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There is a simpler explanation. It is the Peter principle. A person is promoted until failure. All else being equal, if two people are leaders, leader A will b

There is a simpler explanation. It is the Peter principle. A person is promoted until failure. All else being equal, if two people are leaders, leader A will be on average as good as leader B. If one were significantly better, they would be promoted to the next level - eg a retired philanthropist billionaire or enlightened monk or what have you. 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. An analogy: farmers who grew 2 truck loads of bananas meet up to compare farms. On average the farms are 4 square miles. If farmer Joe tells you his farm is half a mile wide, you might guess it is 8 miles high, because the area is expected to be average. There was no causation at work — having a half mile wide plot did not cause the plot to be 8 miles tall. Why should we assume that there is a causal link between high iq and being disliked, when it could be chalked up to correlation between factors of an equivalence relation? High iq allows non-charasmatics to function higher than they normally would, just as charisma may make up for a lack of brains.

ACow_Adonis 9y ago
That's um... neither how stats nor reasoning works :(
- floriferous 9y ago
  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.
  - carlmr 9y ago
    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.
  - ACow_Adonis 9y ago
    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 9y ago
      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 9y ago
      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.
zormino 9y ago
If P and Q are independently randomly distributed, you can't tell anything about Q from the value of P.
- ssivark 9y ago
  ... unless the sample being examined was selected for being above average in at least one of P or Q. In such a sample, P and Q will be anti-correlated. https://en.m.wikipedia.org/wiki/Berkson's_paradox https://en.m.wikipedia.org/wiki/Berkson's_paradox
  - zormino 9y ago
    Ok, that actually makes sense. If they are truly independent, they will be unrelated. However since P+Q=LeadershipScore, and all LeadershipScore are about the same, then a high P indicates a Low Q. The connection between the two only exists because of that third piece of information, LeadershipScore, being held constant. The only part I disagree with is that LeadershipScore will be roughly the same in reality, I think a quick glance at the world's leaders shows some are clearly better in most ways than others.
    - lookACamel 9y ago
      It should be P+Q = L (another random variable) >= THRESHOLD_TO_BE_ACCEPTED_AS_LEADER

ACow_Adonis 9y ago

That's um... neither how stats nor reasoning works :(

floriferous 9y ago
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.
- carlmr 9y ago
  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.
- ACow_Adonis 9y ago
  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 9y ago
    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 9y ago
    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.

zormino 9y ago

If P and Q are independently randomly distributed, you can't tell anything about Q from the value of P.

ssivark 9y ago
... unless the sample being examined was selected for being above average in at least one of P or Q. In such a sample, P and Q will be anti-correlated. https://en.m.wikipedia.org/wiki/Berkson's_paradox https://en.m.wikipedia.org/wiki/Berkson's_paradox
- zormino 9y ago
  Ok, that actually makes sense. If they are truly independent, they will be unrelated. However since P+Q=LeadershipScore, and all LeadershipScore are about the same, then a high P indicates a Low Q. The connection between the two only exists because of that third piece of information, LeadershipScore, being held constant. The only part I disagree with is that LeadershipScore will be roughly the same in reality, I think a quick glance at the world's leaders shows some are clearly better in most ways than others.
  - lookACamel 9y ago
    It should be P+Q = L (another random variable) >= THRESHOLD_TO_BE_ACCEPTED_AS_LEADER