Fairness for Multi-Self Agents

We investigate whether fairness is compatible with efficiency in economies with multi-self agents, who may not be able to integrate their multiple objectives into a single complete and transitive ranking. We adapt envy-freeness, egalitarian-equivalence and the fair-share guarantee in two different ways. An allocation is unambiguously-fair if it satisfies the chosen criterion of fairness according to every objective of any agent; it is aggregate-fair if it satisfies the criterion for some aggregation of each agent's objectives. While efficiency is always compatible with the unambiguous fair-share guarantee, it is incompatible with unambiguous envy-freeness in economics with at least three agents. Two agents are enough for efficiency and unambiguous egalitarian-equivalence to clash. Efficiency and the unambiguous fair-share guarantee can be attained together with aggregate envy-freeness, or aggregate egalitarian-equivalence.