Aggregating incomplete lists

We study the aggregation of partial orders into a complete ordering, and prove both possibility and impossibility results in this context. First, we show that the standard independence of irrelevant alternatives condition is stronger here since even dictatorial aggregation rules may fail to satisfy it. On the other hand, domain restrictions enable non-dictatorial aggregation rules satisfying a number of attractive properties. In particular, we show that anonymous aggregation satisfying a weak form of independence of irrelevant alternatives is possible on a large class of 'extended' Condorcet domains.