[EM] Professorial Office Picking

[Juho]

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
> ----
> Election-Methods mailing list - see http://electorama.com/em for  
> list info

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