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Might be off-topic here but on-topic on Math, Eco or Philo SE. Pls migrate if needed.

I read that: Thinking that all individuals pursue "selfish" interest is equivalent to assuming that all random variables have zero covariance. -- Nero

What does that mean, and what does it have to do with random variables and covariance?

There is an explanation: I read it as saying that people have many interests in common, so pursuing "selfish" interests can also be altruistic to some extent.

Another: That some people do in fact work towards the common good, or conversely, are outright malevolent rather than focused on personal gain

Assuming those are the meanings, I don't see what that has to do with random variables and covariance.

My guess: Given an index I, we list all random variables conceivable: $\{X_i\}_{i \in I}$.

It is clear that $Cov(X_j, X_k) \ \forall j, k \in I$, if well-defined, may or may not be zero.

Is covariance among two random variables an analogy for common interest among two people?

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  • $\begingroup$ Just read on modern interpretations of Adam Smith's Wealth of Nations work. It helps to survey what's been discussed so far before venturing into this kind of ontology. $\endgroup$ – Aksakal Sep 11 '15 at 17:07
  • $\begingroup$ @Aksakal The point is to relate it back to covariance and random variables...? $\endgroup$ – BCLC Sep 11 '15 at 18:21
  • $\begingroup$ Covariance has very little to do with this. As long as there's some randomness the argument will work. $\endgroup$ – Aksakal Sep 11 '15 at 18:54
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Short Answer: No, the analogy doesn't hold up well.

Longer answer:

The analogy would be astute if and only if interests among people were random- they aren't.

Human beings have universal needs along several axes- physical, emotional, arguably spiritual.

This leads me to conclude that in a hypothetical space of all possible interest $s$, there could be defined some directed function $f$ to describe all practical human interest space, and that this function would have some $x$-dimensional vector tendency within space $s$ and therefore human interests would co-vary along those vector tendencies.

Speculative Human Interest Space

It would also follow that any interest pursued according to those vector tendencies would correlate with other human interests-

Speculative Vectors Human Interest Space

In effect, self-interested but human interests correlate with altruistic but human interests in the hypothetical geometric space of all possible interests. That is, the controlling property is the humanness of the interest.

The random variables you mention in the space of all possible covariances have no identifiable similar $x$-dimensional vector tendency, certainly not to the same degree.

With illustrated possible subset of random variables.

I have no doubt that a philosophical answer would look very different indeed.

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  • $\begingroup$ Thanks Thomas Cleberg! ^-^ Is it against SE rules if I were to cross-post given your last line? $\endgroup$ – BCLC Sep 11 '15 at 16:50
  • $\begingroup$ If I were you, if you're interested in the philosophical answer to the question, I would try to formulate the question differently as a philosophical question and then ask that differently formulated question in philo SE $\endgroup$ – Thomas Cleberg Sep 11 '15 at 16:53
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    $\begingroup$ This answer conflates the colloquial definition of random, which approximates the definition of uniformly random, with the definition of a random variable, which is a more general concept. $\endgroup$ – Brash Equilibrium Sep 13 '15 at 5:30
  • $\begingroup$ Other than that, it's a fantastic answer by the way $\endgroup$ – Brash Equilibrium Sep 13 '15 at 5:33
  • $\begingroup$ One thing I'd add though is that if your model could separate account for the reasons outside costly signaling, kinship, reciprocity, reputational benefit, group selection etc, then the residuals should be uncorrelated if none of those processes were in effect. Of course, that separation is basically impossible. $\endgroup$ – Brash Equilibrium Sep 13 '15 at 5:41

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