[EM] Professorial Office Picking

[Warren Smith]

The optimum method ASSUMING honest voting is each professor provides
his utility for each office (in some common units like dollars) and
the max-utility permutation is chosen.  If N professors N offices this
is NxN matrix
of utilities as input.

And no, this is not NP-hard, it is polynomial time, in fact it is the
"maximum weighted bipartite matching problem" also called the
"assignment problem" and efficiently soluble by e.g, the "Hungarian
method."

However...   in practice we could not rely on honest voting nor on
assessment of utilities in common units.   If the "utilities" were, in
fact, dollar values which actually had to be paid by the professors
out of their salary or something, then that'd force a certain amount
of honesty upon them (since they'd have to pay, they could not submit
a bid for a gazillion trillion dollars) and the Hungarian algorithm
would also garner the max money
for the university, both of which would be good.   Voting would
however be pretty painful, need to price every single office.


-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html