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Applications of mathematics when there is not enough of something

The exhibition intends to show in a clear, simple and communicative way –but rigorous at the same time- some of the practical applications of mathematics when solving problems society has to face.

The exhibition intends to show in a clear, simple and communicative way –but rigorous at the same time- some of the practical applications of mathematics when solving problems society has to face.

14/05/2019

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How are the places of a kindergarten or a retirement home assigned? How is the income tax defined? Where do dumping sites and filter systems go, and how is this damage balanced? Who gets the only available kidney for a transplant? As for lottery assigning public homes, do all applicants have the same priority? In short, how are benefits and obligations distributed among society? The exhibition Quan no n’hi ha prou per repartir. Pensar matemàticament has the answers to all of these questions.

The exhibition, which will be open in the Historical Building of the University of Barcelona from May 15 to June 21, is part of the FECYT project Estrategia, cooperación y justicia: matemáticas para la Sociedad (ECOJUST) and it intends to show in a clear, simple and communicative way –but rigorous at the same time- some of the practical applications of mathematics when solving problems society has to face. It deals with the justifications of solutions under the prism of equity and justice. The exhibition is built by an introductory module and five big modules to be installed in the cloister of Pati de Ciències (Sciences’ patio), and has a series of screenings in the big stairs of the Historical Building.

How are benefits and obligations shared among society?

According to the principal investigator and head of the exhibition, the lecturer from the Department of Economic, Financial and Actuarial Mathematics, Javier Martínez de Albéniz, “there are rules to share goods and obligations according to what society thinks is best. Resources are limited and we are competing for them. This is a problem of distributional justice. Mathematics allow us to define these distributional rules in several fields, and justify them. There are different methods and solutions for different problems”.

The exhibition studies problems of distribution of different kinds of resources and explains how to mathematically formalize these in a simple way. It goes through the rules of distribution proposed by the Mathematical Economics and the Social Choice Theory, and at the same time, it analyses critically whether these rules are satisfying in efficiency and equity. Also, the exhibition treats voting systems and power measurement, and it analyses situations of competitiveness among agents to identify the balance strategies, that is the Game Theory. 

 

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