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 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 aggregate rule for this mutual evaluation model, investigate several combinations of criteria, and show that each of these combinations leads to a negative consequence.