You cut, I choose?

As siblings separated by only two years, my brother and I never wasted any chance to express our, shall I say, differences in opinions ;)  A context that we were very particular about was when mother doled out snacks.  We would carefully monitor each other's share, and complain if we felt that it was not equal.  Of course, as we got older, we also teamed up to sniff out where exactly mother had hidden away some awesomely tasty snacks and we were partners in crime ;)

We now live in a world of plenty. And, at the same time, a number of kids do not have siblings either.  Which means there is nobody to fight with, nor is there a need to fight.

But then there are divorces.  Some are bitterly contested.  Recall Harry's advice to his friends on how they should plan for the divorce right from their early days of being married so that the bitterness on who gets what and how much can be easily settled?

How to divvy things up is not a new question.  It is as old as humanity itself.  We kids in Hindu households in the old country grew up with epics that were all about who gets what.  The Pandavas and the Kauravas fought intensely bloody--I mean bloody--battles as a result.  A war that Krishna said was Arjuna's duty to fight in the Bhagvad Gita!

While we can't bring about world peace, math does offer some interesting ways in which interpersonal property splits can be handled.  Well, not math by itself, as this essay points out. 

Perhaps the oldest fair division method on the books—one which has been used by children from time immemorial—is the “I cut, you choose” method for dividing up, say, a cake between two people. One person cuts the cake into two pieces, and the other person gets to choose which piece to take.

Such a system, or any system, assumes that the participants play by the rules.  Imagine tRump in something like this.  That mafia don will simply walk away with it all, and then turn around and accuse you of eating the cake that he stole from you!

Thankfully, other than 63 million, we are not all such horrible humans beings.  We might fight, like how my brother and I did, but we try to fight by the rules and try to be fair.  But, even when we try, methods like "I cut, you choose" don't always end up being fair and equitable.

“Mathematics sets limits on what is achievable ... Then the question is, if you can’t get everything, what properties do you want to give up on?”