We consider weak preference orderings over a set An of n alternatives. An individual preference is of refinement \ell\leqn if it first partitions An into \ell subsets of `tied' alternatives, and then ranks these subsets within a linear ordering. When \elln, preferences are coarse. It is shown...

Indivisible units are randomly allocated among agents with a claim/demand on the resources. The available resources fall short of the sum of individual claims.  The proportional method distributes units sequentially, and the probability of receiving a unit at any step is proportional to the...