In a paper by Ridley, the combining equations included two variable weights, w for the original forecast and q for the antithetic forecast. The weights were allowed to vary independently and unconstrained. However, in that paper as well as in additional research, it turned out that the weights always summed to approximately one. The purpose of this note is to point out this finding, since it can be used to simplify the combining equations; and to reduce and expedite the number of computations required to solve the system of equations. This is accomplished simply by replacing the original independent weights w and q with complementary weights w and (1 − w). The numerical results as implemented in the computer program FOURCAST remain unchanged.
