Not whom you questioned, but ...

> We can do a simple thought experiment here.

Yes, and Yes.

> when the degree attainment rate crosses the 50% mark, do you agree that the median income holder must have a degree?

No. I don't even agree that there is necessarily a single median income holder - there may well be a hundred, sixty with a degree and 40 without.

Also possible that in a hypothetical population with 1,001 people that 1,000 people have a degree but the sole median income earner does not.

I don't question anyone in particular. This is a discussion forum, not a private one-on-one conversation.

> there may well be a hundred, sixty with a degree and 40 without.

So what you are suggesting is that attaining a degree lowers your earnings and then gives you back a commensurate premium, thus restoring you back to the same level as those without a degree? That's a take, I guess, but premium usually comes with certain connotations that isn't that.

> Also possible that in a hypothetical population with 1,001 people that 1,000 people have a degree but the sole median income earner does not.

Again, where is the premium? If the only person without a degree isn't the lowest earner then we know that the person with the least earnings has a degree, but it was asserted that the person with the least earnings is given a premium over those without a degree, so... Are your numbers omitting a space alien or fairy without a degree where we earlier considered them to be people? It's not clear how to resolve this discrepancy.