### Abstract

Social welfare orderings for different scales of individual utility measurement in distinct population subgroups are studied. In Khmelnitskaya and Weymark

(2000), employing the continuous version of Arrow’s impossibility theorem, it was

shown that for combinations of independent subgroups scales every corresponding

social welfare ordering depends on the utilities of only one of the subgroups and is

determined in accordance with the scale type proper to this dictatorial subgroup. In

this article we introduce an alternative completely self-contained proof based on the study of the structure of level surfaces of a social welfare function which provides a real-valued representation of the social welfare ordering.

(2000), employing the continuous version of Arrow’s impossibility theorem, it was

shown that for combinations of independent subgroups scales every corresponding

social welfare ordering depends on the utilities of only one of the subgroups and is

determined in accordance with the scale type proper to this dictatorial subgroup. In

this article we introduce an alternative completely self-contained proof based on the study of the structure of level surfaces of a social welfare function which provides a real-valued representation of the social welfare ordering.

Original language | English |
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Title of host publication | Collective decision making: views from social choice and game theory, A. van Deemen and A. Rusinowska (eds.). Theory and Decision Library C |

Editors | A. van Deemen, A. Rusinowska |

Publisher | Springer |

Pages | 111-123 |

Number of pages | 13 |

ISBN (Print) | 978-3-642-02864-9 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

### Publication series

Name | Theory and Decision Library C |
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Publisher | Springer |

Volume | 43 |

### Cite this

Khmelnitskaya, A. B. (2010). Existence of a dictatorial subgroup in social choice with independent subgroup utility scales, an alternative proof. In A. van Deemen, & A. Rusinowska (Eds.),

*Collective decision making: views from social choice and game theory, A. van Deemen and A. Rusinowska (eds.). Theory and Decision Library C*(pp. 111-123). (Theory and Decision Library C; Vol. 43). Springer. https://doi.org/10.1007/978-3-642-02865-6_8