Here's one simple approach.
- all voters rank all the rooms
- use Borda like personal utility values => last room = 0 points, one
but last = 1 point etc. (also other than this kind of linear scale
could be used)
- find the room allocation that gives the highest sum of utilities
- if there is a tie one can use seniority to break it
- the utility values of each voters are multiplied by some
seniority factor and then summed up again
- the factors could be quite small if one just wants to break the
ties (e.g. 1.0001, 1.0002)
This tie breaking approach is intended to work so that if there is for
example some room that all consider to be the best then that room
would be given to the most senior voter.
Any chances to work?
Juho
P.S. There could be also preferences like "I want a room next to my
closest colleagues". If one wants to support also such preferences one
could allow the voters to rank all the possible room allocation
scenarios and then use some Condorcet method to pick the best
allocation. Since the number of different room allocations may often
be too large for manual ranking one would need some mechanism to
derive the rankings from some simpler set of parameters. One could
e.g. use a fixed questionnaire with a list of questions that the
voters could answer and give different weights. These answers could
then be used to rate each room allocation scenario. In theory one
could also allow voters to give their own algorithm (this is however
probably too complex though for most use cases) that takes a room
allocation scenario as input and rates it (or gives directly a ranking
of all the allocations (or why not even pairwise preferences (that
could lead to personal preference cycles))).
On Jan 23, 2010, at 5:37 PM, 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.
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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