Strategy-proofness of scoring allocation correspondences for indivisible goods

We study strategy-proofness in a model of resource allocation due to Brams and King (Ration Soc 17:387-421, 2005) and Brams et al. (Theory Decis 55:147-180, 2003), further developed by Baumeister et al. (J Auton Agents Multi Agent Syst 31(3):628-655, 2017). We assume resources to be indivisible and nonshareable and that agents have responsive preferences over the power set of the resources, but only submit ordinal preferences over single resources to the social planner. Using scoring vectors, these ordinal preferences induce additive utility functions. We then focus on allocation correspondences that maximize utilitarian social welfare, and we use extension principles (from social choice theory, such as the Kelly and the Gardenfors extension) for preferences to study manipulation of allocation correspondences. We characterize strategy-proofness of the utilitarian allocation correspondence: It is Gardenfors/Kelly-strategy-proof if and only if the number of different values in the scoring vector is at most two or the number of occurrences of the greatest value in the scoring vector is larger than half the number of resources.