The paper considers a voting model where each voter's type is her preference. The type graph for a voter is a graph whose vertices are the possible types of the voter. Two vertices are connected by an edge in the graph if the associated types are “neighbors.” A social choice function is locally strategy‐proof if no type of a voter can gain by misrepresentation to a type that is a neighbor of her true type. A social choice function is strategy‐proof if no type of a voter can gain by misrepresentation to an arbitrary type. Local‐global equivalence (LGE) is satisfied if local strategy‐proofness implies strategy‐proofness. The paper identifies a condition on the graph that characterizes LGE. Our notion of “localness” is perfectly general. We use this feature of our model to identify notions of localness according to which various models of multidimensional voting satisfy LGE. Finally, we show that LGE for deterministic social choice functions does not imply LGE for random social choice functions.
We propose a model where agents are matched in pairs in order to undertake a project. Agents have preferences over both the partner and the project they are assigned to. These preferences over partners and projects are separable and dichotomous. Each agent partitions the set of partners into friends and outsiders, and the set of projects into good and bad ones. Friendship is mutual and transitive. In addition, preferences over projects among friends are correlated (homophily). We define a suitable notion of the weak core and propose an algorithm, the minimum demand priority algorithm (MDPA) that generates an assignment in the weak core. In general, the strong core does not exist but the MDPA assignment satisfies a limited version of the strong core property when only friends can be members of the blocking coalition. The MDPA is also strategy-proof. Finally we show that our assumptions on preferences are indispensable. We show that the weak core may fail to exist if any of the assumptions of homophily, separability and dichotomous preferences are relaxed.
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