Positional independence in preference aggregation

If, for strict preferences, a unique choice function (CF) is used to aggregate preferences position-wise then the resulting social welfare function (SWF) is dictatorial. This suggests that the task performed by non-dictatorial SWFs must be “more complex” than just selecting an alternative from a list using a single criterion. This is because the information required by non-dictatorial SWFs to aggregate preferences cannot be compressed into a CF. It is also shown that the attempt to reduce the working of a SWF to the working of a CF involves the adoption of certain positional requirements, whose relationship with the conditions in Arrow's theorem is established. Copyright Springer-Verlag Berlin Heidelberg 2003