Do incentives suffer the same way as voting systems?

Question

Arrow’s Impossibility Theorem establishes the weakness of voting systems. In posts on social issues, one often sees lament about the ‘misalignment’ of incentives. A natural question to ask, then, is whether there exists a theorem similar to Arrow’s Impossibility Theorem for incentives. Indeed, it might even turn out that that incentives can be shown to be the flip-side (i.e., the dual) of voting systems, and with Arrow’s Impossibility Theorem consequently directly applying to them.