I recently completed two weeks of reservist. As usual, my stint in camp provided fodder for lots of blog posts. This year, the training schedule was especially good. One of the problems with SAF is that there is a tendency for a lot of “wait to rush, rush to wait”. The Singaporean guys would know what I’m talking about.
Well, this year my training schedule was particularly well planned and implemented. There was little unnecessary rushing or waiting. Training for what we needed to know was well taught and carried out.
Besides me getting horribly sick ( that’s a story for another post ), this year was probably the best reservist I had out of the last five.
I managed to find time in the night to read Ian Stewart’s Math Hysteria. I first stumbled onto such kind of writings when I discovered Martin Gardner late in life, some time during my university days. It was such a waste that I didn’t encounter such mathematics-based literature much earlier. Writers like Ian and Martin impart quite substantial knowledge with amazing witty and funny stories, providing mathematical concepts a context in normal life.
Take chapter 12 “Dividing the Spoils”. It totally had relevance to my reservist. Let me explain.
One of the great pains of reservist is the whole bunch of signatures we need to get before we can out process ( i.e. be cleared to finally leave camp ). One of the things that need to be done is area cleaning. The platoons from the various companies would be allocated areas to clean based on the discretion of individual Company Sergeant Majors ( i.e CSMs ).
The thing is this. Everyone is always disgruntled about the area they have to clean. Everyone tends to think some other platoon is getting a better deal by having to clean an easier place. Cleaning the toilets is easier than cleaning the vehicle sheds. Cleaning the vehicle sheds is easier than cleaning the washing bay.
You get the drift.
Now, back to chapter 12. In this chapter, I learned about a class of algorithms called envy free protocols which deal with the concept of fair division.
Two siblings dividing the last piece of cake using divide and choose is a simple and practical example. The first sibling divides the cake into two pieces, and the second sibling chooses which piece to take. Since both siblings wish to maximize their share of the cake, the first sibling will divide the cake evenly in his estimation and the second sibling will take the one perceived as more desirable. Even if there is icing unevenly on the cake that the siblings want, the first sibling can divide the cake to compensate for the perceived benefit of the icing in his view making them even, and then the second sibling chooses the piece he prefers.
No one likes to be a patsy.
Such algorithms help us avoid that.