Green’s Dictionary of Slang

a sinecure that comes to all members of a committee, board of directors etc, as long as they remain members of that group and, in due course, inevitably take their turn at a task; the antithesis of promotion by merit.

1901		Lord Fisher (letter) Jan. 13: Favouritism was the secret of our efficiency in the old days [...] ‘Buggins’ turn’ has been our ruin and will be disastrous hereafter.
1969		New Scientist 28 Aug. 424: Our system is hieratic. It was always possible to maintain this as long as those at the top of the pyramid could keep the rest down [...] When the headman’s axe was no longer seriously accepted as a solution, we invented the law of ‘Buggin’s turn’.