Posterior passing assumes a few things I'm not sure are discussed enough here. Mainly, that there is a singular parameter. In the end, this mode of posterior passing basically becomes a fixed-effect meta-analysis. To that end, I actually think a better comparison would be >
between posterior passing, fixed effects MA, random effects MA, both bayesian and non-bayesian versions. Comparing a pseudo meta-analytic method to ones that don't claim to do so, and arguing for how well it converges to the generative value seems a bit obvious to me.
But to me, it's important to consider that having 60 studies examining the _exact_ same thing (the EXACT same effect, same materials, same everything) seems unlikely. Having 3 studies on the EXACT same thing seems unlikely.
As a consequence, I would assume a random-effects approach would be more plausible, with the assumption that small differences between populations sampled, materials, stereotype content, targets of the stereotype would result in slighlty different, albeit related, parameters.
Oops: that was wrong. I think this is what I mean. 
So, I guess to summarize: 1. PP = full data analysis = fixed-effects meta, assuming IID and sufficiency 2. When can we assume the generative parameter is 100% identical across studies? 3. When we can't [presumably most of the time], random-effects should be incorporated.
