[ACow_Adonis]

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...

[lookACamel]

You forget that "then a leader with higher P is expected to have a lower Q." is conditional on "being a leader". This is Berkson's paradox.

[kingdomcome50]

The statement is saying the P and Q are independent, not unrelated.

P + Q = L (leadership score)

For a group of candidates with equal L, a higher P does indicate lower Q.