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Some recent applications of functional equations to the social and behavioral sciences. Further problems

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Aggregating clones, colors, equations, iterates, numbers, and tiles

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Summary

Recent applications of functional equations to questions of allocation, aggregation, utility, taxation, theories of measurement and dimensional analysis are discussed and open problems formulated.

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References

  1. Aczél, J., NG, C. T., and Wagner C., Aggregation theorems for allocation problems. SIAM J. Algebraic Discrete Methods 5 (1984), 1–8.

    Article  MATH  Google Scholar 

  2. Buhl, U. H. and Pfingsten, A., Eigenschaften und Verfahren für einenangemessenen Länderfinanzausgleich in der Bundersrepublik Deutschland. Finanzarchiv 44 (1) (1986), 98–109.

    Google Scholar 

  3. Aczél, J. and Pfingsten, A., Constituent-sensitive public fund sharing. In Mathematical modelling in economics. Springer, Berlin, 1993, pp. 3–10.

    Google Scholar 

  4. Pokropp, F., Aggregation von Produktionsfunktionen. Klein-Nataf-Aggregation ohne Annahmen über die Differenzierbarkeit und Stetigkeit. [Lecture Notes in Econom. and Math. Systems, No. 74]. Springer, Berlin, 1972.

    Google Scholar 

  5. Van Daal, J. and Merkies, A. H. Q. M., Consistency and representativity in a historical perspective. In Measurement in economics. Physica, Heidelberg, 1987, pp. 607–637.

    Google Scholar 

  6. Aczél, J., A short course on functional equations based upon recent applications to the social and behavioral sciences. Reidel ( Kluwer ), Dordrecht-Boston, 1987.

    Google Scholar 

  7. Nikodem, K., The stability of the Pexider equation. Ann. Math. Sil. 5 (1991), 91–93.

    MathSciNet  Google Scholar 

  8. Chmieliński, J. and Tabor, J., On approximate solutions of the Pexider equations. Aequationes Math. 46 (1993).

    Google Scholar 

  9. Marley, A. A. J., A selective review of recent characterizations of stochastic choice models using distribution and functional equation techniques. Math. Social Sci. 23 (1992), 5–29.

    Article  MathSciNet  MATH  Google Scholar 

  10. Bossert, W., On finira-and interpersonal utility comparisons. Soc. Choice Welf. 8 (1991), 207–219.

    Article  MathSciNet  MATH  Google Scholar 

  11. Roberts, F. S., Merging relative scores. J. Math. Anal. Appl. 147 (1990),30–52.

    Article  MathSciNet  MATH  Google Scholar 

  12. Aczél, J., Determining merged relative scores. J. Math. Anal. Appl. 150 (1990), 20–40.

    Article  MathSciNet  MATH  Google Scholar 

  13. Young, H. P., Progressive taxation and the equal sacrifice principle. J. Public Econom. 32 (1987), 203–214.

    Article  Google Scholar 

  14. Cohen, M. and Narens, L., Fundamental unit structures: a theory of ratio scalability. J. Math. Psych. 20 (1979), 193–232.

    Article  MathSciNet  MATH  Google Scholar 

  15. Luce, R. D., Rank dependent subjective expected-utility representations. J. Risk Uncert. 1 (1988), 305–332.

    Article  Google Scholar 

  16. Luce, R. D. and Narens, L., Classification of concatenation structures by scale types. J. Math. Psych. 29 (1985), 1–72.

    Article  MathSciNet  MATH  Google Scholar 

  17. Narens, L., A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness. Theory and Decision 13 (1987), 1–70.

    Article  MathSciNet  Google Scholar 

  18. Aczél, J., Three problems. In General inequalities 6. Birkhäuser, Basel-Boston-Berlin, 1992, p. 477.

    Google Scholar 

  19. Aczél, J., Gronau, D., and Schwaiger, J., Increasing solutions of the homogeneity equation and of similar equations. J. Math. Anal. Appl. 182 (1994), 436–464.

    Article  MathSciNet  MATH  Google Scholar 

  20. Aczél, J., Roberts, F. S., and Rosenbaum, Z., On scientific laws without dimensional constants. J. Math. Anal. Appt. 119 (1986), 389–416.

    Article  MATH  Google Scholar 

  21. Moszner, Z., Une généralisation d’un résultat de J. Aczél et M. Hosszû sur l’équation de translation. Aequationes Math. 37 (1989), 267–278.

    Article  MathSciNet  MATH  Google Scholar 

  22. Moszner, Z., Sur une forme de la solution de l’équation de translation. C.R. Math. Rep. Acad. Sci. Canada 12 (1991), 285–290.

    MathSciNet  Google Scholar 

  23. Förg-Rob, W., Differentiable solutions of the translation equation. [Grazer Math. Ber., No. 287]. Karl-Franzens Univ., Graz, 1988.

    MATH  Google Scholar 

  24. Aczél, J. and Moszner, Z., New results on “scale” and “size” arguments justifying invariance properties of empirical indices and laws. Math. Social Sci. 28 (1994), 3–33.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Waterloo, Waterloo, Ont, N2L 3G1, Canada

    J. Aczél

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  1. J. Aczél
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Editors and Affiliations

  1. Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

    János Aczél

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© 1995 Birkhäuser Verlag Basel

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Aczél, J. (1995). Some recent applications of functional equations to the social and behavioral sciences. Further problems. In: Aczél, J. (eds) Aggregating clones, colors, equations, iterates, numbers, and tiles. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9096-0_4

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  • DOI: https://doi.org/10.1007/978-3-0348-9096-0_4

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-7643-5243-1

  • Online ISBN: 978-3-0348-9096-0

  • eBook Packages: Springer Book Archive

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