Social choice with a continuous ordering function

The purpose of this paper is to get some fresh insights into social choice problems by treating the aggregation procedure as a continuous ordering of the reports individuals give of the value they attach to different states of the world where these reports are treated as a continuous path in n dimensional space. This approach allows us to ask different sorts of questions that belong more naturally to a continuous framework. It also allows us to exploit readily available tools of algebra and analysis in order to get some different insights into the kind of information conditions that make coherent collective decisions possible, or cause them to fail. What the paper says, roughly, is that the initial reports must contain sufficient information to allow their dimension to be reduced in a consistent manner. In particular it shows that an additive welfare function of the Bergson- Samuelson sort seems to have some properties that give it a natural appeal. JEL Categories: C65, D71.