the marginal meshing like this can seemingly gives us a way to recover the crunch of Correspondence let's say the ground shook of respondents is between a 2 and B 1 and a 3 and B 2 and a 1 and B 3 right so I would argue this would be the only correspondence that satisfied the marginal matching constraint well it could be not a by direction but then like it might not fulfill the properties until unless some of the unless some of the values have like no probability mass then like you can do whatever right so argue this is the only way that you