On Democratic Fairness for Groups of Agents
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We study the problem of allocating indivisible goods to groups of interested agents in a fair manner. The agents in the same group share the same set of goods even though they may have different preferences from one another. Previous work on this model has shown positive results that hold either asymptotically or for groups with a small number of agents. Using the concept of democratic fairness, which aims to satisfy a certain fraction of the agents in each group, we provide fairness guarantees that hold for general instances. In particular, we show that for two groups with any number of agents, there exists an allocation that is envy-free up to one good and yields at least half of the maximin share for at least half of the agents in each group.
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