companies will start using it this fall. For companies, it is an excellent source of information. They can identify the preferences of their employees, gather information about their clients.

You mentioned smart schools.

We organized a poll in a school with 400 students and there are many other ongoing projects. The results were very encouraging. The purpose of the poll was to determine what students and teachers considered as the most serious disciplinary transgressions. The poll gathered informative data, which will significantly improve decision-making. Besides, the mere benefit of consultation, and the fact that the students were involved in the decision made the whole process much stronger. Teachers, for their part were enthusiastic: they understood things they couldn’t understand before. For example, in one classroom, they understood that they needed to focus on petty theft. In another final year classroom, there were problems with racism. These assessments helped teachers focus on the real problems and their remedy. And children feel that they are involved in running the school.

We are preparing several smart school applications for this fall. But the real explosive growth concerned the applications for smart cities, those, for example, that allowed to optimize a participatory budget. In the Czech Republic, about twenty municipalities use our tools. Four Tunisian cities have used Democracy 2.1 to approve participatory budgets. Portugal is one the most advanced European countries in this field. Votes are also organized in non-profit organizations or other communities, for example in France, or even in China.

You are truly a pioneer of electronic voting. What role does it play in your project?

Electronic voting is much more effective and accessible today. It is also more suited to complex voting systems, with multiple votes, like in Democracy 2.1. Since the beginning of the year, we have been developing a platform for electronic voting, that you can try on our website Anyone can set up a vote. In our experience, a vast majority of urban citizens is in favor of electronic voting. We also offer a “paper” version, so that nobody feels disadvantaged but only 10% of people decided to use the traditional ballot.

Of course, the organization of electronic voting raises important issues in terms of authentication and computer security, not to mention the fact that voting at home instead inside a polling booth could expose voters to pressures or security problems. This is a significant problem.

In the few countries where you have set up the system – the United States, China, Tunisia – what was the reaction of the voters?

We received very positive reactions everywhere, especially in Tunisia. We also observed that non-democratic extremists are very intelligent. Tunisia is the only country where the “Arab Spring” had a successful outcome. It is a free country and only a small percentage of the population is extremist. In such a context, the adoption of a model like Democracy 2.1 makes a lot of sense. If we succeed, it will be an enormous breakthrough. Imagine that the first country to adopt this new form of democracy is a Muslim country!

The enthusiasm shown by the voters in this type of voting system is fundamental. The majority system, in conventional voting systems, has many flaws. For example, voters anticipate the behavior of other voters and incorporate it into their choice; or they give their vote to the candidate, among those who seem to defend good options, that are mostly likely to win. Voting for the “lesser evil” is, in my opinion, a sign of malfunction of democracy. Democracy cannot work well with truncated choices. We should be able to make choices that are richer, more varied and less dependent on the context. In this sense, there really is a democratic deficit today. The low participation rate is also a symptom.

By giving people more votes, positive as well as negative, Democracy 2.1 confers a playful side to the vote and allows to narrow down the choices. The playful aspect is by no means insignificant: it helps motivate voters – in the same way that serious games motivate people in learning situations. But motivation comes mostly from a sense of intellectual and moral comfort: voters can express themselves in a more accurate and nuanced manner that is more faithful to their opinions. We’ve noticed this in cities and schools where we tested our system: people are generally more interested, they want to know more and are much more active. Offering them a wider range of choices allows them to customize their vote, to match it with what they really want. We have left behind us the industrial era, the one size fits all philosophy, the times when Henry Ford would say, not without humor, that people could choose the color of their Model T, as long as it was black. It’s the same in politics.

You sometimes mention, in this regard, the idea of “social satisfaction” that is integrated in your voting system.

It is a crucial point. We can define it like this: when a person votes, and when at least one option of their choice wins, they experience “satisfaction”. If none of their options wins, they feel rather frustrated – as if the others had made the decision for them!

This idea takes its relevance in “apolitical” applications, where there are more than two options. Social satisfaction can vary if you have chosen two or six of the eight selected options. You can even build a social satisfaction index, based on the average number of options that everyone was pleased to see validated. This index also measures the degree of consensus.

The situation is somewhat different in political elections, when there are fewer options. If there are two mandates involved and none of “my” candidate is selected, the index is 0. If one of my candidates is elected, the index is 0.5; if two are elected, the index is 1. Note that, for conventional elections, the satisfaction index is necessarily low. With our system, more people will receive their share and therefore, be satisfied. They can truly feel that their vote had an impact.

Let’s get to the core of your standard model for political elections. There are two vacant seats, and each voter has four positive votes and two negative votes. Why?

Democracy 2.1 is a general voting system, and you can have any number of winners. Why chose the model that you mention in parliamentary elections? In theory, we could perfectly have three seats. But that’s not necessary. The fundamental difference is between one and two, not two or three. From two to three, it unnecessarily complicates the election and too much is asked to voters. The key is simply to ensure that the number of votes is greater than the number of seats, to produce an effect of multiple votes. Why did we chose the exact double? Again, we could assign each voter five or even six votes. But again, the marginal benefit of additional voices will be reduced.

We are undertaking many experiments because we don’t know, at this day, where is the optimum. I’m not saying that the optimum is 4 votes for systems with 2 mandates. I believe, however, that 3 would be too little. Regarding the number of negative voices, 2 is the maximum. This is a consequence of the theory of games, which is one of the pillars of the system. The model shows that it is better to have twice as many positive votes than negative votes – otherwise the election turns into a killing game! I even think that in most long-term political systems, the optimum number of negative votes is 1 and not 2. Therefore, 4 positive votes and 1 negative vote.

The key is the effect of multiple votes. There are even situations where the negative voice is not desirable, for example in a situation of non-homogeneous political groups where there is a religious minority. If there are tension between the communities, the negative vote is not desirable because it can be used to exclude minorities.

Game theory teaches us that people with bad intentions only cooperate when they can obtain an immediate benefit. On the other side, some people are not very familiar with each other, but have positive intentions: they do not make decisions for their own benefit, but also for society. They will cooperate, even if they cannot take any immediate benefit, because they share a common goal, a common vision. On the “positive” side, implicit cooperation works; on the positive side, it does not work if there isn’t any immediate benefit for both parties. This is a huge advantage of the “positive” part of the political spectrum.

But there are situations where there is an implicit cooperation between the “negative” sides, for instance, in the case of ethnic or religious intolerance. In this sense, fanaticism and sectarianism can cement implicit alliances. Negative vote must be established with caution, and in some situations, they are best avoided!


  • Democracy 2.1 (Official website)
  • Democracy 2.1 in China
  • Recalculating democracy (Politico, March 2015)

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