The generation of a social welfare function under ordinal preferences

Abstract

Against the background of recent impossibility theorems, the paper establishes a number of rules for the formation of social preferences to ensure the generation of a Bergson-Samuelson social welfare function of the desired ‘individualistic’ form. It demonstrates that such welfare functions can indeed exist under conditions of simply ordinality of individual preferences and a lack of interpersonal comparability, for the general n-person case with only weak restrictions upon individual preferences. A valuable tool of social welfare theory for the single-profile case is therefore restored under a wide set of conditions. By examining Kemp and Ng's justification for their A3 condition in this context, we are able also to highlight a number of key differences between the conditions satisfied by many political constitutions and the requirements for achieving the positive existence of a Bergson-Samuelson social welfare function. In particular the paper focusses here on the weighting systems on individual preferences that are consistent with generating an individualistic welfare function and examines the information content of individual ordinal preferences which must be utilized if the desired welfare function is to result.