I don't think this works, because "fairness" is not defined as "divide up food equally" (or even "divide up resources equally"). It is the algorithm that, among other things, leads to dividing up the pie equally in the circumstances described in the original post

Yes; I meant for the phrase "divide up food equally" to be shorthand for something more correct but less compact, like "a complicated algorithm whose rough outline includes parts like, '...When a group of people are dividing up resources, divide them according to the following weighted combination of need, ownership, equality, who discovered the resources first, ...'"