I understand why ridge regression (equivalent to using a Gaussian prior on the coefficients in a Bayesian setting) works well in the presence of multi-collinearity, but couldn't one argue that other shrinking priors would also help? (e.g. say a Laplace prior, as in LASSO).
Moreover, if OLS is effectively equivalent to using a uniform prior (with a Gaussian likelihood), what type of priors can arguably with multi-collinearity? In other words, what conditions does a prior have to have to help with multi-collinearity?