Evaluationwise strategy-proofness

We consider manipulation of collective decision making rules in a framework where voters not only rank candidates but also evaluate them as “acceptable” or “unacceptable”. In this richer informational setting, we adopt a new notion of strategy-proofness, called evaluationwise strategy-proofness, where incentives of manipulation exist if and only if a voter can replace an outcome which he finds unacceptable with an acceptable one. Evaluationwise strategy-proofness is weaker than strategy-proofness. However, we establish the prevalence of a logical incompatibility between evaluationwise strategy-proofness, anonymity and efficiency. On the other hand, we show possibility results when either anonymity or efficiency is weakened.