My friends, I have a problem and I am asking you to help me solve it. The math department is moving into the South Wing of the Building from the North Wing. In this move each teacher is obviously going to get a new classroom. Each classroom varies in its desirability due to size, temperature, windows, proximity to bathrooms, student center and math office, etc. As math chair, it is my job to devise a method of assigning classrooms to each teacher. This method must be viewed as fair by all teacher involved and they must feel that they have had a role in the outcome.
As a class, we have just completed exhaustive investigations into estate division. I felt this work could help us in this process. In using this method, though, the questions arise; a) how does one place value on a classroom and b) what do we do if a teacher is to pay the difference of her fair share into the estate (obviously a teacher is not expected to pay money in order to teach in a classroom). If the method of estate division does not seem plausible in this situation (although I feel, with some manipulation it could) come up with a method of your own. This method, though, must have the same characteristics of Estate Division. For example, in Estate Division, if one sibling did not get an article of the estate they wanted, they were compensated with money. How do we compensate when a teacher does not get the room they wanted? (Other valuables in a math department are free hours, choice of courses to teach next year, classroom materials like cabinets tables etc., as well as office space.)
Your methods will be presented and defended before the math department and the next department meeting. The validity of your method will be rated by the teachers and your grade will result from the ratings. If your method is chosen as the one the department implements, then extra credit will be given and the method will be described in the upcoming newsletter.
Good Luck