Historical perspective
The proposal for FDR control in BH was motivated by the paper of Soricç (1987) which was a strong and emotional call for the necessity to controlled inference because of the increased error resulting from multiple inferences. Otherwise, he warned, the expected number of `false discoveries` becomes large relative to the number of discoveries. Since BH has been published we have learned of independent previous efforts in the direction in which we went: looking for suitable error control in face of multiplicity, when the full protective power of the FWE is not necessary.
Shaffer (1997) has noted that an informal effort in this direction had already been attempted by Elkund in an unpublished work in Swedish. This work has been reported by Seeger (1968) who also attributes the procedure to Elkund. Seeger proved that when all tested null hypotheses are true the procedure controls the FWE at level q, but when some hypotheses are true while other are false (i.e. when m0 < m), this is not the case. Apparently Seeger's second result, that the procedure does not always control the FWE at the desired level, had diminished the interest in the procedure at the time it was proposed, to the point it became completely unknown (e.g. no mentioning in Hochberg and Tamhane , 1987).
Independently, Simes (1986) proposed a global test of the single intersection hypothesis. He gave a nice proof (by induction) of the error controlling property of the test, which is essentially Seeger’s first result. Simes suggested also suggested this procedure as an informal multiple testing procedure, but then Hommel (1988) showed - as Seeger had done before - that it does not control the FWE in the strong sense. Therefore, in the realm of FWE control, the procedure cannot be used for making the multiple inferences about the individual hypotheses. It can, and was used, to derive several other testing procedures e.g. by Hochberg (1988) and Hommel (1988), but these procedure are less powerful. Sen (1998a) points out that this equality is actually the classical Ballot Theorem related to uniform order statistics. Interest in the procedure as a multiple testing procedure came, in view of the FDR criterion it controls (BH): see, for example, its implementation in the new SAS MULTPROC software. For a review of the global testing procedure and its extensions see Hochberg and Hommel (1997).