How to split an inheritance

If I had to put an example of something useful for the everyday life that I learned at the postgraduate courses I took at the University of Alicante I would possibly mention a lecture on intelligent agents by Faraon Llorens. And I say this, not because Faraon was my boss at the time I took the course and the idea of going back to Alicante seems always present at the back of my mind, but because I really mean it.

I don't know if Faraon, as I do, comes from a family divided because of the way an inheritance was split, or just because negotiation algorithms naturally arise in the context of intelligent agents. Either way, for some time negotiation protocols have been the object of interest for this guy, that no need to say he is a natural at negotiation himself.

A negotiation protocol is set of of formal rules that can be programmed on a computer, for several agents to decide how to share a resource. The case of wanting to split a resource in equal parts does not usually have an interest in intelligent agents (not that I am aware) but it has received a bit of attention in maths. And no need to say that this negotiation protocol is especially useful when instead of intelligent agents (computer programs), it is humans who have to share.

The most simple protocol for dividing a resource (let us say a cake) between two people is composed of two simple steps:

- Split step: one of players splits in two parts that he considers equal.

- Choice step: The other picks up a part.

If the partition done by the first person is not fair, the second person has the option to resolve the dispute by choosing the piece that he considers bigger. On the other hand, the person who splits has no reason to open any dispute procedure if he does not like the outcome of the split procedure. After all, the first player had the freedom of splitting in equal halves, therefore by complaining he would admit he did not make a good job, not having anyone to blame but himself.

Easy, right? If you want to know more about negotiation protocols you could enrol on the course Faraon Llorens teaches, or alternatively read the book “How to cut a cake”, by Ian Stewart.

But now, can the concept be used for dividing an inheritance between two brothers? When I had to advise a friend of mine how to write his last will for dividing his inheritance in equal shares among his two siblings, I advised him to do exactly as just described. However, when I slept over the idea a little bit (the same night) I realised that the described method is still not enough for a real world legal document.

There is the possibility that the person in charge of splitting the inheritance never does it, blocking the resolution of a last will. Similarly, the person who chooses can also block the resolution by not choosing the half he wants.

It may sound unlikely, but this kind of blocking behaviour does happen in the real world, where people not only are lazy, but they can also use their blocking power as a punishment or as a pressure action to foster their position in some other parallel negotiation.

The solution for avoiding any blockage is also simple:

- During the split step: One the persons has the option to split during a period of “n” days. Should the split happen then we pass to the next step (choice). However, should the split not happen during those “n” days, then the second person has the right to propose a split. To be more general, every “n” days that there is no proposed partition, the option of proposing a partition is passed to the other person, who could alternate in time every “n” days as long as both of them wish.

- Choice step: the person who did not partition chooses. If the chooser delays the step longer than “n” days, the one who split gets the option of choosing. Again, to be more general, every “n” days that a choice has not been done yet, the choice turn passes to the other person.

The described variant of the protocol ensures a resolution within “n” days, as long as one of the persons wants to achieve a resolution. This formulation is perfectly suitable for dividing an inheritance.