In this research, the scientists looked at ways to make social choice systems work well in mixed strategy situations. They discovered a new idea called mixed Bayesian monotonicity that makes implementation better. In environments with at least three people, they found that mixed Bayesian implementation is linked to this new idea along with incentive compatibility and closure. For systems involving two people, mixed Bayesian monotonicity simplifies to Bayesian monotonicity. They also found that virtual implementation in mixed Bayesian equilibrium is more flexible than in other strategies. Overall, this study uncovers essential conditions for making rules work in a variety of situations.