We propose the solution concept of directional equilibrium for the multidimensional model of voting with general spatial preferences. This concept isolates alternatives that are stable with respect to forces applied by all voters in the directions of their gradients, and it extends a known concept from statistics for Euclidean preferences. We establish connections to the majority core, Pareto optimality, and existence and closed graph, and we provide non-cooperative foundations in terms of a local contest game played by voters.
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