Fairness Relations -- Concepts, Properties, and Applications to Networking, Data Analysis and Optimization

Summary form only given. Social aspects of computing, as they appear in group decision making, fair distribution, equity of transfer etc. can often not be expressed by simple function evaluations alone. Relational mathematics, which is studied in mathematical economics and social choice theory, provides a rich and general framework and appears to to be a natural and direct way to paraphrase corresponding optimization goals, to represent user preferences, to justify fairness criterions, or to valuate utility. In this talk, we will focus on the specific application aspects of formal relations for design, control and data mining problems. The talk will have two main parts. In the first part, we want to recall some concepts from mathematical economics, esp. the Arrow theorem and the relational approach by Suzumura, and then present a suite of relations that are able to represent fairness as mediator between user preference and application domain dominance. Starting with the "classical" fairness relations maxmin fairness, proportional fairness and lexicographic minimum, we can recover their mutual relationships and their design flexibility in order to define further relations, with regard to e.g. multi-resource problems, ordered fairness, self-weighted fairness, collaborative fairness, and fuzzy fairness. In the second part, we want to illustrate and demonstrate the application of these concepts to basic data processing and optimization tasks, for example in data analysis and the network design and control domain. In this part we will also study the tractability of related problems as well as algorithmic approaches by meta-heuristic algorithms derived from well-known evolutionary multi-objective optimization algorithms or extension of sorting algorithms.