Social choice rules and real-valued representations
Abstract Under commonplace assumptions, it is shown that social choice rules can be given real-valued representations. The usefulness of this characterization is that the general structure of abstract choice rules can be analyzed by investigating the form of their representation and the particular structure of rules can be analyzed by examining the properties of functions that represent them. After the possibilities of representation have been fully analyzed, this is demonstrated with the use of several examples. The analysis suggests a useful technique for studying social choice rules.