Thanks! Your idea is interesting – I put a comment on that post.
Something you are probably aware of is that accepting “anonymity” (allowing the sequence to be reordered arbitrarily) requires us to reject seemingly intuitive principles like Pareto (if you can make someone better off and no one worse off, then you should).
Personally, I would rather keep Pareto than anonymity, but I think it’s cool to explore what anonymous orderings can do.
Hospital statistics have been published for several years now on Hospital compare. Similar programs exist for outpatient and nursing home quality metrics. This is largely due to effort by the Obama administration.
(Of course, this might just shift the “inadequate equilibrium” question to: if these statistics are published, how come so few people use them?)