Calculating the nearest political party
euandi2021 shows the overlap between the political parties’ positions and the user's preferences. In order to simplify the interpretation of the results, the latter are expressed in terms of a percentage of overlap. 0% indicates that a political party and a user’s preferences do not overlap at all, 100% indicates that they completely overlap.
Technically, for calculating a user’s closest candidate, we use the so called “Manhattan (or city-block) distance”, which expresses how close the two respective points are one from another in an n-dimensional space.
At the heart of euandi2021 lies a series of political arguments – or issues – on which it is possible to take a position. For example, euandi2021 offers to users to take a position regarding the statement " Social programmes should be maintained even at the cost of higher taxes". Users can choose from the following answer categories: 'Completely agree', 'Tend to agree', 'Neutral', 'Tend to disagree' and 'Completely disagree'. euandi2021 also allows users to choose the option 'no opinion'.
For calculating the overlap, we first translated the answers given by the users into numbers, using the following key:

Completely disagree = 0,
Tend to disagree = 25,
Neutral = 50,
Tend to agree' = 75,
'Completely agree = 100.

The same values were given to the positions taken up by the political parties. We then started off to calculate the distance between the positions of each user and political party on every statement, and then the average matching percentage for all the 35 statements.

Calculation of Uni-dimensions
Every statement can have some effect on one uni-dimensions. The resultant effect is defined with values: 1 (positive polarity), -1 (negative polarity). Positive polarity means that only positive answers (50-100) increase the value and negative polarity means that only negative answers (0-50) increase the resulting value. Statements with polarity 0 are not included in a uni-dimension calculation.
The resulting value regarding all answered questions (Sd) for a political party or user can vary from 0 to 100, where 100 means total agreement.
For example, if four statements pertain to the uni-dimension “Covid-19”, the first two have polarity value of 1 for the dimension and the other two have polarity of -1, the user has to answer “Completely agree” to the first two and “Completely disagree” to the third and fourth statement to get maximum score on the radar dimension (i.e., be placed on the extreme right end of the health-economy comtinuum).
The following list documents how 17 (out of the 35 statements in total) were grouped in order to lead to the scores for the four uni-dimensions.

COVID-19: HEALTH (-) vs. ECONOMY (+)
There should be fewer restrictions for people who have been vaccinated against Covid-19 than for those who have not been vaccinated (-)
The fight against Covid-19 should be a priority, even if it comes with economic losses (-)
Wearing masks in public spaces should be compulsory, in case social distancing cannot be guaranteed (-)
If their job permits, employees should be able to decide freely whether to work from home or at the office (-)

ECOLOGICAL: SUSTAINABILITY (-) vs. ECONOMIC GROWTH (+)
Renewable energy sources (e.g. solar or wind energy) should be promoted, even if this leads to higher energy costs (-)
The promotion of public transport should be fostered through green taxes (e.g., road taxing) (-)
Even more should be done to promote electric mobility and replace gasoline and diesel with electric cars (-)
Short-haul flights should be replaced by more environmentally friendly means of transport, even if this leads to longer travel times (-)
A general speed limit should be introduced in German highways (-)

FEDERALISM: CENTRALIZATION (-) vs. DECENTRALIZATION (+)
The solidarity contribution should be entirely abolished (+)
Structural civil protection against extreme weather events, such as floods, should be shifted to the exclusive competence of the federal government (-)
Education policy should remain a competence of the Länder (+)

EUROPEAN INTEGRATION: PRO-EU (-) vs. ANTI-EU (+)
The EU should have its own powers to collect taxes (-)
On foreign policy issues the European Union should speak with one voice (-)
The European Union should strengthen its security and defence policy (-)
The EU should rigorously punish Member States with excessive budget deficits (-)
The single European currency (Euro) is a bad thing (+)
Users should be aware that the uni-dimensions serves as an illustrative tool that provides an overview of the political parties and their views on these specific dimensions alone.

Political Landscape
The political landscape is based on similar assumptions as the uni-dimensions, but goes a step further. Namely, while the uni-dimensions represent the political spectrum in four separate dimensions, the political landscape further reduces the complexity of politics and offers only two major dimensions: an economic and a cultural one.
Both of these dimensions range from zero to one hundred. In order to determine the position of political parties and users in this two-dimensional space, we need to calculate their respective coordinates on the X and Y axes.
The initial position of a political party on an axis is 50% (neutral). Its position on an axis is calculated over all statements using the same formula as the uni-dimensions. Statements with polarity 0 are not included in a landscape dimension calculation. 1 shifts the position on an axis to the positive, and -1 to the negative side.
The political landscape representation is based on the assumption that, in most political systems, citizens’ and political parties’ opinions on individual issues can be aggregated to a limited number of issue dimensions. In the graphical representation offered to the user, the position of parties (and of the user) on each axis is the average of all positions across issues pertaining to each dimension.
The computation of such averages, on each of the two axes, depends on a priori considerations, both in terms of which dimension an issue belongs to, and which side of the dimension a specific issue positions belongs to.
According to a structure of attitudes of the German political space, we have assigned 16 (out of the 35 statements in total) to each of the two dimensions according to the following table:

ECONOMIC DIMENSION: LEFT (-) vs. RIGHT (+)
Social programmes should be maintained even at the cost of higher taxes (-)
Government spending should be reduced in order to lower taxes (+)
The state should provide stronger financial support to unemployed workers (-)
Bank and stock market gains should be taxed more heavily (-)
Taxation on top earners should be increased (-)
A general rent cap (Mietendeckel) should be introduced to curb the rising rents (-)
The debt brake should be relaxed to allow more public investment (-)
A universal, unconditional basic income should be introduced (-)
Citizens' insurance should be introduced to replace the dual health system, i.e. the coexistence of private and statutory health insurance (-)

CULTURAL DIMENSION: LIBERAL (-) vs. CONSERVATIVE (+)
Immigration into the country should be made more restrictive (+)
The legalisation of same sex marriages is a good thing (-)
Legalizing personal cannabis consumption is a good thing (-)
Euthanasia should be legalised (-)
The church tax should be abolished (-)
Gender neutral language, like for example the asterisk, should be made compulsory in public communication of state institutions (-)
The abortion laws should continue to be reformed to make it easier for women to have an abortion (-)

Both the position of the user and the position of parties are presented to the viewer as points in a two-dimensional space. Please note that this visualisation does not influence the “Party match” result, it is only an independent attractive visual positioning of party and voter profiles, and that all statements concern one single dimension, except one (“The solidarity contribution should be entirely abolished”, affecting the economic and federalism dimensions). Also, two statements were included (“The Nord Stream 2 gas pipeline should be completed”, and “Defense spending should be increased to 2% of gross domestic product (GDP) to meet NATO criteria”) that do not pertain to any of the two dimensions of the political landscape, or any of the four dimensions of the uni-dimensions; therefore, these contribute to calculate the party matching % but do not influence the visualization tools.