Serial Priority in Project Allocation: A Characterisation

We consider a model in which projects are to be assigned to agents based on their preferences, and where projects have capacities, i.e., can each be assigned to a minimum and maximum number of agents. The extreme cases of our model are the social choice model (the same project is assigned to all agents) and the house allocation model (each project is assigned to at most one agent). We propose a natural extension of the dictatorial rule (social choice model) and the serial priority rule (house allocation model) to cover the intermediate cases, and call it the {\em strong serial priority rule}. We show that, when minimum and maximum capacities are common to all projects, a strong serial priority rule is characterised by the axioms of {\em strategy-proofness, group-non-bossiness, limited influence, unanimity}, and {\em neutrality}. Our result thus provides a bridge between the characterisations in Gibbard (1973), Satterthwaite (1975), and Svensson (1999). We also provide an independent characterisation of the serial priority rule in the house allocation model, and demonstrate some new relations between the axioms.