I like to read various Stack Exchange websites, and one of them has a wonderful discussion of how you might divide a sandwich between three people fairly. Most of us are familiar with the two-person version: one person cuts and the other person gets the first choice. But what about if there are three people, or more?
This discussion on the Math Stack Exchange site addresses that issue. I highly recommend you read it.
Two things: 1) the two-person version I mentioned is logically fair but not fair in practice: make sure to find the comment that addresses that. And 2) there are stochastic and deterministic solutions, and most of them address problem that are harder than “fair” division: that no one involved in the process feel “deceived”, that everyone in the process feel that their piece is the best possible piece (not envy other users), that no group can conspire to get better pieces, etc. Of course, there’s geek humor in abundance, too.