Well, this system is somewhat optimised for practicality. A truly 'fair' system would allow people to submit blind bids, for how wide a slice they would like, with the smallest bid taking the slice. Eg:

   * Everybody writes down how much pizza they would like on a folded piece of paper.
     You put down 15 degrees, I put down 25 degrees, etc.  

   * The papers are opened and the person who bid the lowest gets their 
     requested slice

   * Repeat until all the pizza is gone.

Essentially you are running a blind auction to split up a limited resource. While being a fairer adaption of my original solution, it does turn out somewhat more unwieldy in practise :-)