  The recently introduced theory of compressive sensing (CS) enables the
reconstruction of sparse or compressible signals from a small set of
nonadaptive, linear measurements. If properly chosen, the number of
measurements can be significantly smaller than the ambient dimension of the
signal and yet preserve the significant signal information. Interestingly, it
can be shown that random measurement schemes provide a near-optimal encoding in
terms of the required number of measurements. In this report, we explore
another relatively unexplored, though often alluded to, advantage of using
random matrices to acquire CS measurements. Specifically, we show that random
matrices are democractic, meaning that each measurement carries roughly the
same amount of signal information. We demonstrate that by slightly increasing
the number of measurements, the system is robust to the loss of a small number
of arbitrary measurements. In addition, we draw connections to oversampling and
demonstrate stability from the loss of significantly more measurements.
