### 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 |
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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 |

Pages | 515-530 |

Number of pages | 16 |

ISBN (Electronic) | 978-3-642-56038-5 |

DOIs | |

Publication status | Published - 2002 |

Event | Fourth 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 |

### Conference

Conference | Fourth International Conference on Econometric Decision Models Constructing and Applying Objective Functions 2000 |
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Country | Germany |

City | Hagen |

Period | 28/08/00 → 31/08/00 |

### Keywords

- EWI-24041
- IR-88067

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## Cite this

Khmelnitskaya, A. B., Tangian, A. S. (Ed.), & Gruber, J. (Ed.) (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) https://doi.org/10.1007/978-3-642-56038-5_28