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Much work has been devoted, during the past twenty years, to using complexityto protect elections from manipulation and control. Many results have beenobtained showing NP-hardness shields, and recently there has been much focus onwhether such worst-case hardness protections can be bypassed by frequentlycorrect heuristics or by approximations. This paper takes a very differentapproach: We argue that when electorates follow the canonical political sciencemodel of societal preferences the complexity shield never existed in the firstplace. In particular, we show that for electorates having single-peakedpreferences, many existing NP-hardness results on manipulation and controlevaporate.

The Shield that Never Was: Societies with Single-Peaked Preferences are More Open to Manipulation and Control