Thinking that all individuals pursue "selfish" interest is equivalent to assuming that all random variables have zero covariance

Question

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?

Answer 1

Taken most literally, the statement says that the claim that people optimize their own well-being without regard for others is equivalent to saying that no random variables ever interact with each other. It seems that the second claim is probably strictly stronger than the first: I can imagine a society in which people optimize strictly for their own well being (for example, a subsistence farming society where families need not interact with other families), but I cannot imagine random variables ever always having zero covariance.

Taken a little more generously - someone making the above claim might be trying to say that the pursuit of one's self interest never benefits or harms someone else. This claim also doesn't seem accurate:

1. There are cases where an individual's self interest hurts someone else, for example, when they are competing for some common thing).
2. There are cases when an individual's self interest benefits someone else, for example when someone is able to specialize in performing some task or providing some product, and trades that product or service to someone else who needs it.

Answer 2

I believe the analogy is meaningful as a critique of the ideal "self" implied in old models of rational self-interest.

Suppose possible "interests" vary randomly within a very large population of selves. To achieve zero correlation among these blind social atoms would still be vanishingly unlikely. Yet this zero correlation is implied in the ideal definition of "selfish."

This is why it is impossible to achieve "perfect diversity" in a financial portfolio. Even without considerations of "human nature," an idealized model of "rational self-interest" is incoherent and worse than useless. In reality, of course, what we mean by "self-interest" is already loaded with correlations.

Answer 3

Let $X$ be any non-constant random variable. Then the covariance between $X$ and $2X$ is not zero. Therefore it is false that all random variables have zero covaraince. Therefore the statement

A. Thinking that all individuals pursue "selfish" interest is equivalent to assuming that all random variables have zero covariance.

is equivalent to the statement

B. Thinking that all individuals pursue "selfish" interest is equivalent to assuming something false.

which in turn is equivalent to

C. It is false that all individuals pursue "selfish" interest.

So either 1) The person who said A intended to express statement C (in a very contorted way for some reason) or 2) the person who said A was confused.