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This article presents a preference accumulation model that can be used to implement a number of different multi-attribute heuristic choice rules, including the lexicographic rule, the majority of confirming dimensions (tallying) rule and the equal weights rule. The proposed model differs from existing accumulators in terms of attribute representation: Leakage and competition, typically applied only to preference accumulation, are also assumed to be involved in processing attribute values. This allows the model to perform a range of sophisticated attribute-wise comparisons, including comparisons that compute relative rank. The ability of a preference accumulation model composed of leaky competitive networks to mimic symbolic models of heuristic choice suggests that these 2 approaches are not incompatible, and that a unitary cognitive model of preferential choice, based on insights from both these approaches, may be feasible.