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Democracy 2.1

Janeček Method (D21) is an electoral system created by Czech mathematician Karel Janeček. Janeček Method (D21) is a modern voting and electoral method. Its main advantage is an effect of multiple votes which enables casting multiple plus votes, and in certain cases, also a minus vote. Multiple votes enable us to express a wider scope of preferences, thereby reflecting the complexities of social choice more accurately. The system was developed ostensibly in response to corruption within the Czech political system. Though it has not yet been used in any general elections, D21 has found use in several participatory budgeting programs conducted by cities and countries around the world, including the New York City. The game Prezident 21 was introduced in 2016 in order to help familiarize people with the D21 system.

social choice participatory budgeting electoral system

1. Background

According to Transparency International's Global Corruption Barometer 2013, a majority of Czech citizens believe political corruption in the country to be widespread.[1] In March 2011, Janeček founded the Endowment Fund Against Corruption (NFPK) whose stated objective was exposing prominent cases of corruption.[2] It was suggested that the country's voting system itself needed to be revamped[3][4] so the basis of "Democracy 2.1" was formulated in 2012 and was beta tested the following year.[5]

2. Founder of the Method - Karel Janeček

Karel Janeček is a Czech mathematician, philanthropist, entrepreneur, anti-corruption campaigner and author of voting system Janeček Method (D21) and online game Prezident 21. At the beginning of his career he started the firm RSJ Algorithmic Trading. In 2004 the RSJ Company became the Designated Market Maker for the London Stock Exchange Derivatives Market – NYSE Liffe. He founded many foundations. For example, the Anti-Corruption Endowment aimed at giving a helping hand to victims of fraud, aggression and irrational bureaucracy; Fund helping people in need in Czech republic, Neuron fund for the Support of Science or Karel Janeček Foundation in support of the development of an active civil society. He graduated from the Faculty of Mathematics and Physics of Charles University in Prague in the field of Probability and Mathematical Statistics. Karel gained MBA in Finance at Bradley University, Peoria, Illinois, USA and PhD. in the field of Mathematical Finance of Carnegie Mellon University in Pittsburgh, Pennsylvania, USA.[1]

3. Rules of the System

The basic features of the voting method presented herein is that the voter can identify in a single ballot more than one preference by applying systematically capped multiple votes. This principal introduces a new dimension to the voting methodology. It permits voters to cast multiple votes that are either upvotes or downvotes. The number of upvotes have to be at least twice the number of seats to be filled in the election. The upper boundary of the total number of votes is pegged to the number of ballot options. Hence it can fluctuate based on the number of candidates and the degree of desired consensus to be achieved. Though the method's general definition proposes to limit a total number of votes to a half of the number of options, in practice no more than 2x(N+1) votes are recommended, where N represents a number of seats to be filled.

Application under the multiple winner scenario

Suppose we want to choose W winners out of T ≥ 4 candidates. A voting system follows the method described herein if and only if:

● Each voter is allowed to cast up to P ≥ W (plus) upvotes and up to M (minus) downvotes, where P ≥ 2M (i.e., number of upvotes has to be at least twice as large as the number of downvotes), and P ≤ T/2. In most cases, it's recommended to use P ≥ 2W (optimizing the effect of more votes) and P ≤ T/3.

● Each voter can cast no more than one vote for any candidate.

● The number of upvotes cast by each voter must be at least twice the number of downvotes cast.

● Each vote has the same absolute weight (+1 or -1). The W candidates receiving the greatest net sum of all votes win.

Hence, if there are two seats per district and a competing party nominate one or two candidates, voters may cast up to four upvotes and up to two downvotes, which they may distribute across all candidates in the district with only one vote per candidate. The same rules and rationale apply in single-winner elections.

The most important difference between the Janeček Method (D21) and other voting systems used in politics is the notion of multiple-vote. It weakens populism and extremism. Multiple positive votes accentuate the candidates with the broadest support thanks to the effect of overlapping preferences. The negative vote takes the role of detecting the options that voters disapprove of. The whole system can eliminate the controversial possibilities thanks to the combination of plus and minus votes. The consequence is that the result should divide the society as little as possible.[6]

The inability to cast all of one's votes on a single candidate encourages voters to use their remaining votes on other candidates, with whose positions they agree even if they are of a different party affiliation.[3][7]

4. Effect of Systematically Capped Multiple Votes

To demonstrate the impact of capping the multiple votes at the certain maximum we will use a one-winner scenario. Suppose that we have one seat per district and all voters have two upvotes. For the purposes of the illustration, suppose the following candidates are competing:

  • One right-wing "extremist" 4 with 20% of preferences.
  • Two right-wing "democratic spectrum" 5 candidates, each with 15% of preferences.
  • Two left-wing "democratic spectrum" candidates, each with 15% of preferences.
  • One left-wing "populist" 6 with 20% of preferences.

In the most common majoritarian system, first-past-the-post (FPTP), 7 either the left-wing populist or right-wing extremist would win. Under a two-round system, both of them would qualify for the second round of voting. A key characteristic of the method described herein is existence of a second vote, which each voter may give to another candidate, as follows:

  • A supporter of the right-wing extremist is likely to give his second vote to someone from the democratic right or withhold his second vote. Less probably, he will give his second vote to a candidate from the democratic left, and least probably to the populist candidate of the left wing.
  • A supporter of a democratic right-wing candidate will give his second vote most probably to the second democratic candidate of the right wing, less probably to a democratic left-wing candidate, least probably to the right-wing extremist.
  • Supporters of left-wing candidates will behave accordingly, with designations of "right" and "left" reversed.

The results of voting under the Janecek Method (D21) can be expected as follows:

  • The right-wing extremist will get just over 20% of votes.
  • The right-wing democratic candidate will get just over 30% - he will get votes from his supporters (15%) and most votes from supporters of the second democratic right-wing candidate (15%), and some second votes from supporters of the right-wing extremist.
  • Similarly, the left-wing democratic candidate will get just over 30%.
  • The left-wing populist will get just over 20%.

The analysis shows that in our model one of the candidates of the "democratic spectrum" will be elected. In standard voting systems non-extremist candidates must compete with one another in a zero-sum contest for votes, meaning that right-wing or left-wing extremists or populists are more likely to win or advance to the second round to the detriment of candidates with broader appeal. A key characteristic of the voting method described herein is the fact that candidates with broader appeal are less likely to attack one another to their mutual detriment. On the contrary, they might partially support each other in pre-election campaigning in order to attract the second votes of the primary voters of the opponent, leading to convergence of their political positions.

Capping the number of upvotes allows voters to express their strongest preferences hence resulting in consensual outcome with maximum utility.

5. Effect of Downvote

An option of casting a downvote is another feature of the proposed method, which allows voters an even wider scope to express their preferences by letting them designate a candidate they do not want to see elected. It is important to note that the idea of a downvote is not a novel concept. It was first proposed as Negative Voting (NV) by Boehm in an unpublished essay in 1976 and further developed by other scholars.

In the method proposed herein, a downvote and an upvote have the same absolute weight (-1 or +1). In itself, the availability of a downvote will probably result in a significantly higher rate of voter participation, especially in a climate of political polarization, public skepticism or disapproval of current political elite. Moreover, the existence of downvotes further diminishes the electoral strength of extremism and populists, as they provide an important mean to filter notoriously corrupt and criminal actors from a political system.

Since number of downvotes is strictly limited the results of large-scale experimental studies demonstrate that downvotes are not generally used in retaliatory manner. Moreover, overall on average 56.1% of voters in the experiments exercised the right of casting a downvote. Hence the option of expressing a disapproval by casting a downvote with set forth limiting parameters did not results in increased polarization of electorate (voters in our experiments). On the contrary, the majority of voters representing different ideological positions reached consensus in their casting of downvotes for the same candidates. The latter phenomenon requires further investigation.

6. Official Proposal

The proposal to utilize Democracy 2.1 and two-seat voting districts was submitted to the Czech government, and rejected. As of 2015, D21 has not been used to decide any major general elections in the country or elsewhere.[4]

7. Development

In April 2015, D21 worked alongside Stanford University in creating digital ballots for participatory budgeting programs in several New York City districts. In addition to the actual ballots were experimental ones that tested the voting algorithm, which were said to showcase the system's increase in voter consensus as well as satisfaction.[3][8]

D21 was one of many digital tools included in a 2016 study conducted by the Democratic Society of Scotland in regards to participatory budgeting. According to the study, participants found that the system increased voter engagement by making them think more carefully about decisions and furthermore helped clarify voter priorities.[9] The system was considered for participatory budgeting experiments in Cascais, Portugal.[4][10]

8. Use in Municipalities

8.1. Říčany

Karel Janeček's system was first used in March 2015 in Říčany in aim of testing and developing the new platform used for municipal decisions. The objective of choosing this method was to motivate people to take interest in what is happening in their municipality. The system makes it easier for them to get involved in making public decisions to raise general welfare and transparency of public procurements.[11]

It was possible to vote by every computer, tablet and smartphone with a connection to the internet. Since 2015, there were many decisions about public investments and cultural events made by this system.[12]

8.2. New York

One of the biggest project where the Janeček's methode was used took place in 2016 in the city of New York. It was the largest participatory budgeting project in North America. In this project people were asked to distribute $38 million among various different projects proposed by the members of the community to improve the life in the city. 28 out of the 51 districts were involved in this voting and around 68 voters have participated.

One of the advantage of this system was that voting was possible only online on the voting spots or anywhere by a computer or smartphone. That's why the final ballot counting was much faster and more error-free. It is also less expensive and more ecologic as there is no need to use paper ballots.[13]

Every city or company can try to use an online system of Democracy 21 for making the decision in the workplace, school or between friends. The aim of Karel Janeček is to show the effectivity and simplicity of D21 in elections in municipalities to adopt it one day in national politics.[14]

9. Difficulties

It would be very difficult to adopt this voting system at a political level. Modification of the voting system is a significant change of legislation requiring 3/5 of the deputies' votes. The social games organised by Karel Janeček have showed that if his method was used, most of the current (2019) MPs would not be elected.[15][16] According to the Czech political scientist Perottino, another reason why it will be difficult to adopt a new voting system is that generally, the elite is more conservative,[16] meaning MPs will hardly agree on such a radical change.

The system was also criticized by Perottino for its complexity compared to the proportional voting system used currently. He claims it will be difficult for the electors to understand the new system and use it efficiently.[17] In addition, it will be more complicated for the administration to determine the election results.[16]

D21 has already been used in more than 180 in about 250 voting events.[16]

10. Criticism

Negative voting has been described as "ill-advised" in cases where it could be used against a religious or ethnic minority.[7] Concerns have also been raised that the minus vote could encourage negative campaigning.[18]

Political scientist Karel Sál has criticized Janeček Method (D21), claiming Janeček's assumption that a new electoral system alone could cleanse Czech politics is "at least naive" and further criticizes the system's basis on the ideals of rational choice theory. Sál also highlighted the technical difficulty of amending the Constitution of the Czech Republic in order to implement D21 into Czech elections.[19]

One of the main Janeček's objective, he would like to achieve is to diminish extremist electoral strength.[20] This point has been questioned by some specialists in political sciences. They claim that the existence and competitiveness of extremist parties is essential for a well functioning democracy for several reasons.[21][22]

There is a theory that limitation of extremism on the political level can cause the mushrooming of the ideology in other forms. Those ways of extremism could become underground and be hardly monitored so potentially more dangerous.[16][22]


  1. "Czech Republic 2013 - World's largest opinion survey on corruption - Transparency International" (in en). 
  2. "Anti-corruption campaigner ‘targeted’ by Prague underworld | Téma". 2012-01-31. 
  3. "Alumnus Gives Voters A Better Way to Decide - News - Carnegie Mellon University" (in en). Carnegie Mellon University. 2016-03-07. 
  4. Cunningham, Benjamin (2015-08-13). "Recalculating democracy" (in en-US). POLITICO. 
  5. "ParticipateDB: The Digital Engagement Tool Directory" (in en). 
  6. "Janecek method". 
  7. "Czech philanthropist exports own-developed election system | Prague Monitor" (in en). 
  8. "New York City Tests Digital Ballot in Participatory Budget Vote" (in en-US). Civic Hall. 
  9. The Democratic Society for the Scottish Government (February 2016). Digital tools and Scotland’s Participatory Budgeting programme (Report). 
  10. Pincha, João Pedro. "Lex Paulson: "Nova Iorque tem muito a aprender com Cascais"" (in pt-PT). 
  11. "Občané Říčan si vyzkouší unikátní hlasování díky projektu Demokracie 2.1 - ŘÍČANY (oficiální stránky města)". 
  12. "Říčany". 
  13. "D21 English". 
  14. "Řešení pro školy". 
  15., Beneš & Michl. "Prezident 21" (in en). 
  16. "Janečkova Demokracie 21: Volby jako hra". 
  17. "Jaký volební systém pro Českou republiku?" (in cs). 2015-12-10. 
  18. Haury, Caroline (2014-10-31). "Democracy 2.1: The idea of empowering voters through a new election system" (in en-US). Friedrich Naumann Foundation for Freedom Brussels. 
  19. Sál, Karel (2015-05-29). "The Democracy 2.1 election system under the magnifying glass" (in cs-cz). 
  20. "The use of Janecek method in politics". 
  21. "Should extremist parties be banned in the EU?" (in en-US). 2012-11-14. 
  22. "Democracy’s New Normal: The Impact of Extremist Parties". 
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