3 ms·

What do you mean by "arbitrarily long"? There's this related procedure for N cake eaters, which is straightforward: 1. Arbitrarily choose an order 2. Repeat w

What do you mean by "arbitrarily long"? There's this related procedure for N cake eaters, which is straightforward: 1. Arbitrarily choose an order 2. Repeat while not everyone has a slice: a. First person without a slice cuts a slice b. Each other person, in order, who's without a slice may either take the slice or pass it c. If everyone else has passed, the cutter must take that slice It's quadratic time -- worst case you go fully around the (remaining) circle for every slice -- but that's still not a very big number even for four or five political parties. How many parties are there actually going to be? (I'm not exactly sure how this maps to the article's scheme, either; the point is that I'm not sure it's all that complex.)

learnstats2 8y ago
From the relevant wikipedia page: "envy-free divisions of connected intervals to 3 or more people cannot be found by any finite protocol." - I can agree that your algorithm is quadratic, and therefore, that your algorithm is not envy-free. Your suggested algorithm seems to be unfair because the first party to choose has a clear advantage over the parties who choose later and did not cut: depending on the order of the parties there is also likely to be collusion. The immediately easiest (and politically realistic) way to game your system is to split yourself into multiple parties and then cut your allies/sock puppets a massive slice.