Activities for Math Thought

The activities are an opportunity for you to further explore the various aspects of the subjects we're covering, with more flexibility than the usual problem sets offer. I will be suggesting activities throughout the semester. You do not have to do all of them -- pick and choose among those that sound interesting to you, or come up with your own ideas!

I will be adding to this page as I have ideas. Feel free to suggest any ideas to me!

Activity 1
Model a real-life situation with a 2x2 (or 2x3, or 3x3) ordinal game. Analyze the game, with or without the theory of moves as seems appropriate to the situation. Look for dominant strategies, Nash or non-myopic equilibria. Finally, discuss how well your model matches reality.
Due 3/7.

Activity 2
Design a problem for an exam, and provide the solution.
Due 3/30 for Exam 2 problems, 4/27 for Exam 3 problems, 5/2 for Final problems

Activity 3
Do a theory of moves analysis on a 2x2 or 3x3 game. Make up the game that represents the initial situation (you can either just make up the table or for additional points, start with a ``story'', like in the first activity). Do not use the Prisoner's Dilemma or Chicken. Then do a complete analysis of where the theory of moves takes you -- for each starting position, is it a non-myopic equilibrium? Does either player have a dominant strategy in their initial choice?
Due 3/30

Activity 4
Attend one of the science talks this term (Puzzles in Science, for instance) and write a discussion/reaction.

Activity 5
Investigate the voting method used in Cambridge MA, and write a brief description of how the method works,giving your own examples. Consult MIT's interactive website .

Activity 6
Research what experts believe about actual fairness and relevance of various voting methods. One option: does anybody recommend we should replace our current method of electing the president with some other method -- Borda for instance? Why? Another option: look into methods we haven't learned about. The method used in Cambridge is referred to above; there is also approval voting, Charles Dodgson (Lewis Carroll) devised a method, and there are many others. Activity 7
Find an example of a real-life situation (other than those mentioned in the book) where a voting method other than plurality is used. Describe it in detail, and either give an example of the results of a specific election/vote or make one up to demonstrate how it works (or both).

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@wheatonma.edu

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