Presenting Objects for Random Allocation

For random allocation, whether a desirable rule exists hinges on the domain of agents' preferences, whose formation is affected by how objects are presented. We hence propose a model studying how to present objects so that the induced preference domain allows for designing a good rule. Motivated by practices in reality, we model the objects as combinations of several attribute values and a presentation of objects concerns a choice of presenting attributes and a ranking of them. Agents are assumed to formulate their preferences in a lexicographic manner according to the given presentation. We show that, the domain of preferences induced by a presentation allows for a strategy-proof, efficient, and envy-free rule if and only if the presented attributes are conditionally binary. Under two technical conditions on the number of objects, this result still holds when envy-freeness is weakened to equal treatment of equals