Guidelines for using the D21 – Janeček method

Rules of D21 – Janeček method

• The basic element of the D21 – Janeček method is that the voter can identify more preferences in a single ballot than the number of seats to be filled.
• Only one vote per candidate/option is allowed.
• All votes have the same absolute value.
• The voter can, but does not have to, use all available votes.
• The voter can cast a minus vote/downvote an option he disagrees with.
• In order to cast a minus vote, one must cast at least two plus votes.
• The number of plus and minus votes depends on the specific situation, see the recommendations below.

Example: In a presidential election there are 9 candidates, but only one will become president. As voters we have 3 plus votes and 1 minus vote available (see table below). We can distribute either all of these votes or just some of them (for example only two votes). We can assign only one vote per candidate. If we really disagree with someone, we can vote against them with a minus vote. But in order to cast a minus vote, we must cast at least two plus votes. Why? Because elections should be mainly based on positive attitudes.
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The effect of multiple votes, as presented in the D21 – Janeček method, favours more consensual candidates. (1) It also significantly reduces the motivation for strategic voting, so people do not have to opt for the “lesser evil”. The option of the minus vote helps to uncover controversial candidates and contributes further to consensus. It therefore strengthens the effect of more votes. (2) The minus vote could motivate more voters to turn out to the polls. (3)
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1. D21 - Janeček Method focuses on strong preferences. That allows it to find a candidate who has a strong and broad support among voters.
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2. This does not have to be true each time. Theoretically, there can be a candidate who is consensual (receives a lot of additional votes) and polarising at the same time when they get a lot of additional plus votes and also a lot of minus votes.
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3. DOLINSKI, D. and DROGOSZ, M. (2011), Regulatory Fit and Voting1. Journal of Applied Social Psychology, 41: 2673-2688. doi:10.1111/j.1559-1816.2011.00841.x.

Number of votes in the D21 – Janeček method

For the number of winners W and for a large number of candidates, we recommend the number of plus votes PL:The number of votes in the D21 - Janeček method depends mainly on the number of winners. If the number of candidates (options) is too low, it will limit the number of votes. The key difference between the D21 - Janeček method and approval or combined approval voting is the capped number of votes, which gives each vote a higher relative value. This way, the D21 - Janeček method focuses only on strong (mainly positive) voter preferences. It combines the effect of more votes with the motivation to think critically. When the number of votes is unlimited, such as in approval voting, voters often have the tendency to use votes excessively (especially minus votes), as they are not motivated to think about which candidates are closest to their opinions.

‍PL(W) ≐ [2W - (W-2) × Φ],
where Φ = ½ (√5 – 1) ∿ 0,618.

The number of plus and minus votes is reduced when there are fewer candidates participating, i.e. it would not make sense to allow voters to cast four plus votes in a two-winner election, if only four candidates are running.

When C is the number of candidates. The number of plus votes is then:

This formula is extrapolated from the rule: We add n^th additional plus vote(s) to the W plus vote(s) if the number of candidates is greater than or equal to C ≥ (W + n) × (n + 1). Thus, we add the W+1^st plus vote to the W plus vote(s) if
C ≥ (W + 1) × 2, the W + 2^nd if C ≥ (W + 2) × 3, and so on.
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The number of minus votes M is then

M ≐ P/3 ,

The total number of (plus and minus) votes must always be less than the number of candidates, P+M < C. Should this condition not be met, the number of minus votes must be reduced until the condition of P+M < C is met.

Why is the optimal number of votes limited even if the number of candidates is getting higher?

In one-winner elections, there is no substantial difference between 21 and 121 candidates. If the number of competing candidates is high, not even voters with a high interest in politics will be familiar with all of the candidates. Therefore it makes no sense to add additional plus votes, because the “effective” number of candidates will stay relatively stable. The formula for PL provides an optimal level of consensus for a very high (theoretically unlimited) number of candidates. (PL can differ for different applications.)

When (not) to use minus vote(s)?

We do not recommend the use of minus votes in political elections with ethnic or religious minorities running for office. Minus votes are also not favourable in apolitical elections with only positive-oriented options (e.g. charity projects) or where a strictly positive atmosphere is required (e.g. when children propose and vote on projects). The minus vote can be introduced “incrementally” - after voters have some experience using multiple plus votes.

What to do when multiple candidates get the same number of votes?

First-place ties will happen very rarely in elections with many voters. When it does happen, the winner is the candidate who received more plus votes. If two or more candidates received the same number of net votes and plus votes, the winner is selected by drawing lots.
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Table 1: Recommended number of votes for a large number of candidates

Table 2: Recommended number of votes for a limited number of candidates
(PDF) >