On a tangential note, something that's always bothered me about write-ups of "envy-free" division is that they assume a couple of things I don't think are true:
- That someone cutting a cake always executes exactly the cut they planned.
- That once the cake has been divided, no one will experience envy because their piece is worth, to them, at least their "fair share" of the total.
Take the classic example of envy-free division of one cake among two people. The solution is simple enough that most people understand it instantly: person A divides the cake into two portions however they please, and person B then selects one of those portions, A receiving the other. Everyone will agree that this is intuitively fair. But it's certainly not fair for either of the two reasons I dispute -- A might still envy the portion of the cake that went to B, imagining a different world where the entire cake was theirs... or A might slip up with the knife and create one portion which is obviously better than the other portion, which B then chooses.
Rather, I think the benefits of envy-free division come from two other points:
- The parties involved agree beforehand that the process is fair. This requires them to be able to understand it, which is easy for the two-person division and quite difficult for more than two.
- Instead of assuming that division goes off without a hitch, we can observe that if you receive a portion you're unhappy with, it's because you messed up. The blame falls on you rather than someone else.
I think he's describing a different problem, since he mentions majority voting. If I was splitting a cake with 2 other people (A and B), A suggested fair division into thirds, and B suggested half for me and half for B, B's suggestion would clearly win the vote.
No, there's no name AFAIK. I learned it from Robin Hanson (well-known blogger and economics professor at GMU). It's different from envy-free cake cutting, which doesn't involve voting.
Or more specifically, https://en.wikipedia.org/wiki/Envy-free_cake-cutting
On a tangential note, something that's always bothered me about write-ups of "envy-free" division is that they assume a couple of things I don't think are true:
- That someone cutting a cake always executes exactly the cut they planned.
- That once the cake has been divided, no one will experience envy because their piece is worth, to them, at least their "fair share" of the total.
Take the classic example of envy-free division of one cake among two people. The solution is simple enough that most people understand it instantly: person A divides the cake into two portions however they please, and person B then selects one of those portions, A receiving the other. Everyone will agree that this is intuitively fair. But it's certainly not fair for either of the two reasons I dispute -- A might still envy the portion of the cake that went to B, imagining a different world where the entire cake was theirs... or A might slip up with the knife and create one portion which is obviously better than the other portion, which B then chooses.
Rather, I think the benefits of envy-free division come from two other points:
- The parties involved agree beforehand that the process is fair. This requires them to be able to understand it, which is easy for the two-person division and quite difficult for more than two.
- Instead of assuming that division goes off without a hitch, we can observe that if you receive a portion you're unhappy with, it's because you messed up. The blame falls on you rather than someone else.