Norm and Inequality from mathematical sociology perspective

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In the research report, I examined discussions on equality and justice by Rawls, Barry, and Sen in order to elucidate what exactly has been meant by the word "fairness (Kouhei in Japanese)" in the normative theories. It became clear that "fairness" was regarded as something whose meaning is so clear that it is unnecessary to explain. This is rather strange, considering the fact that concept of fairness played a key role in those discussions for justifying the norm and/value advanced in each theory. In order to find the daily conception of "fairness" concept, experiential theories of fairness judgments, such as equity theory or status value theory, were then examined.The report discusses that fairness (Kouhei in Japanese), in its essential form, is the order that "treat everyone identically as far as they have identical qualifications". Then, it is shown formally that order of fairness can be expressed as a two-level function or a combination of two functions, one of which dictates the specifics of allocation while the other defining the range of fairness consideration (who should be included, i.e., WHO IS "EVERYONE"). Formal characteristics of unfairness and its implications are discussed mainly in its relation with evolution of universalism in the realm of fairness judgment.