No-envy and Arrow's conditions

This paper analyzes the concept of envy-freeness in the framework of Arrovian social choice theory. We define various no-envy conditions and study their relationships with Arrow's condition of independence of irrelevant alternatives. We also propose a new condition, called Minimal Equity, that says that each individual must have the conditional power to veto at least one social state (for instance, a social state which is particularly unfair to him). We show that, under unrestricted domain, Pareto Optimality and a weak independence condition, Minimal Equity leads to an impossibility result.