Estevan Muguerza, AsierMaura, RobertoValero, Óscar2023-04-272023-04-272023Estevan, A., Maura, R., & Valero, Ó. (2023). Quasi-metrics for possibility results: Intergenerational preferences and continuity. Mathematics, 11(2), 395. https://doi.org/10.3390/math110203952227-739010.3390/math11020395https://academica-e.unavarra.es/handle/2454/45203In 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.application/pdfeng© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.Quasi-pseudo-metricsParetoAnonymityDistributive fairness semiconvexitySocial welfare (pre)ordersPossibility resultinfo:eu-repo/semantics/article2023-04-27info:eu-repo/semantics/openAccess