Can you elaborate on what’s wrong with his comment? The Peter principle looks like it has some legs (after a couple minutes of searching), and the analogy sounds reasonable to me.
On the second part I can kind of follow your argument. But what has this got to do with the Peter Principle? I didn't see the argument being tied back to people being promoted until incompetence, which is not even what the article suggests. But the P and Q argument does make sense. IQ is helpful, charisma is helpful. If you have a lot of charisma you need less IQ to get there.
I find that part of the argument statistically sound.
Sure. Just heads up, I won't comment on the Peter principal, as I view both the definition of leadership and the complexities surrounding it far too complex to sum up in a simple parable, though I'm sure anyone with real world experience thinks it has some legs.
Paragraph 2, about the person being promoted until failure, I can't gleam any explanatory content from, myself. Then there's this sentence:
"If P and Q are qualities correlated with leadership, if P and Q are independently randomly distributed, then a leader with higher P is expected to have a lower Q."
This is false. You don't have variables that are simultaneously independent and let you say something about one based on the other. Its like saying "there is and is not a relationship between P and Q". Leaving aside the additional gymnastics and problems of having both correlate with leadership...
I could go into a discussion about expected values, averages, etc, but I can't tell what farmer banana P's and Q's have to do with the price of fish or peter's principal, so I don't think the language in the original is well specified enough for there to be much benefit to doing so...
