Positional information and preference aggregation

A new version of independence (I+) is proposed for social welfare functions based on the following notion of agreement. Two weak orders R and R' on a finite set S agree on a pair {x, y}, denoted by R vertical bar(+)({x; y}) = R'vertical bar(+)({x, y}), if R vertical bar({x, y}) = R'vertical bar({x, y}) and [z R* x and z R* y for some z is an element of S] if and only if [z' (R')* x and z'(R')*y for some z'is an element of S]. The last part says that x and y are strictly under z with respect to R exactly when x and y are strictly under z' with respect to R'. Some examples and results on social welfare functions that satisfy (I+), Pareto, and nondictatorship are given.