Michael Rouse wrote:
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.
(...)
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.
Sounds a bit like matrix voting, where there are n positions and every
voter submits n ballots (one for each position), the point being to find
the assignment of candidates to positions to optimize some criterion.
That criterion could be utility (Range-like) or "minimize thwarted
minorities" (Condorcetian). The constraints are that no candidate can
occupy more than one position, and no position can be empty (so
obviously there are more candidates than positions).
One may also ask whether the matrix voting should be proportional or
majoritarian. In the latter case, which is probably easier to figure
out, if a majority conspired to vote the exact same set of ballots,
these would dictate all n positions, whereas if proportional, it would
only affect n * (size of majority / number of voters).
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