Impossibility theorems on mutual evaluation

Arrow's impossibility theorem, which is a classical result in social choice theory, shows that it is impossible to design a democratic rule for social decision making that obeys some reasonable criteria. In the Arrow's model, each individual of a society has a preference order among given alternatives and the society needs to agree on a preference order that aggregates individuals' preference orders. In this paper, we consider a model where each individual has a preference order on all the individuals but herself/himself. We introduce some reasonable criteria of an aggregation rule for this mutual evaluation model, investigate several combinations of these criteria, and show that each of these combinations leads to a negative consequence.