> In contrast to this cake division algorithm, it leaves awkward leftovers.
An important difference is that your rule only ensures that each person feels that they received at least 1/n of the total. This article is about the "envy-free" criterion, which is stronger: each person feels that nobody received more than they did. That's what makes the algorithm in the article so much more complicated.
(In particular, with the envy-free criterion it's very difficult to reduce the problem with a step like "That person is now out; they have their fair share", because the remaining people might subsequently divide the remaining cake in some bizarre way which makes one of the other divisions look enviable. Towards the end of the article it touches on how the new algorithm solves this: search for "domination relationships".)
An important difference is that your rule only ensures that each person feels that they received at least 1/n of the total. This article is about the "envy-free" criterion, which is stronger: each person feels that nobody received more than they did. That's what makes the algorithm in the article so much more complicated.
(In particular, with the envy-free criterion it's very difficult to reduce the problem with a step like "That person is now out; they have their fair share", because the remaining people might subsequently divide the remaining cake in some bizarre way which makes one of the other divisions look enviable. Towards the end of the article it touches on how the new algorithm solves this: search for "domination relationships".)