When preferences explicitly include a spatial component, it can be challenging to assign weights to geographic regions in a way that is both pragmatic and accurate. In multi-attribute decision making, weights reflect cardinal information about preferences that can be difficult to assess thoroughly in practice. Recognizing this challenge, researchers have developed several methods for using ordinal rankings to approximate sets of cardinal weights. However, when the set of weights reflects a set of geographic regions, the number of weights can be enormous, and it may be cognitively challenging for decision makers to provide even a coherent ordinal ranking. This is often the case in policy decisions with widespread impacts. This paper uses a simulation study for spatial preferences to evaluate the performance of several rank-based weight approximation methods, as well as several new methods based on assigning each region to a tier expressing the extent to which it should influence the evaluation of policy alternatives. The tier-based methods do not become more cognitively complex as the number of regions increases, they allow decision makers to express a wider range of preferences, and they are similar in accuracy to rank-based methods when the number of regions is large. The paper then demonstrates all of these approximation methods with preferences for water usage by census block in a United States county.
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