A stereotype is a relation of the form X ⇒ Y. It maps a class of people/individuals/what have you to a property X. For example, people who wear glasses are smart. Occasionally, some individuals may conceive the relation as Y ⇔ X. E.g. Smart people wear glasses. I suspect this is due to reasons unrelated to the stereotype (e.g. inability to distinguish between ’=>’ and ’<=>’). I hope this is not common among the general population—the average human can’t be that irrational, right? I shall give a charitable interpretation of the masses, and discuss only the relation ‘X ⇒ Y’.
It would be better to think of it as X correlates with Y, or X is evidence for Y. And unlike your ⇒ relation, which you never adequately specified, these two relations are symmetric.
A kind of causation. X implies Y. X may be strong evidence for Y, but Y may be extremely weak evidence for X, so the two relations are not really symmetric.
It would be better to think of it as X correlates with Y, or X is evidence for Y. And unlike your ⇒ relation, which you never adequately specified, these two relations are symmetric.
Correlations are symmetric, but is evidence for may not be (depending on how you interpret the phrase): P(A|B) ≠ P(B|A) (unless P(A) == P(B)).
However, the likelihood ratio (P(B|A)/P(B|~A)), a.k.a., the quantity you actually care about when updating on new evidence, is symmetric.
A kind of causation. X implies Y. X may be strong evidence for Y, but Y may be extremely weak evidence for X, so the two relations are not really symmetric.
You seem to be confusing causation and “evidence for” implication. DON’T. Wet streets are evidence for rain, but when streets do not cause rain.