Before revision:  In addition to welfare approximation, we also study profit approximation using similar mechanisms but with a different threshold and show that a fraction of the optimal profit can be achieved with a large number of participants. Lastly, we extend the model to accommodate for non-binary decision and general utility functions .
After revision:  In addition to welfare approximation, we also study profit approximation using similar mechanisms but with a different threshold and show that a fraction of the optimal profit in the limit, where the fraction is the correlation between the virtual value and the aforementioned transformed value .