Fair division

How do you make progress when you need to divide something up between two people but they can’t agree on what is a fair split.

The classic example is how to fairly cut a cake.

The answer is for one person to cut the cake and the other person to choose which piece they have. The first person has an incentive to cut the cake as accurately as possible into two equal pieces. If they don’t cut the cake equally then the other person will take the large piece.

This idea has many applications in real life situations such as dividing assets between a divorcing couple. It can also be used to divide up things that people don’t want but have to have, for example household chores can be divided up by one person and the other chooses which they want to do.

Things can get more difficult with an indivisible item, but this can be simplified by using cash to balance up the split. For example, if two children have inherited a house then they need to divide this between them. They could sell the house and split the money but one, or both of them, may prefer to keep the house. In this case one could propose a split of say, the house less $200,000 for one person and $200,000 for the other person (the amount would depend on how the person valued the house). The other person would then choose whether they wanted to have the house and make a $200,000 payment to their sibling, or whether they would rather just have the $200,000.

Today’s takeaway: The tactic of divide and choose can be used to resolve many negotiation problems.

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