A new equity condition for infinite utility streams and the possibility of being Paretian

We investigate the properties of a new equity condition, Hammond Equity for the Future (HEF), capturing the following ethical intuition: A sacrifice by the present generation leading to a uniform gain for all future generations cannot lead to a less desirable utility stream if the present remains better off than the future. Since HEF is a weak condition when compared to other consequentialist equity conditions, it is of interest to establish whether it to a greater extent can be combined with Paretian conditions. We show that this is not the case: HEF is not compatible with the Strong Pareto condition when social preferences are upper semi-continuous in the sup norm topology. If we impose that the social preferences are complete, transitive and continuous in the sup norm topology, and satisfy an Independent future condition, then HEF cannot even be combined with the Weak Pareto condition.