Often preferences in a group of agents are such that any sensible goal must admit a tie between all alternatives. The standard formulation in mechanism design demands that in this case all alternatives must be equilibrium outcomes of the decision making mechanism. However, as far as the idea of an equilibrium is to predict the outcome, we could equally well require that there are no equilibria at all. Although this may seem innocent, it allows the mechanism designer to implement goals that are impossible to enforce with any other implementation concept, like mixed Nash implementation, subgame perfect implementation, or Nash implementation using undominated strategies.