The impossibility of social evaluations of infinite streams with strict inequality aversion

We are concerned with the problem of aggregating infinite utility streams and the possible adoption of consequentialist equity principles when using numerical evaluations of the streams. We find a virtually universal incompatibility between the Basu-Mitra approach (that advocates for social welfare functions and renounces continuity assumptions) and postulates that capture various forms of strict preference for a reduction in inequality like the Strong Equity Principle, the Pigou-Dalton Transfer principle, or Altruistic Equity