D21 – Janeček method

D21 – Janeček method, also known as Democracy 2.1, is an electoral system applicable for both single-winner and multi-winner voting, which allows voters to cast multiple 'plus' (positive) votes, and, in certain instances, 'minus' (negative) votes. It is similar to approval voting and combined approval voting. The method was developed by Czech mathematician Karel Janeček.

This voting method has yet to be used in any general elections. It has been used in several participatory budgeting programs conducted by cities, including New York City.

Background
The D21 – Janeček method was developed in response to corruption within the Czech political system. According to Transparency International's Global Corruption Barometer in 2013, a majority of Czech citizens believed that political corruption in the country was widespread. In March 2011, Janeček founded the Endowment Fund Against Corruption (NFPK), aiming to expose prominent cases of corruption. Suggestions were made that the country's voting system needed an overhaul. The method, originally formulated in 2012, was tested the following year.

The method was created by the Czech mathematician and campaigner, Karel Janeček. He has also worked on projects like Prezident 21, an initiative focused on helping voters understand the 2018 Czech presidential election.

Electoral system
The system is based on the effect of more votes, which means that voters are allowed to grant a 'plus vote' to more candidates than there are seats, unlike limited voting where voters can cast fewer votes than there are seats, and plurality-at-large where voters cast as many votes as there are seats. All votes are of the same absolute value and each candidate can only receive one vote from each voter, which distinguishes the D21 method from cumulative voting. Voters are not obliged to use all of their votes.

In some cases, voters can also use a minus vote, provided they cast at least two plus votes. Minus votes carry the same absolute value as plus votes. It is advised against using the minus vote feature in countries where ethnic or religious minorities run for office.

The number of votes is determined by the number of seats available and the number of ballot options. The total number of votes is decided based on a mathematical algorithm which takes both of these factors into account. The table below shows the number of votes when there is a sufficiently high number of candidates. The number of plus votes is independent of the number of minus votes, which means that in the variant of the D21 voting method without the minus vote, the plus vote count stays the same.

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


 * Each voter is allowed to cast up to P ≥ W (plus) plus votes and up to M (minus) minus votes, where P ≥ 2M (i.e., number of plus votes has to be at least twice as large as the number of minus votes; ideally, ), and P should not exceed half the total number of candidates T/2.
 * Each voter can cast no more than one vote for any candidate.
 * Each vote has the same absolute weight (+1 or -1). The W candidates receiving the greatest net sum of all votes win. In case of parity between two candidates, the one with more plus votes wins.
 * The voter can, but does not have to, use all available votes.

Hence, if there are two seats per district and a competing party nominates one or two candidates, voters may cast up to four plus votes and (if minus vote is employed) up to one minus vote, 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.

Effects
The system aims to reduce the chance of populist and extremist candidates getting elected, as they would struggle to garner votes from other candidates' supporters. The fact that voters are allowed to vote for candidates of different political affiliations is expected to lead to a broader consensus by the author. It is meant to reduce strategic voting, as voters are less motivated to vote strategically when they do not have to choose between their sincere choice and the "lesser evil".

The use of a negative vote is also theorized to help prevent controversial candidates from getting elected and to support positive campaigning, as negative campaigning would lead to worse outcome for both candidates.

Official proposal
A proposal to implement the method in two-seat voting districts was submitted to the Czech government but was rejected. As of 2023, D21 has not been used to decide any major general elections in the country or elsewhere.

Development
The system was considered for participatory budgeting experiments in Cascais, Portugal. In 2015, the D21 system was introduced to the public through a voting game Prezident 21, where people could suggest candidates for 2018 Czech presidential election, as well as vote for them with D21 voting method using three plus votes and one minus vote. More than 300,000 people in the Czech Republic have participated.

D21 – Janeček method has been employed in election polls to study the method empirically and to identify voter overlaps between candidates and parties in the Czech Republic consistently since 2015.

Říčany
The D21 system was first used in Říčany in March 2015, with the aim of testing and developing the new platform for municipal decisions. The objective of choosing this method was to motivate people to take interest in what was happening in their municipality. It was suggested that system made it easier for them to get involved in making public decisions to raise general welfare and transparency of public procurements. The town allows for voting via the internet, and it has been used on several occasions since 2015.

New York
The method is used in the city of New York for participatory budgeting since 2015. In 2015, it asked voters 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.

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

Political scientist Karel Sál has criticized D21 – Janeček method, 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 that the specific version of D21 proposed at the time would face technical difficulties of amending the Constitution of the Czech Republic in order to implement it in the Czech Republic.

One of Janeček's main objectives with this method is to diminish extremist electoral strength. 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.

The system was also criticized by the political academic Perottino for its complexity compared to the proportional voting system used currently in the Czech general election, suggesting it might be difficult for voters to understand and use the new system effectively. However, an experimental presidential election in 2023 has shown that voters cast fewer invalid votes in the D21 voting method than in plurality voting. On the other hand, they did make more mistakes in the conditional minus vote without invalidation the plus votes. In addition, it was argued that it would be more complicated for the administration to determine the election results.

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 could be more dangerous.