[EM] Professorial Office Picking

[Michael Rouse]

Steven E. Landsburg (author of The Armchair Economist), had an 
interesting problem here: 
http://www.thebigquestions.com/2010/01/21/office-politics/ (in reference 
to an original question of the New York Times ethics column here: 
http://www.nytimes.com/2010/01/03/magazine/03FOB-Ethicist-t.html)

Basically, you have a bunch of professors of different seniority wanting 
a bunch of rooms of different desirability. The original article at the 
Times suggested a lottery. Steven Landsburg suggested a market, where 
professors bid what they wanted for a particular room.

Here's my comment:

******

Why not use a rank order ballot grid? Have room locations across the top 
(x-axis) and people's names down the left (y-axis). Each professor could 
rank the rooms in order of their own preference, and rank the potential 
occupant in each room in order of preference, all on one handy grid. 
People could then trade their votes (or something more tangible for 
votes) in order to get the room they want. On a certain date, finalize 
the votes, determine the allocation of rooms to maximize overall 
satisfaction, and start moving in.


It might be difficult to find the peak utility order (probably NP-hard), 
but it should be manageable --- you probably don't have to worry about 
hundreds of professors, and that's what computers are for. Plus, if a 
professor leaves, you might be able to determine more easily who gets 
his or her office.


As an interesting extension, it may be possible to come up with a 
similar way to match students, professors, periods, and classes, though 
that would be even more complex. It would be kind of fun to watch a 
course election, though, with groups lobbying for particular lectures at 
particular times, or banding together to get the professor they want.


******

I was wondering if those on this list had other suggestions. I make no 
claim as to the suitability of my suggestion,  I just thought it was an 
interesting problem.

Michael Rouse
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