Many real-world problems can be modelled as resource allocation problems implying indivisible goods to distribute among a set of agents. Many of these problems, implying human agents expressing some preferences on the set of objects to allocate, have also in common the notion of social fairness, that is, the fact that the collective decision must reflect the individual preferences. This notion of individual preference representation is also crucial in resource allocation problems: since many of these problems require the expression of non-additive preferences, one may introduce a compact language for expressing preferences, to avoid falling in the combinatorial trap.

In this talk we will focus first on the modelling of fair resource allocation problems, borrowing the notion of fairness from microeconomics. We will then introduce a compact representation language based on propositional logic for representing these resource allocation problems, and analyze the impact of compact representation on the complexity of finding a fair allocation, for the notions of fairness introduced in the first part.