[EM] Professorial Office Picking

[Raph Frank]

Something like a CTT auction could be used here.

Each bidder submits a sealed ballot containing the dollar value of each office.

For all possible permutations work out the sum of all the bids.

Assign the offices to the arrangement that gives the highest sum.

For each bidder,
- determine the office configuration if that bidder was excluded
- If the result changes, the bidder must pay the difference between
the 2 results, with the bidder excluded

The process is only carried out once every year.

In most cases, no payment would be required.

Honest bidding is the best policy.

Also, it is the difference in bids that matters.  A bid of

A: $100
B: $50
C: $0

is equivalent to

A: $50
B: 0
C: -$50

You could add some additional rules like

The 90th percentile difference between max and min is set as the
limit.  If a bid has a greater than that difference between max and
min, it is rescaled.  This makes collusion more difficult.

1 office (X) is removed from the poll.  A random bidder is selected
(opt-outs are probably allowed) and is given any payments and also
office X.  If there are many bidders, this reduces negative sum nature
of the cash part of the problem.  X would likely be set as a
reasonably good office, but not the best.