On Ordinal Data Science and its role in Socially Acceptable ICT Design [chapter]

Gerd Stumme
2020 Mensch - Technik - Umwelt: Verantwortung für eine sozialverträgliche Zukunft  
Comparing and ordering things is a basal ability of mankind for organizing its physical and social environment. While many hierarchical relationships can be derived from numerical measures like length or voltage, many others cannot appropriately be captured this way. We argue that the newly emerging field of data science up to now lacks engagement in developing analysis methods for such ordinal data. By the example of an already existing approach in this domain, Formal Concept Analysis, we will
more » ... t Analysis, we will discuss its capabilities as a knowledge representation and argue -based on its philosophical foundations -why it is an important building block for socially acceptable IT design. Ordinal Data Order is a predominant paradigm for perceiving and organizing our physical and social environment, to infer meaning and explanation from observation, and to search and rectify decisions. For instance, we admire the highest mountain on earth, observe pecking order among animals, schedule events in time, and organize our collaborations in hierarchies. The notion of order is deeply embedded in our language, as every adjective gives rise to a comparative (e.g., better, more expensive, more beautiful). In many cases, entities can be ordered through real-valued valuation functions like size or price. This process of quantification has been boosted by different factors, including i) the development of scientific measuring instruments since the scientific revolution, ii) the claim that the social sciences should use the same numerical methods which had been successful in natural sciences, and iii) nowadays by the instant availability of an enormous range of datasets to almost all aspects of science and everyday life. As real numbers constitute an ordered field, i.e., a field equipped with a linear order, the analysis of such data benefits from the existence of the algebraic operators of fields (the existence of 0 and 1, addition, subtraction, multiplication, division) together with total comparability (i.e., every pair of its ele-I. . 2 Stevens' levels of measurement have been (and still are) heavily disputed. A particularly controversial question that is discussed since Stevens' paper for over 70 years is whether computing the mean of ordinal data is an allowed operation or not, see, e.g., Lord, On the Statistical Treatment of Football Numbers, American Psychologist 8.12 (1953), 750 and Zand Scholten/Borsboom, A reanalysis of Lord's statistical treatment
doi:10.5771/9783748910770-181 fatcat:7qawx64lazdtpmjdzmfwmnwc3q