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Quasi-Metrics for Possibility Results: Intergenerational Preferences and Continuity

Author

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  • Asier Estevan

    (Departmento de Estadística, Informática y Matemáticas, Institute INARBE, Public University of Navarre, Iruñea-Pamplona, Navarre, 31006 Pamplona, Spain)

  • Roberto Maura

    (Department of Economics, London School of Economics, London WC2A 2AE, UK)

  • Óscar Valero

    (Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain
    Institut d’ Investigació Sanitària Illes Balears (IdISBa), Hospital Universitari Son Espases, 07120 Palma de Mallorca, Spain)

Abstract

In this paper, we provide the counterparts of a few celebrated impossibility theorems for continuous social intergenerational preferences according to P. Diamond, L.G. Svensson and T. Sakai. In particular, we give a topology that must be refined for continuous preferences to satisfy anonymity and strong monotonicity. Furthermore, we suggest quasi-pseudo-metrics as an appropriate quantitative tool for reconciling topology and social intergenerational preferences. Thus, we develop a metric-type method which is able to guarantee the possibility counterparts of the aforesaid impossibility theorems and, in addition, it is able to give numerical quantifications of the improvement of welfare. Finally, a refinement of the previous method is presented in such a way that metrics are involved.

Suggested Citation

  • Asier Estevan & Roberto Maura & Óscar Valero, 2023. "Quasi-Metrics for Possibility Results: Intergenerational Preferences and Continuity," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:395-:d:1033229
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    References listed on IDEAS

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