Propositional belief merging and distributive justice

Abstract

Belief merging is a field from Artificial Intelligence which studies the fusion of independent and equally reliable sources of information and it is an important tool for decision making in multi-agent systems. On the other hand, Distributive Justice, which is presented in the areas of Economics, Ethics, Political Philosophy and Moral Psychology, is concerned in specifying what is meant by a just distribution of goods among members of a group. We propose to integrate both areas by introducing and studying the rationality of different operators from belief merging, that take into account some theories of distributive justice. The theories of egalitarianism and sufficientarianism are our central focus in this thesis. From egalitarianism, we study T-conorm and OWA operators from the Fuzzy Logic literature, and from sufficientarianism, we study headcount, shortfall and FGT operators. The aspect of rationality of these operators are measured by logical properties. Besides the original logical properties from belief merging, we consider other properties from social choice theory to describe the behavior of egalitarian and sufficientarian operators. Furthermore, we prove what are the conditions needed to be achieved for these operators satisfy some egalitarian or sufficientarian logical properties.