Fairness for multi-self agents

Are fairness and efficiency compatible in behavioral welfare economics? Assuming multi-self agents, who may not be able to integrate their various objectives into complete and transitive rankings, we call an allocation unambiguously-fair if it fair according to every self of every agent. We show that efficiency is generically compatible with the unambiguous fair-share guarantee, and — in two agent economies — with unambiguous no-envy. But in some larger economies, no efficient allocation satisfies unambiguous no-envy or unambiguous egalitarian equivalence. These non-existence results persist if the agents integrate their objectives into complete but intransitive rankings. Even if unambiguously envy-free Pareto optima exist, they may not arise as market equilibria from equal endowments. Finally, we show that there are Pareto optima with the unambiguous fair-share guarantee that are envy-free for at least one complete and transitive aggregation of the agents' preferences, and others that are egalitarian-equivalent according to at least one such aggregation.