To utilize the multi-user diversity in broadcast channels, the channel state information (CSI) of each user must be known at the transmitter. To reduce the overhead of CSI feedback under random beamforming the question of which receivers should feed back their CSI is investigated. Using the closed form expression for the SINR distribution, thresholding functions T(n) are designed to meet specific design criterion as a function of the number of receivers. Specifically three design criterion are proposed. The asymptotic limits of the successful thresholding functions T(n) are found. If T(n) scales slower than log n, asymptotically no performance is lost. If T(n) scales faster than log n, all multi-user diversity is lost.