The Price of Anarchy in Spatial Social Choice

Except for a few strategy-proof mechanisms on the real line, spatial social choice mechanisms are usually manipulable. But is it wise to treat all manipulations as equally bad? We use the price of anarchy to make finer distinctions than between "strategy-proof" and "manipulable. " The price of anarchy measures how much strategic behavior can alter the cost in social choice. Supported by experimental economics data, our measure employs a novel minimal dishonesty criterion to refine the set of Nash equilibria. Using the price of anarchy, we study standard spatial selection rules and uncover a class of selection rules that are immune to the negative consequences of manipulation despite remaining manipulable. This is in contrast to standard approaches that sacrifice other beneficial properties, e.g., unbiased tie-breaking, to gain strategy-proofness. The concepts herein could be applied to other social choice scenarios in which a publicly known mechanism relies on private information.