It's Complicated

Summer must be a time for divorce.

A few friends of mine have their problems with marriage resolved by way of a divorce recently.  The common issue - a third party.  The complication of having a third party is always under-estimated. Consider this: two cake lovers wish to share a cake so that each is satisfied that they have a fair share.  How to divide the cake between the two?  It's not that hard when there are only two cake lovers involved - A cuts, B chooses.  The problem gets tricky when a third cake lover is brought into the picture.  How to divide the cake among the three so that each is satisfied that they have a fair share?  I'll give you a moment to deliberate on it.
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Don't get frustrated if you can't think of an answer.  The question, posted hundreds of years ago, was left unresolved until 1944 when a group of Polish mathematicians came up with a somewhat right solution.  A tripartite situation is more tricky that one can imagine.  Anyone who thinks that he (seems that it's always he) can resolve a tripartite marriage is either completely stupid or hopelessly arrogant.

Ironically, if one can divide a cake fairly among three persons, he can divide it among four, five, six or more (see How to Cut a Cake if you are interested).