Thanks for the birthday wishes, guys.
Oh dear, I suppose this goes right on top of the other birthday posts. You should really talk here more.
I was going to say...I was thinking to myself "I already wished RY a happy birthday? Wow my memory is really going down the tank... But then I realized that was my post from last year.
...Yeah... I'm not exactly the most talkative of individuals online. You guys should see my FA journals
; I've had an FA for almost 6 years, but have made only two journals (one of which is a repost of someone else's journal).
...Anyway, cue random staff thread content!
In honor of Pi Day, I'll briefly gloss over the geeky overanalysis of a mundane conundrum that occasionally involves pie. When one wishes to divide a resource (particularly a relatively homogeneous resource such as pie) between two entities who each seek to maximize their own benefit, one way to accomplish as much is to have one person perform the division while the other chooses between the two divided parts. The one who chooses is satisfied, since they can choose what they consider to be the better slice. The one who divides the resource is also satisfied, since they can divide the two resources such that neither has more value to them than the other. This process is quite simple, and in fact is frequently taught to children to handle this very problem. Wikipedia refers to it as divide and choose
, or alternatively, the pie rule
What if there are three
people to share between, though? Can the problem be addressed in the same way? It's easy to imagine having one person cut while the other two then each choose a piece, leaving the remaining piece to the one performed the division. However, this solution lends itself to a risk of unfairness for whoever makes the second selection, especially if they're subjected to a conspiracy by the other two.
Let's say that Alice, Bob and I agree to divide a pie by the previously described variant of divide and choose, with Alice making the division and Bob making the first selection. Alice breaks off two tiny pieces of crust, leaving the vast majority of the pie as the third piece. Bob then takes most of the pie. Lacking a better available option, I take one of the two pieces of crust, and Alice takes the other. This scenario allows Alice to give Bob as favorable of a result as she wants, and after the pie is split, Alice and Bob can then meet independently and split the pie between the two of them without me being present. They'd each get half the pie (since I wouldn't be present for that division, and divide and choose does work fairly when used for only two people), and I'd be left with a small piece of crust.
I think it goes without saying that I wouldn't willingly agree to having the second choice in an arrangement like this. Even if I trusted Alice and Bob to not conspire against me, I'd be upset if Bob took the largest piece, leaving me with only the second largest.
Is there another way to perform this division that is more fair for all involved parties? It's a question I've asked myself for a while in the recent past. It turns out there is in fact a way to do so, as I came to realize by stumbling across a Wikipedia page which described the process. It's an interesting intellectual exercise to try and work out for yourself (a hint: it may be necessary to divide the pie into more than three pieces), but if you would rather not do so, you can read into the solution to this problem here