The Arrow problem in the group choice theory (the problem analysis)

A space of group choice operators that satisfy the condition of “independence of irrelevant alternatives” (Arrow operators) is introduced into the problem of the Arrow paradox. Relations are studied between ranges of Arrow operators that are characterized by additional characteristic properties of the operators and various constraints on the original binary relations and those which are specified by the operator. A newly formulated principle of alternative neutralities establishes that outside the unanimity principle there is no Arrow operator which would “process” the transitive relations of voters into collective relations from the same class and also meet the conditions of neutrality to alternatives and to the voters and monotoneity and non-imposedness of the group decision. The chief concept of the research is “list mechanisms” that generate Arrow operators.