# Draft:Janeček Method (D21)

Janeček Method (D21), also known as D21, formerly known as Democracy 21, is an electoral system[1] created by Czech mathematician and political activist Karel Janeček.[2] The system was developed in response to corruption within the Czech political system.[3] As opposed to a single-vote system, D21 offers voters the opportunity to cast both multiple and negative votes.[4] 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.[5][6][7][8] The game Prezident 21[9][10] was introduced in 2016 in order to help familiarize people with the D21 system. The voting method is researched and analysed by the Institute H21.

The Method has a wide range of applicability in group decision-making processes, including choosing an individual(s) to hold public office in modern representative democracies. Unlike other voting methods, Janeček Method (D21) adds an additional dimension to the non-ranked voting space by introducing two new features that incorporate requirement criteria for the method. Its most important contribution to the voting methodology is introduction of Systematically Capped Multiple Votes requirement that sets a ceiling for the total number of votes each voter can cast on a single ballot. This feature is intended to incentivize positive election campaigns, as candidates would “share” votes from the electorate, and hence would be encouraged to cooperated and move toward consensus. Its second novel feature derives from the Method’s option of a Minus vote, in which case a 2:1 Ratio of Plus to Minus Votes limits the number of Minus votes allowed to no more than half of the number of Plus votes. Initially, the option of Minus votes was introduced and envisioned as a mechanism voters can use to diminish the chances of corrupt and extremist candidates winning. Application of a Minus vote option is not considered a crucial feature and requires a discretionary approach. Janeček cautions that this feature has to be employed with prudence and restraint to avoid retaliatory voter behavior and prejudiced election outcomes. For example, it is not advised to exercise a Minus vote option in elections in communities where a religious minority comprise a part of the electorate.

## Background

Initially Janeček coined a novel voting system, at that time denoted as the 2:1, based on multiple votes with a downvote option, in January 2012 as an outcome of his anti-corruption activism. According to Transparency International's Global Corruption Barometer 2013, a majority of Czech citizens believe political corruption in the country to be widespread.[11] In March 2011, Janeček founded the Endowment Fund Against Corruption (NFPK) whose stated objective was exposing prominent cases of corruption.[12] It was suggested that the country's voting system itself needed to be revamped[13] so the basis of the Method was formulated in 2012 and was beta tested the following year.[14]

The 2:1 was designed to help voters weed out known corrupt candidates entering the political arena. To inform and educate the public about the 2:1, Janeček started the Positive Evolution movement which, along with other initiatives, included 13 lectures in large Czech cities in the fall of 2012. Later in his public speeches and lectures Janeček referred to the system as D1.9. In April 2013 Janeček formulated a general definition of his proposed voting method, labeling it D21. He emphasized that allowing a greater number of Plus votes than the number of winners had a significant effect on voter behavior and election outcome.[15]

## Description

The Janeček Method (D21) permits voters to cast multiple votes that are either Plus or Minus in a single ballot. The Method can be applied in elections with single as well as multiple seats. Under the Janeček Method (D21) voters are given more Plus votes than there are seats to be filled, with the upper boundary of votes being pegged to the number of ballot options. Hence the total number of allowed votes can fluctuate based on the number of candidates and the degree of desired consensus to be achieved. Consensus implies the degree of homogeneity within a set of individuals, measured by a scale for the similarity of preferences.[16] The latter can be determined by applying Tastles’ and Weirman’s (2005) measure of the probability distribution over a discrete set of choices with ordinal values that yields a single value ranging from 0 to 1, with ‘0’ representation complete disagreement and ‘1’ full agreement.[17]

Though the Method’s general definition proposes to limit the total number of votes to half of the number of options, in practice no more than 2(N+1) votes are recommended, where N represents the number of seats to be filled. This feature is defined as the systematically capped multiple votes requirement.

The Janeček Method (D21) also gives voters an option of expressing disapproval by casting Minus votes. However, the number of Minus votes cannot exceed half the number of Plus votes allowed. A voter is permitted to use a Minus vote only after casting at least double the number of Plus votes. The latter requirement is the second unique feature of the Method – the 2:1 ratio of Plus to Minus votes.

## Original Definition

Under the Janeček Method (D21) in an election with W winners out of T ≥ 4 candidates:

• Each voter is allowed to cast up to PW plus votes and up to M minus votes, where P2M (i.e., the number of plus votes has to be at least twice as large as the number of minus votes), and P ≤ T/2.[18]
• Only one vote per candidate is allowed.
• Each vote has the same absolute weight (+1 or -1).
• The W candidates are the recipients of the greatest net sum of all votes.

## Voting Process

The Janeček Method (D21) ballots show a list of the running candidates for the election seat(s). A voter can indicate support for several candidates by casting an allowed number of Plus votes next to their names (with one vote per name), determined by the systematically capped multiple vote criterion. Optionally, a voter can also indicate a disapproval by casting Minus votes, allowed by the 2:1 Ratio Plus to Minus criterion of the Method.

All votes have the same absolute weight, count equally, and do not specify preferences between them. Only one vote, Plus or Minus, per candidate is permitted. Final tallies show how many net voters support each candidate. The candidate with the highest score is the winner.

## Effect of systematically-capped multiple votes

The effect of the systematically capped multiple votes is demonstrated on a one-winner hypothetical scenario with six contenders running for election: A, B, C, D, E, F. The candidates’ ideological profiles are presented below:

 Ideological Profile Left-wing “Populist” Moderate-Left Moderate-Right Right-wing “extremist” Candidates A B and C D and E F

Moderate, or Centrist, candidates, regardless of left or right-wing positions on specific issues, are those who stand behind the basic guarantees of democratic pluralism, accountability and inclusion.[19] Political extremists are those who stand outside the democratic consensus and seeks to use political power to fundamentally alter democratic processes and institutions.[20] Populists, on the other hand, while nominally part of the democratic spectrum, have no natural political allies outside their own party. They, like extremists, may base their appeal on demagoguery, spreading misinformation, half-truths and fake news.[21]

For the purposes of illustration, suppose voter preferences are divided the following way:

 Candidates A B C D E F Voter Preferences 21% 17% 12% 13% 16% 21%

In this situation, under the most common majoritarian first-past-the-post (FPTP) system, either Candidate A, the left-wing populist, or Candidate F, the right-wing extremist, would win the election. Under a two-round system, both, Candidate A and Candidate F would qualify for the second round of voting.

Now we will apply the Janeček Method (D21) to the same scenario by giving each voter two votes instead of one. Now voters can cast their second vote for a candidate other than their first preference. In this case the following outcome might emerge:

• Candidate F, the right-wing extremist, supporters are likely to give their second vote either to Candidate D or Candidate E, moderate-right candidates, or withhold their second vote. Less probably, they will give their second vote to Candidates B and Candidate C, moderate-left candidates, and least probably to Candidate A, the left-wing populist. This assumption is based on research findings suggesting that as individuals’ preferences become more extreme, their views intensify.[22] In addition, it has been shown that individuals who are preoccupied with an issue tend to screen out information that conflicts with their predispositions.[23] Hence it can be purported that supporters of the left-wing populist will be unlikely to cast their second vote to candidates with opposite political views.
• Candidate E supporters will most probably give their second vote to Candidate D, another moderate-right candidate. It is less likely they would cast their second vote for candidates B and C; least probably for Candidate F, the right-wing extremist; and unlikely for Candidate A, the left-wing populist.
• Candidate D supporters are likely to cast their second vote for Candidate E, as they both represent the same ideological profile.
• Supporters of left-wing candidates will behave accordingly, with designations of “right” and “left” reversed.

This scenario under the Janeček Method (D21) can yield the following outcome:

 A B C D E F A 21% 10% 11% 0% 0% 0% B 0% 17% 17% 0% 0% 0% C 0% 12% 12% 0% 0% 0% D 0% 0% 0% 13% 13% 0% E 0% 0% 0% 16% 16% 0% F 0% 0% 0% 7% 7% 21% Total 21% 39% 40% 36% 36% 21%
• Candidate A will remain with 21% of votes;
• Candidate B will get 39% -- 17% from his original supporters + 12% from Candidate C supporters + 10% from Candidate A supporters;
• Candidate C will get 40% -- 12% from his original supporters + 17% from Candidate B supporters + 11% from Candidate A supporters.
• Candidate D will get 36% -- 13% from his original supporters + 16% from Candidate E supporters + 7% (1/3) of Candidate F supporters.
• Candidate E will get 36% -- 15% from his original supporters + 13% from Candidate D supporters + 7% (1/3) from Candidate F supporters.
• Candidate F will remain with 21% of his original votes.

As this example reveals, under the Janeček Method (D21) the moderate-left candidate, Candidate C, 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. As the example above demonstrates, under the Method 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 from their opponents’ supporters, which should lead to convergence of their political positions.

The implication and significance of the Janeček Method (D21) feature of setting a ceiling for the total number of votes allowed, as defined by the systematically capped multiple votes requirement, are especially notable in comparison with Approval Voting (AV), under which each voter can approve any number of candidates. Contrary to the Janeček Method (D21), AV does not limit the number of votes each voter can cast on a single ballot. This may result in inflation of votes, creating a risk of a less preferred candidate by the majority of voters winning while making it harder for the most favorable and most consensual candidate to be elected. AV tends to favor candidates who offend the fewest number of voters and have smallest number of opponents. As a result, it incentivizes voters to vote strategically.[24] Some of the strategies include Bullet Voting, when a voter approves a single candidate, and Compromising, when a voter approves candidates who are otherwise considered unacceptable to the voter. Both allow voters to block a candidate, increasing the probability an alternative wins.[25] Research shows that under AV individuals with low political interest will tend to support only one candidate. Hence these individuals along with ideological group with bullet preferences may have a greater power to decide elections under AV.[26] The extreme flexibility of votes makes AV vulnerable to majority decisiveness[27] and to erosion of the majority principle.[28][29] The Janeček Method (D21) mitigates these two drawbacks of AV by restricting the number of votes under the systematically capped multiple votes feature. The latter requirement nudges voters to express their preferences more precisely and rewards well-informed voters, resulting in sincere voting behavior and a more consensual outcome.

## Effect of Minus vote

The option of a Minus vote, which is proportionally conditioned upon a number of Plus votes cast, allows voters to designate a candidate they do not want to see elected. As mentioned earlier, this option was originally incorporated into the Janeček Method (D21) to prevent corrupt candidates from entering into governments. Hence the interplay and effect of a Minus vote is demonstrated in the following hypothetical scenario.

• Two parties: Right-wing and Left-wing, are nominating two candidates for a one-seat election. One of these candidates is corrupt (-) while the other one is honest (+). So, the four running candidates are: L+, L, R+, R.
• Each voter is given 2 Plus and 1 Minus votes.
• Though ideally the candidate’s integrity and honesty would be a decisive criterion for voters, this scenario assumes the worst possible case, where all voters will favour party loyalty over personal integrity when identifying their preferences. Hence, they will give their preference to the corrupt candidate from their party rather than the honest one from the opposition.
• In addition, these voters can apply tactical voting.[30] Voters will cast their Minus votes in a manner intended to benefit their preferred party candidate rather than register disapproval of another. Hence, tactical voters may be willing to cast Minus votes against the opposition party’s honest candidate, rather than its corrupt one, if they deem it to benefit their own preferred candidate.

Even under this pessimistic scenario, the option of a Minus vote acts as a filtering system against corrupt actors. The honest candidates L+ and R+ are elected as soon as the difference between the size of the right-wing and left-wing electorate is not too great. Specifically, L+ and R+ win as soon as the ratio between the number of right-wing voters nr and the left-wing voters n1 is more than 3 to 4 and less than 4 to 3. In the case that voters do not vote tactically, i.e. where they give their minus votes to the corrupt candidate of the opposing party, the filtering effect happens for a ratio of votes between 1 to 2 and 2 to 1. The conclusion above holds that both of the honest candidates win as soon as:

nr / (n1 + nr) ${\displaystyle \in }$${\displaystyle \left({\frac {3}{7}}\right)}$, ${\displaystyle \left({\frac {4}{7}}\right)}$.

It is important to stress that a Minus vote is a relatively new concept and hence it is often dismissed too quickly based on the argument that it may result in encouraging negative campaigning and a more negative election atmosphere in general. The results of the experiment study conducted during the 2017 Presidential election in France demonstrate this tendency as most participants cast more "against" votes than "in favor" votes when such opportunity was allowed by the ballot.[31]

An option of a Minus vote under the Janeček Method (D21) addresses this argument in two ways. First, an option of a Minus vote is consistent with the results of the In Situ experimental study on Evaluative Voting (EV) with a scoring scale of (-1, 0, 1) where a candidate who is not approved receives grade “-1” with less frequency compared to a candidate who is not approved under the scale (0, 1, 2). This tendency can be explained by the different interpretation of the “-1” and “0” grades. The grade “-1” is certainly interpreted as a ‘rejection’ grade; hence voters cast it only for the candidates they really dislike.[32] Hence a possibility of a Minus vote allows voters to elaborate on their preferences, giving them a wider spectrum of choice.

Second, the Method’s 2:1 Ratio of Plus to Minus Votes requirement – contrary to voting systems that allow a negative vote without setting a limit on a number of disapprovals a voter can cast on a single ballot –discourage potential negative voting tendencies resulting from the inflation of the minus votes.

## Usage and Application

### Practical Application

The Janeček Method (D21) has been used extensively in opinion polls and public decision-making processes run by cities, governments, political parties and non-profit organizations using the “D21” software platform. It has been widely used in participatory budgeting (PB) processes at organizational and city levels.[33] The Janeček Method (D21) has been adopted by over 60 municipalities across different countries in their budgeting procedures. Starting in 2016 New York City has used the "D21" software platform in decision-making processes on public space development in each district.[34] Over this time almost 270,000 residents voted using the "D21" software platform for projects to be executed in their districts.[35]

The Method has been implemented as the Participatory Budgeting solution for Scottish councils as part of the Government's “PBScotland” nationwide initiative.[36][37] Hosting statutorily audited elections for Czech Republic's monopolist Collective Rights Management Organisation (with 3.47 million members represented). Implementing a nation-wide engagement project with the office of the President of Senegal to consult and co-design a 10 year Economic Plan. Supporting France’s newly elected En Marche! Party to set its agenda after a successful presidential election.

Since 2016 the "D21" software platform has also been used for participatory budgeting in schools in the Czech Republic, with a total of 10,927 students from 41 schools, across seven cities voting on their school projects.[38] The Foundation for Community Consensus (FCC), the Institute H21’s Indian partnership organisation, conducted PBs using the Janeček Method (D21) in 9 schools in Delhi and Rajasthan, with 2,000 students participating. The "D21" software platform has also been used in 5 states (Delhi, Chhattisgarh, Tamil Nadu, Haryana and Rajasthan) for urban planning and rural development projects with more than 300,000 citizens participating. It has also been adopted by the United States Department to introduce young African tech-leaders to digital polling and analytics across five developing countries, as part of the Young African Leaders Initiative (YALI) Tech Camp program.[39]

In recent years the "D21" software platform widened the scope of its services beyond voting. By employing the principles of Human centered design, it facilitates civic participation in community decision making.

### Experimental Studies

Although it has not yet been used in any political elections, the Janeček Method (D21) was applied in three large scale experimental studies in the Czech Republic, conducted by Institute H21 (formally known as Institute for Democracy 21). These ran in parallel with the actual elections, with participants “voting” for real candidates. These were Prezident 21, the 2018 Presidential Election Terrain Research, and the 2018 Senate Election Study.

1. Prezident 21 (P21) was an online election game, which ran between December 2016 and January 2018. In this game, the public could vote for the 2018 presidential candidates in the Czech Republic via a real-time, online voting application using the "D21" software platform. Anyone who wished to participate could vote online, using up to three Plus and one Minus votes distributed across nine candidates. Overall more than 300,000 participants took part in the election game with 165,000 actually voting for the official presidential candidates. The P21 results were considerably different from the actual election outcomes. In the game, Jiří Drahoš was the winner, while the winner of the real-world election, Miloš Zeman, finished last. Zeman’s poor performance in the P21 game reflects both the non-random nature of the voter sample in the game and Zeman’s tendency to attract negative votes.
2. The 2018 Presidential Election Terrain Research involved a survey of 2,568 people during the first-round of election on January 12 and 13, 2018. The survey participants were asked to vote for presidential candidates using the Janeček Method (D21) with three Plus and one Minus votes. The goal of this study was to compare real election results with those of surveys. Jiří Drahoš was again the winner, while Zeman finished in fifth place.
3. The 2018 Senate Election Study was conducted during the 2018 Senate election in the Czech Republic, where the Janeček Method (D21) was applied along with First-past-the-post (FPTP), Approval Voting, Dis&approval Voting, Majority Judgement, and Instant-Runoff Voting (IRV) methods in five precincts. A total of 4,096 people (approximately 800 in each district) participated in the study that took place from September 28 to October 6, 2018. Though all voting methods produced the same winners, candidates’ positions varied under each method. The results show that the Janeček Method (D21), similarly to Approval Voting, favours candidates with broader appeal even if they lack strong support. In addition, the Janeček Method (D21) along with other methods, which allow voters to express disapproval, penalizes polarizing candidates. The latter can be seen in changing runner-up positions in three precincts. According to Institute H21 analysis, the results of this study strongly suggest that the Janeček Method (D21) rewards consensual while highlighting controversial or extremist candidates.

## Janeček Method (D21) and Voting Criteria

This section will apply three criteria – Condorcet winner (CW), Monotonicity, and Strategyproofness – to the Janeček Method (D21).

### Condorcet winner (CW)

CW requires that if there exists an alternative that would win a head-to-head contest between itself and any other choice, the voting method must always choose that alternative.[40] It is important to stress that the CW criterion is not satisfied by most voting systems.[41] Here two important points need to be raised. The first involves whether it is important that a voting method satisfies this criterion.[42] To try to answer this, consider an election with three running candidates – A, B, and C – where A ${\displaystyle \succ }$B ${\displaystyle \succ }$C for n + 1 voters, and B ${\displaystyle \succ }$C ${\displaystyle \succ }$A for n voters, n ${\displaystyle \in }$N. The Condorcet winner is A, while the winner under the Janeček Method (D21) is B. While A’s victory is gratifying for all n + 1 voters, since A is their first choice, for n voters it is a defeat because their least-preferred candidate won. Under the Janeček Method (D21), with B being a winner, n voters now have their first-choice candidate; n + 1 voters have their second choice; and no voters have their least-favorite choice. From a social utility point of view, Candidate B is more rational, though this candidate is not the Condorcet winner. Therefore, the Method’s unique features enable detection of scenarios where election of CW is not desirable. The second of these points is that, in cases when the CW is desirable, it is hard to construct a scenario under the Janeček Method (D21) in which the CW criteria will not be satisfied. It can be argued that the CW is satisfied by the Method whenever the criterion is desired.

Moreover, this example demonstrates that the Independence of Irrelevant Alternatives (IIA) in Arrow’s Impossibility Theorem is not necessarily desirable axiom to satisfy. Under the Janeček Method (D21), candidate C, as the irrelevant alternative, changes the voting result to a more desirable outcome from the perspective of overall social utility.[43]

### Monotonicity

Though there is a discrepancy in the definition of monotonicity in regard to different voting methods among various theorists, the Janeček Method (D21) is monotonic under Fishburg and Brams’s (1983) description. Under the Method, it is impossible for a candidate not to be elected if some voters increase their support for him/her. It is also impossible under the Method for a candidate that is not elected under a given distribution of voters’ preferences to become a winner if some voters switch their preference to another candidate.

### Strategyproofness and Sincere voting

While virtually all voting procedures for multicandidate elections are susceptible to strategic manipulation, some are deemed more prone to manipulations than others.[44] The scenario above demonstrates, the unique features of the Janeček Method (D21) – the Systematically Capped Multiple Votes and the 2:1 Ratio of Plus to Minus Votes requirements – encourage sincerity while rewarding informed and unwedgeable voting. Discourages arbitrary vote allocation.

## Criticism

Negative voting has been described as unsuitable in cases where it could be used against a religious or ethnic minority.[45] Concerns have also been raised that the minus vote could encourage negative campaigning.[46]

Political scientist Karel Sál has criticized assumption that a new electoral system alone could cleanse Czech politics 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 the Janeček Method (D21) into Czech elections.[47]

One of the main Janeček's objective, he would like to achieve, is to diminish extremist electoral strength.[48] This point have been questioned by some specialists in political sciences. They claim that the existence and competitiveness of extremist partys is essential for a well functioning democracy for several reasons.[49][50] 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.[51]

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