That's why I said "over the shared frontier" in my first post and more precisely in my second post I said "over the overlapping x values for which both are defined."

It was a claim that applies to a range of x-values where both curves are defined.

Of course if you go beyond those x-values where only one of the two are defined, then trivially the one that is defined constitutes the Pareto frontier in that region. Which is what I understand to be your point?

The post I was replying to said "performs strictly better at the same cost per task". That claim was obviously not true, there are costs where Opus cannot do the task and Sonnet can, so Opus can't be performing strictly better that the same cost. It seems that you agree that it is not true.

You could make it true by artificially dropping some of the data points, but, like, why?

(Again, this is moot given the updated graph.)

> Of course if you go beyond those x-values where only one of the two are defined, then trivially the one that is defined constitutes the Pareto frontier in that region.

Not so! It's only sound to do that at the low end of the cost axis (x) or the high end of the performance axis (y). You can't do it at the low end of the performance axis or the high end of the cost axis.