We have different measures of stochastic dominance and variability that are widely used, e.g., first-order stochastic dominance, mean-preserving spreads etc.
Do we have similarly widely used measures of affiliation/correlation? Specifically, given real random variables $X$, $Y$, $X'$, and $Y'$, are there correlation partial orders that allow us to say the pair $(X, Y)$ is more affiliated/correlated than the pair $(X',Y')$?
I guess one such measure is to compare the correlation coefficients: $\operatorname{corr}(X,Y)$ vs $\operatorname{corr}(X',Y')$ but this seems to throw out a lot of information about the variables and the dependencies between them.