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 REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
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Cf. B. Schlink, Abwiigung im Verfassungsrecht, Berlin 1976, p. 131 ft.
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At least if it does not contain too many steps. I have therefore used a five-step scale. Yager uses a seven-step scale that includes the steps "very little" and "very high". A seven-step scale has the advantage of being the most differentiated scale that can be grasped as a whole - as psychologist assure us. (The grading scale in German legal state exams includes seven nominal steps: from "insufficient" to "excellent", which are- with the sole exception of "insufficient" - numerically divided in groups of three.) For most legal applications a five-step scale seems preferable to me. in law instances of more than three or four aspects occurring at the same time are rare (with the possible exception of criminal sentencing). Besides, the reluctance of the courts and legal writers to give a definite ranking will grow with the number of steps in a scale, since the number of possible combinations will grow rapidly (n!). Not every constitutional law practitioner will be as decisive as Rosenberg in John Grisham's The Pelican Brief (London, 1992): "His ideology was simple; government over business, the individual over government, the environment over everything. And the Indians, give them whatever they want."
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With reference to civil rights as a system of values this is also the criticism of R. Alexy (Theorie der Grundrechte, Frankfurt a.M. 1986, p. 138 ft.): cardinal scales are unrealistic since they are too demanding, and ordinal scales lead to a "tyranny" of the top value since the degrees of injury cannot be taken into account. Thus Alexy insists on individually evaluating a legal case - at least as long as there is no model of a comparable case. The technique of comparing cases according to their strength is highly elaborated by the well-known HYPO conception; e.g. see K.D. Ashley, Modeling Legal Argument: Reasoning with Cases and Hypotheticals, Cambridge, MA, 1990; D. B. Skalak and E. L. Rissland, Arguments and Cases: A Inevitable Intertwining, Artificial Intelligence and Law 1 (1992) pp. 3-44. From German writing an analysis of sit-down blockades by L. Kuhlen is worth mentioning: Regel und Fall in tier juristischen Methodenlehre, ARSP- Beiheft 45 (1992), pp. 101-128.
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An introduction to the fuzzy logic way of thinking rather than techniques can be found in: Bart Kosko, FUZZY THINKING. The New Science of Fuzzy Logic, New York 1993. One might love or hate that very personal book- in any case it is most worthwhile. More literature can be found in the following articles on legal application of fuzzy logic: L. Philipps, Unbestimmte Rechtsbegriffe und Fuzzy Logic, Festschrift for Arthur Kaufmann, Fr. Haft, W. Hassemer, U. Neuman, W. Schild, U. Schroth (eds.), Heidelberg 1993, pp. 265~280; the English version: Vague Legal Concepts and Fuzzy Logic. An Attempt to Determine the Required Period of Waiting after Traffic Accidents, INFORMATICA E DIRITTO vol. 2 (1993) pp. 37-51; L. Philipps, Kompensatorische Verkntipfungen in der Rechtsanwendung - ein Fall for Fuzzy Logic, Festschrift for Gtinther Jahr, M. Martinek, J. Schmidt, E Wadle (eds.), Tiibingen 1993, pp. 169-180; J. Heithecker, Fuzzy Logic und der "Tierhalter", KI 1993, pp. 7-10; L. Philipps, Ein bil3chen Fuzzy Logic for Juristen, Institutionen und Einzelne im Zeitalter tier Informationsthechnik, M.- T. Tinnefeld, L. Philipps, K. Weis (eds.), Mtinchen 1994, pp. 219-224; K1. KOhler ! J. Laeverenz, Moderne Technologien und das Haftungsrisiko des Arbeitnehmers. Ein Fuzzy-Logic-Expertensystem zur Ermittlung des Haftungsanteils, Institutionen und Einzelne im Zeitalter der Informationsthechnik (s.above), pp. 225-248; L. Philipps, Eine Theorie der unscharfen Subsumtion - Die Subsumtionsschwelle im Lichte der Fuzzy Logic, will soon be published in the Archiv fflr Rechts- und Sozialphilosophie (~sP).
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I also experimented with other variations of the conditional, but the results did not convince me. Cf. Th. Tilli, Fuzzy-Logik, Munich 1991,'p. 167 ft. However, the following complementary formulas, which are inspired by the "G6del Implication". could be worth mentioning: (a) Va(x,y) = 0 if x'> y, else y (b) Vb(x,y)= 1 if y> x', else y In (a) all instances that do not qualify are indiscriminately excluded; as for the winners, a fine tuning is done. In (b) all that qualify are indiscriminately accepted; if necessary, a fine tuning is done on the losers' side.
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Other forms of AND and OR connections are used in fuzzy logic, too. However those require multiplication and are thus not useable with ordinal scales.
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i suspect another problem at this point: There are decisions in which one might be ready to accept a low degree of fulfilment for other compensation, but not that the criterion is totally missing. (This was not the case in our example.) Yager would - if the example in his article (annotation 4) can be taken to be personal - buy a car of lower comfort because the price and fuel consumption are more important to him. But would this still be true if the car's comfort would be literally "null"? Yager's decision-making method might suggest that the difference between little or no comfort would disappear when set beside a medium level criterion. Perhaps the reasonable solution would be to include criteria that must not be completely absent in the description of the decision situation rather than try to represent them by improving the formula.
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Cf. H.-J. Koch / H. Riigmann, Juristische Begriindungslehre, Munich 1982, p. 176 ft. ; K. Larenz, Methodenlehre der Rechtswissenschaft, 6th d., Berlin Heidelberg 1991, chap. 5, 2.
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