As we discussed throughout the semester, there are multiple procedures we can apply to help streamline and even automate such tasks. While there are numerous approaches to take, we will limit our review to: Divide and Choose, Fink’s Lone Chooser, and Knaster’s Sealed Bid procedures.
For this project we created a game that tasks players with dividing a set of playing cards with the intention of forming a poker hand, in conjunction with two cards which only they know about. We decided to make this game because it creates a situation where the goods are discrete, subjectively valued, and non-independently valued. The game is also immediately understandable to anyone with experience playing card games, and involves very little abstraction on our part. With this game, and with a simple-but-effective AI, we simulated thousands of Adjusted Winner divisions and evaluated whether a fair division reliably occurred.
Note: the app is currently available at http://stromquistcake.appspot.com/
For the plots that show proportionality, there appear to be 5 bidders, so 20% would be the nominal proportional value for each, correct? Another way to read the data is that you are showing the perecentage of a proportional share. Great job!
For your results, how is it possible that T (the denominator in U/T) is anything but 1000?
You say your approach is not envy-free, but where do you measure envy?
For the second project, you dismissed cake-cutting algorithms without trying them, implemented a bang-per-buck approach, but did not compare it with anything else. The web page code for this part has something to do with pizza, quiche, etc., but is not documented in your report.
While I believe there may be good work here, you did not follow the specification for the project which makes it difficult for me to evaluate what you did.
I will read the theorems and proofs over break and revise this write-up then.
The plots on page 6 are for the performance of your algorithm. By what method did you fit your data to the quadratic shown there?
The last player gets so much more bandwidth than the others, so this could be made fair by randomizing who goes last, or you could redistribute the last player's extra bandwidth to the others perhaps?
I didn't see that you measured envy but if you have any data on that and want to add it, I can repost your report.