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.
