  We use an algebraic viewpoint, namely a matrix framework to deal with the
problem of resource allocation under uncertainty in the context of a
qualitative approach. Our basic qualitative data are a plausibility relation
over the resources, a hierarchical relation over the agents and of course the
preference that the agents have over the resources. With this data we propose a
qualitative binary relation $\unrhd$ between allocations such that
$\mathcal{F}\unrhd \mathcal{G}$ has the following intended meaning: the
allocation $\mathcal{F}$ produces more or equal social welfare than the
allocation $\mathcal{G}$. We prove that there is a family of allocations which
are maximal with respect to $\unrhd$. We prove also that there is a notion of
simple deal such that optimal allocations can be reached by sequences of simple
deals. Finally, we introduce some mechanism for discriminating {optimal}
allocations.
