Talk:Divide and choose

Merge Pie method

Pie method seems mainly a duplicate of this article. I propose to redirect pie method here and distribute what little extra it has as appropriate. Divide and choose seems the better name. Dmcq (talk) 22:29, 7 August 2009 (UTC)

Having though a bit more about it I'm withdrawing the proposal, the other article has a valid existence separate from this one as a fair division method for more than two people. Dmcq (talk) 22:42, 7 August 2009 (UTC)

Pie method now redirects to an entirely unrelated issue. I remove the link from here. --Erel Segal (talk) 13:58, 2 September 2014 (UTC)

Gender-neutral "chooser chooses"

Two IPs have reworded the explanation from the arbitrary-gender "she" to a gender-neutral "the chooser/cutter". Aside from the awkward wording ("the chooser chose the piece that is more valuable in the chooser's eyes"), it's also unnecessarily ambiguous to say "two partners can act in a way that guarantees that, according to each person's own subjective taste, each allocated share is at least as valuable as the other share" - the chooser is not acting "according to each person's own subjective taste", they're just acting according to their own taste. There may be a way to make these paragraphs both gender-neutral and easily understandable, but this isn't it. --McGeddon (talk) 14:43, 20 February 2017 (UTC)

I agree. I would reword it to "he/she" form, so for example "the chooser chose the piece that is more valuable in his/her eyes". Arbitrary-gender "she" in this case feels quite odd. Illioplius (talk) 22:10, 16 August 2017 (UTC)

N-1 cuts for fairness when personal valuations match

In the simple case that all N participants have the same preference function, is there a simple algorithm that gives each 1/N of the total value, assuming that each participant is trying to maximize their own portion? I am seeking an algorithm where the right to cut a piece from the remaining cake is assigned in turn N-1 times according to some rule (which could in theory include allowing some participants to have more than one of these turns). Then the right to choose one of the resulting N pieces is given in turn to each participant by some rule.

Is described somewhere in Wikipedia article, to which we could link from this article? If not, is there any publication on this that we could reference and describe in this article? Personally, I can think of a simple approach but would much rather find a citation for a solution than get into a discussion of whether "my solution" is unacceptable original research or acceptable routine calculation. 64.132.59.226 (talk) 12:41, 29 March 2018 (UTC)

Nevermind. I found the algorithm in Last diminisher and added some language to explain how the algorithm simplifies in this degenerate case. 64.132.59.226 (talk) 20:37, 29 March 2018 (UTC)

Envy

"but to the two involved partners, the division is fair—no partner envies the other."

That is wrong. The chooser has always the chance to get more out of it, because he might have difference preferences then the cutter. The cutter never gets more then an equal share (for his preferences). So the chooser is the only one with a chance of getting more value out of it. So the cutter could envy that. I would. — Preceding unsigned comment added by 80.253.213.10 (talk) 09:20, 18 October 2021 (UTC)

It is more correct to say that the cutter would not envy the share of the chooser. That is, he would not want to exchange his part with the chooser's part.

It is true that the cutter may envy the role of the chooser in the procedure. This is a different kind of envy.

--Erel Segal (talk) 21:07, 18 October 2021 (UTC)