What’s bothering me is, mathematically that is the answer, but practically the apple is a non uniform shape so you cant really determine where a third of the apple truly is and it has seeds in the middle meaning two of the kieces will have seeds one the one getting the two cut off pieces won’t so its not truly shared equally.
“Equal” has a slightly different meaning in fair division problems. It doesn’t mean “the exact same quantity of matter”, so not being able to judge exactly 1/3 of the apple doesn’t super matter (though your seed problem can be solved by cutting diagonally through the apples rather than along one side), but rather, that each person gets a portion they value at least as much as the others; maybe some people are willing to take a smaller piece if it means they have no seeds, maybe some people are going to peel their piece so they care more about having the largest internal volume, maybe some people plan to plant the seeds and so they actually value them, maybe some people only care about having the biggest piece.
In practice, for three people this can take as few as 2 cuts or as many as 6; since there’s two apples and we can do 2 cuts with one stroke here, there is a fair division solution, but it only works if things go perfectly:
The first person cuts the apples into 3 shares they think are of equal value (perhaps they hate apple cores, so they cut one side off both as above)
The second person points out which share(s) they think are the best
The third person takes the share they consider to be most valuable
The second person takes the share they consider to be most valuable
The first person takes the remaining share, which, since they cut, they must consider equal to the other two.
If the second person doesn’t think at least two shares are of equal value, the problem becomes impossible to resolve without more knifeplay.
What’s bothering me is, mathematically that is the answer, but practically the apple is a non uniform shape so you cant really determine where a third of the apple truly is and it has seeds in the middle meaning two of the kieces will have seeds one the one getting the two cut off pieces won’t so its not truly shared equally.
“Equal” has a slightly different meaning in fair division problems. It doesn’t mean “the exact same quantity of matter”, so not being able to judge exactly 1/3 of the apple doesn’t super matter (though your seed problem can be solved by cutting diagonally through the apples rather than along one side), but rather, that each person gets a portion they value at least as much as the others; maybe some people are willing to take a smaller piece if it means they have no seeds, maybe some people are going to peel their piece so they care more about having the largest internal volume, maybe some people plan to plant the seeds and so they actually value them, maybe some people only care about having the biggest piece.
In practice, for three people this can take as few as 2 cuts or as many as 6; since there’s two apples and we can do 2 cuts with one stroke here, there is a fair division solution, but it only works if things go perfectly:
If the second person doesn’t think at least two shares are of equal value, the problem becomes impossible to resolve without more knifeplay.
If anyone is interested, there’s this video by Up and Atom that neatly shows the complexity.