A foundation for dominant strategy voting mechanisms

We study deterministic voting mechanisms by considering an ordinal notion of Bayesian incentive compatibility (OBIC). If the beliefs of agents are independent and generic, we show that any OBIC mechanism is dominant strategy incentive compatible under an additional mild requirement. Our result works in a large class of preference domains (that include the unrestricted domain, the single peaked domain, a specific class of single crossing domains) and under a weaker notion of OBIC that we call locally OBIC. We also discuss the implications of assuming unanimity on our results.