The factors by which the expected number of collisions could be reduced by the implementation of Proximity Warning Instruments (PWI) having various performance characteristics are estimated. If both aircraft involved in an encounter are equipped with high performance PWI (sharp range and altitude cut-offs, and 2 deg relative bearing accuracy) then it is estimated that the expected rate of collision could be reduced by factors of ten or more at typical closing speeds. See-and-avoid itself is estimated to be highly effective, as judged by the number of potential collisions that are avoided, but the residual collision risk is unacceptable to the public and large effort is being made to mitigate it. The collision risk per operation tends to increase as the square of the number of operations so that the cost of providing separation assurance per operation will ultimately limit the growth of traffic unless technological progress provides more economical solutions. Collisions involving general aviation aircraft cause a very small fraction of general aviation fatalities and represent a very difficult technical problem because most of these collisions occur in traffic patterns where the angular coverage and associated display requirements are severe for airborne equipment solutions and the aircraft are likely to be outside the coverage of ground based equipment solutions. For the typical general aviation aircraft the principal effect of collision risks appears to be the operational and cost burdens of minimizing the risk to instrument flight rule (IFR) operations. (Author0.