Before revision:  One advantage of the proposed mechanisms is their informational robustness as they depend only on certain }  moments of the valuation distributions . In contrast, previous mechanisms proposed to solve this question, such as the second-best mechanism, typically require the knowledge of the entire valuation distribution. Also, our study extends the results to non-binary decision environments with general utility functions. Lastly, we show that if the threshold is instead set equal to the cost, the proposed mechanism can achieve a non-negligible fraction of the optimal profit in the limit, where the fraction is the correlation between the virtual value and the aforementioned transformed value .
After revision:  One advantage of the proposed mechanisms is their informational robustness as they depend only on certain } moments of the valuation distributions .