[EM] Professorial Office Picking

[Terry Bouricius]

Would we agree that voting methods do best when voters give their sincere rankings to avoid GIGO distortion? Since all voting methods can be subject to strategic voting strategies with incomplete, exaggerated or insincere ballot information, might it not be a good idea to select two or more voting methods with different (ideally contrary) inherent strategy options, and then select the vote tabulation algorithm by lot AFTER the ballots are cast? This might give all voters an incentive to give sincere ballot information, since that would be the safest individual strategy. 

Alternatively, the threat of assigning all offices by lot might be used as a stick to prompt all voters to come to a unanimous agreement using an iterative or "bidding" process.

Terry Bouricius
  ----- Original Message ----- 
  From: Juho 
  To: election-methods Mailing List 
  Sent: Monday, January 25, 2010 5:59 AM
  Subject: Re: [EM] Professorial Office Picking


  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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