  We consider the social welfare function a la Arrow, where some voters are not
qualified to evaluate some alternatives. Thus, the inputs of the social welfare
function are the preferences of voters on the alternatives that they are
qualified to evaluate only. Our model is a generalization of the peer rating
model, where each voter evaluates the other voters (except for
himself/herself). We demonstrate the following three impossibility results.
First, if a transitive valued social welfare function satisfies independence of
irrelevant alternatives and the Pareto principle, then a dictator who is
qualified to evaluate all alternatives exists. Second, a transitive valued
function satisfying the Pareto principle exists if and only if at least one
voter is qualified to evaluate all alternatives. Finally, if no voter is
qualified to evaluate all alternatives, then under a transitive valued social
welfare function satisfying the weak Pareto principle and independence of
irrelevant alternatives, all alternatives are indifferent for any preference
profile of voters.
