Interactions in an effect network: Depicted are different relationships between variable pairs and variables, or actors and variables. A solid line with an arrow between two variables A and B indicates a ‘The more of variable A, the more of variable B’ relationship (1), while a dotted line with an arrow indicates a ‘The less of variable A, the more of variable B’ relationship (2). Similarly, a solid line between an actor C and a variable D indicates an ‘Actor C wants to increase variable D’ (solid line, 3) or an ‘Actor C wants to decrease variable D’ (dotted line, 4) relationship.

Effect network of an assessment process through xAI: An effect network showing how the assessment process of the proclaimed fairness of an ADM system can succeed. The actor interested in this assessment is the general public. Here, the understandability and the robustness of the explanation are crucial factors which lead to a trustworthy assessment of the ADM system.

Effect network of an assessment process through xAI including the operator of the ADM-system: An effect network showing how the assessment of the fairness of an ADM system can be influenced by a negligent actor, the operator of the ADM System, who wants to hide discrimination in their ADM system.

ADM systems are based on two different source codes: The first one to compute a statistical model from input data and the second one that uses this statistical model to compute a classification/score/ranking for new data.

ADM systems constitute a large group of software systems, including expert systems with man-made rules. When such a system contains a learned or learning component, it is a member of those artificial intelligence systems that are based on machine learning. The article focuses on algorithmic decision making systems with a learned or learning component.

Synchronous accountability process: Visualization of the accountability process according to Bovens.

Asynchronous accountability process: Transparency about past decisions and actions plus access to examinability mechanisms help to establish an asynchronous accountability process between different actors and forums.

Risk matrix: Risk matrix with 5 classes of application areas with risk potentials ranging from ‘post-hoc analysis is sufficient’ in class 0 to the prohibition of AI systems in class 4.

Algorithms without a training phase: Two algorithms without a training phase, a) uses only the new data, while b) uses old data for comparison. Such algorithms are said to be unsupervised.

Algorithm with a training phase: ADM System where a model is first trained by using the feedback of a quality assessing algorithm and then used to actually compute the categorization or ranking.

Specificity of an algorithm: If there are two types of citizens, terrorists and innocent people, an Algorithmic Decision Making System for terrorist identification searches for pattern in data where it is known which person belongs to which category. It deduces rules regarding the most important properties associated with terrorists. Given new data on people, the algorithm will decide for some that they are suspicious and for others that they are not. The percentage of found terroristists of all terrorists is called the sensitivity of the system, the percentage of correctly announced non-terrorists of all non-terrorists is called the specificity of the algorithm.

The principle of k-means-clustering: - an unsupervised learning algorithm - is based on data with a known categorization, symbolized by two different colors. Any new data point (black data point) is evaluated by its k closest neighbors. In this case, the nearest neighbor is grey, so for k = 1, the black point would be assigned to the category represented by the grey color. However, for k = 3, the majority of the neighbors would be white, so the black data point would be assigned to the "white" category

Entwicklung eines algorithmischen Entscheidungssystems: Die Entwicklung eines algorithmischen Entscheidungssystems setzt die Interaktion vieler Personen und Institutionen voraus. Es werden viele Entscheidung entlang einer langen Kette der Verantwortlichkeiten getroffen, welche die Qualität des finalen Systems beeinflussen.

Development of an Algorithmic Decision Making System: The design of an algorithmic decision making (ADM) system requires the interaction of various persons and institutions. In a long chain of responsibilities various decisions are made that all have an influence on the final quality of the resulting system.

Development of an Algorithmic Decision Making System (with numbers): The design of an algorithmic decision making (ADM) system requires the interaction of various persons and institutions. In a long chain of responsibilities various decisions are ade that all have an influence on the final quality of the resulting system. With numbers.

Development of an Algorithmic Decision Making System (with phases): The design of an algorithmic decision making (ADM) system requires the interaction of various persons and institutions. In a long chain of responsibilities various decisions are ade that all have an influence on the final quality of the resulting system. With phases.