i'm too lazy to look it up but i'm pretty sure i've read about how the development of some complicated bureaucratic systems basically looked like "let's make a council which will decide things", "oh we need MORE representatives to satisfy X, Y and Z fractions", "oh it's so big it's useless we need a smaller council which will actually work", repeated however many times. so from this pov the OP's statement appears right on as far as effectiveness goes, except "competence" is more than just that, or at least there's more than that to a government - for example, if it exists at all, it should have at least minimum redundancy, so taking out one person won't break the whole thing. for very small values the relationship might look differently but in general, yeah.

@Ashton: division by zero?