[en] The aim of this work is to study the mathematical formalism behind fair decision-making in society. We study the properties of a social well-being function that accommodates individual preferences and meets a series of justice requirements. Arrow’s impossibility Theorem is obtained under general conditions and without regarding interpersonal comparisons. It is by modifying those conditions that social preferences, which depend on the justice principles considered, are obtained. The focus of attention is the leximin principle, which seeks the benefit of the least advantaged members of society. Two social justice theories based on this principle are analyzed: Rawl’s theory [19], centered on the equality of primary goods and dealing with the preferences and utilities of individuals; and Sen’s theory [28], which is concerned with equality of the capabilities and works with functionings. Finally, through Herrero’s formalism [13], we see the application of Sen’s theory in the resource allocation problem.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: F. Javier Martínez de Albéniz