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By János Aczél (auth.), János Aczél (eds.)

ISBN-10: 3034890966

ISBN-13: 9783034890960

ISBN-10: 3764352434

ISBN-13: 9783764352431

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For the more general equation (2) and, even more so, for (1), to given production functions gl, ... , gm' aggregators;;, ... ,In (and F) and a macroeconomic function G may possibly be found so that the "deficit" Vo\. 50, 1995 Functional equations in the social and behavioral sciences 43 be small (with general F or with F(y, ... ,Yn) = YI + ... + Yn) in the sense of (3') or (3"). This too is unsolved (but see "Added in proof" at the end of this paper). Probabilistic models (including stochastic choice models) are becoming popular among mathematical psychologists and people interested in group decision making.

9] MARLEY, A. A. , A selective review of recent characterizations of stochastic choice models using distribution and functional equation techniques. Math. Social Sci. 23 (1992), 5-29. , On intra- and interpersonal utility comparisons. Soc. Choice Welf. 8 (1991),207-219. [Il] ROBERTS, F. , Merging relative scores. l. Math. Anal. Appl. 147 (1990), 30-52. , Determining merged relative scores. l. Math. Anal. Appl. 150 (1990), 20-40. [13] YOUNG, H. , Progressive taxation and the equal sacrifice principle.

The general strictly monotonic (or just nonconstant) continuous solutions of (4) are U(x) = a log x (a + band U(x) = axe + b i= 0, c i= 0, b arbitrary constants). Functional equations in the social and behavioral sciences Vol. 50, 1995 45 3. Speaking of homogeneous functions, a seemingly special question, when homogeneous functions are increasing, turned out to be of quite general and deep interest and surprisingly difficult. The analysis of properties of automorphism groups of structures to delineate broad classes of models that have numerical representation have lead Cohen, Luce and Narens ([14], [15], [16], [17]) to binary operations with the numerical representation x 0 = yf(x /y) y X H where f is strictly increasing and f(x)/x strictly decreasing.

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Aggregating clones, colors, equations, iterates, numbers, and tiles by János Aczél (auth.), János Aczél (eds.)

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