On Maxsum Fair Cake Divisions

We consider the problem of selecting fair divisions a heterogeneous divisible good among set agents. Recent work (Cohler et al., AAAI 2011) focused on designing algorithms for computing maxsum—social welfare maximizing—allocations under fairness notion envy-freeness. Maxsum allocations can also be found alternative notions such as equitability. In this paper, we examine properties these allocations. particular, provide conditions when maxsum envy-free or equitable are Pareto optimal and give examples where with optimality is not possible. prove that have weakly greater than agents structured valuations, derive an approximate version inequality general valuations.