Social welfare functions for different subgroup utility scales

Anna B. Khmelnitskaya

doi:10.1007/978-3-642-56038-5_28

Social welfare functions for different subgroup utility scales

Anna B. Khmelnitskaya

Discrete Mathematics and Mathematical Programming

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

This paper characterizes social welfare functions for different scales of individual utility measurement in distinct population subgroups. Different combinations of ordinal, interval, ratio, and translation scales are studied. We consider situations when utility comparisons among subgroups of individuals by unit and/or zeropoint can or cannot be made, that is when subgroup utility scales are dependent or independent. We show that for combinations of independent subgroup utility scales every corresponding social welfare function is completely determined by the opinions of only one subgroup of individuals when there is not more than one subgroup with ratio or translation scale measurable utilities. Otherwise it also might be determined by the union of subgroups corresponding to ratio and translation scales, and is in agreement with the utility scales of the decisive coalition. We also investigate social welfare functions admissible given various combinations of interval scales with a common unit that combine individual utilities from different subgroups, or with a common zero that lead to the existence of a dictatorial subgroup.

Original language	English
Title of host publication	Constructing and Applying Objective Functions
Subtitle of host publication	Proceedings of the Fourth International Conference on Econometric Decision Models Constructing and Applying Objective Functions, University of Hagen, Held in Haus Nordhelle, August, 28 — 31, 2000
Editors	Andranik S. Tangian, Josef Gruber
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	515-530
Number of pages	16
ISBN (Electronic)	978-3-642-56038-5
ISBN (Print)	978-3-540-42669-1
DOIs	https://doi.org/10.1007/978-3-642-56038-5_28 https://doi.org/10.1007/978-3-642-56038-5
Publication status	Published - 2002
Event	4th International Conference on Econometric Decision Models Constructing and Applying Objective Functions 2000 - University of Hagen, Hagen, Germany Duration: 28 Aug 2000 → 31 Aug 2000 Conference number: 4

Publication series

Name	Lecture Notes in Economics and Mathematical Systems
Publisher	Springer
Volume	510
ISSN (Print)	0075-8442

Conference

Conference	4th International Conference on Econometric Decision Models Constructing and Applying Objective Functions 2000
Country	Germany
City	Hagen
Period	28/08/00 → 31/08/00

Keywords

Arrovian social choice
Social welfare function
Interpersonal utility comparisons

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Khmelnitskaya, A. B. (2002). Social welfare functions for different subgroup utility scales. In A. S. Tangian, & J. Gruber (Eds.), Constructing and Applying Objective Functions: Proceedings of the Fourth International Conference on Econometric Decision Models Constructing and Applying Objective Functions, University of Hagen, Held in Haus Nordhelle, August, 28 — 31, 2000 (pp. 515-530). (Lecture Notes in Economics and Mathematical Systems; Vol. 510). Springer. https://doi.org/10.1007/978-3-642-56038-5_28, https://doi.org/10.1007/978-3-642-56038-5

Khmelnitskaya, Anna B. / Social welfare functions for different subgroup utility scales. Constructing and Applying Objective Functions: Proceedings of the Fourth International Conference on Econometric Decision Models Constructing and Applying Objective Functions, University of Hagen, Held in Haus Nordhelle, August, 28 — 31, 2000. editor / Andranik S. Tangian ; Josef Gruber. Berlin, Heidelberg : Springer, 2002. pp. 515-530 (Lecture Notes in Economics and Mathematical Systems).

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Khmelnitskaya, AB 2002, Social welfare functions for different subgroup utility scales. in AS Tangian & J Gruber (eds), Constructing and Applying Objective Functions: Proceedings of the Fourth International Conference on Econometric Decision Models Constructing and Applying Objective Functions, University of Hagen, Held in Haus Nordhelle, August, 28 — 31, 2000. Lecture Notes in Economics and Mathematical Systems, vol. 510, Springer, Berlin, Heidelberg, pp. 515-530, 4th International Conference on Econometric Decision Models Constructing and Applying Objective Functions 2000, Hagen, Germany, 28/08/00. https://doi.org/10.1007/978-3-642-56038-5_28, https://doi.org/10.1007/978-3-642-56038-5

Social welfare functions for different subgroup utility scales. / Khmelnitskaya, Anna B.

Constructing and Applying Objective Functions: Proceedings of the Fourth International Conference on Econometric Decision Models Constructing and Applying Objective Functions, University of Hagen, Held in Haus Nordhelle, August, 28 — 31, 2000. ed. / Andranik S. Tangian; Josef Gruber. Berlin, Heidelberg : Springer, 2002. p. 515-530 (Lecture Notes in Economics and Mathematical Systems; Vol. 510).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - This paper characterizes social welfare functions for different scales of individual utility measurement in distinct population subgroups. Different combinations of ordinal, interval, ratio, and translation scales are studied. We consider situations when utility comparisons among subgroups of individuals by unit and/or zeropoint can or cannot be made, that is when subgroup utility scales are dependent or independent. We show that for combinations of independent subgroup utility scales every corresponding social welfare function is completely determined by the opinions of only one subgroup of individuals when there is not more than one subgroup with ratio or translation scale measurable utilities. Otherwise it also might be determined by the union of subgroups corresponding to ratio and translation scales, and is in agreement with the utility scales of the decisive coalition. We also investigate social welfare functions admissible given various combinations of interval scales with a common unit that combine individual utilities from different subgroups, or with a common zero that lead to the existence of a dictatorial subgroup.

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Khmelnitskaya AB. Social welfare functions for different subgroup utility scales. In Tangian AS, Gruber J, editors, Constructing and Applying Objective Functions: Proceedings of the Fourth International Conference on Econometric Decision Models Constructing and Applying Objective Functions, University of Hagen, Held in Haus Nordhelle, August, 28 — 31, 2000. Berlin, Heidelberg: Springer. 2002. p. 515-530. (Lecture Notes in Economics and Mathematical Systems). https://doi.org/10.1007/978-3-642-56038-5_28, https://doi.org/10.1007/978-3-642-56038-5

Social welfare functions for different subgroup utility scales

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