Proportional Cake-Cutting among Families

The classic cake-cutting problem is extended from individual agents to groups of agents. Applications include dividing a land-estate among families or dividing disputed lands among states. In the standard cake-cutting model, each agent should receive an individual subset of the cake with a sufficiently high individual value. In our model, each group should receive a subset with a sufficiently high ”group value”. Six ways to define the aggregate group value based on the values of the group members are examined: four based on cardinal welfare functions and two based on ordinal preference relations. Our results show that the choice of the group value function has crucial implications on the existence and applicability of fair division protocols. JEL classification: D63