# [EM] Professorial Office Picking

Abd ul-Rahman Lomax abd at lomaxdesign.com
Mon Jan 25 13:07:39 PST 2010

```At 03:13 PM 1/25/2010, Juho wrote:
>>Sure. But equal ranking must be allowed, otherwise noise is
>>introduced. Borda with equal ranking (and therefore empty ranks,
>>otherwise equal ranked votes are reduced in strength) is Range. Why
>>not just use Range, allowing greater precision. One could use a
>>Range method with N*R resolution, where the "Borda" version has N
>>equal to 1.
>
>Range style ratings would give more accurate utilities but I used
>Borda style to get rid of strategies.

And I pointed out that "strategies" are not to be "gotten rid of"
because they indicate real preference strength, much more than they
distort it. Why would you rate your favorite 100% and everything else
0%. It must be really important to you, in order for you to
absolutely wipe yourself out of participating in any other "pairwise contests"!

>  Borda style utilities will
>distort the true utilities somewhat but the end result may still be
>quite fair.

Sure. I either suggested borda ranking and analysis or thought of it
before proposing range, I forget which. Close enough, perhaps. It
certainly is simple to vote! Unless you have a block of rooms that
are equally good for you, in which case ranking is actually harder if
equal ranking isn't allowed.

>  I didn't include equal rankings since that would not make
>any big change in the level of distortion.

It certainly can make a big change. It can strongly overemphasize
some preference strengths and underemphasize others. Suppose that
there are five rooms to be allocated. A>B>C>D>E provides equal voting
power in each adjacent pair. But suppose that the real situation is
A>B=C=D>E. This is fine as to A and E, but lousy as to B and D, and,
further, suppose that in Range, the utilities are, respectively,
4,3,3,3,0. The vote in the D:E pair is seriously undervalued. If it
comes down to a choice between D and E for a room, the voter has
indicated weak preference with a pure Borda ballot when, in fact, the
preference is strong, D would be almost as acceptable as A.

>  Forcing the voters to
>decide whether A>B or B>A is correct instead of allowing them to vote
>A=B is quite ok.

Bad basic concept, too common among voting systems students. Forcing
voters is never a good idea (or so rarely that it should immediately
raise suspicion)! And in this case, what is the problem with allowing
voters who have no preference between A and B to rate or rank them equally?

>  Picking a random order doesn't distort the outcome
>too much even if the voter could not make up his/her mind on which one
>of the two rooms is better.

Robson Rotation introduces some element of fairness here, perhaps,
but this is an election with a quite small number of voters. There
are much simpler solutions that could be even fairer, but a
single-ballot deterministic solution is likely to be suboptimal, or,
alternatively, so complex to vote that nobody would like it.

>  The method is thus already noisy as it is
>and therefore equal rankings might not add very much.

Eh? A high-res range ballot would not be "noisy." What's often
missing in these analyses is that "exaggeration" in a range ballot
conveys useful information, not noise.

>  If equal
>rankings will not add any complexity to the method they are ok though.
>(DIfferent ways to count the points in case of equal rankings would
>have different impact on the method.)

Borda with equal ranking (and, then, correspondingly empty ranks) is
trivial to vote and count. It is, in fact, Range voting. Obviously,
the naive Borda response to equal ranking (start with the bottom rank
and give it 0, then give each increasing rank one more point) is not usable.

Rather, a Borda ballot with equal ranking would be a ballot with as
many ranks as choices, and voters would then mark the rank for each
choice. Thus overvoting (equal ranking) necessarily results in empty ranks.

>[...]  Do you think there are some "iterative methods" that
>would achieve more accurate results (or would be necessary for
>efficiency or other reasons)?

Sure. If the preference information is collected, analysts could
divide the rooms into blocks of professors seeking them, and,
possibly, blocks of rooms that are equal for a set of professors,
simplifying the problem. Setting aside issues of seniority or other
preference for particular professors, assuming they are peers, then,
the block of professors involved could decide to use, say, random
choice to provide a choice sequence, or some other method. What would
be done, I'd suggest, is that a final choice would be made by each
professor in sequence, the professor chosen by some algorithm,
including chance as a possibility when there is no clear assignment
from the preference information.

So at each iteration, the choice is of one professor, who then
chooses the room from the set indicated by the preference ballots,
reducing the set of professors and rooms by one with each iteration.
Between iterations, any two professors, or set of professors, may
swap rooms before the next choice is made. After the choices are all
made, voluntary swaps remain as a possibility, continuously.

Where professors have equally ranked rooms, proposed assignments
could be made en masse, with individual assignments then occuring by
consent within this block.

Specifying an exact algorithm in advance could be so much more work
than actually doing iterative assignment this way that it would not
be worth it.

However, I suggested an Asset election to create a representative
body that could efficiently "negotiate" the whole process on behalf
of the professorial community, and that includes determining what
specific methods are to be used. An Asset election is very simple:
each eligible member votes for one person to represent them, and that
can be oneself, but it gets more efficient if one chooses someone
else. Choose the person you most trust to do a decent job at the
task, which includes choosing who is most trusted to do a decent
job..... This creates a reduced subset of the original electorate,
which then cooperates to form "seats" on the committee, with 3 seats,
the reduced set, I now call electors, can elect a seat whenever they
can agree to assign N/3 votes to it.

If it can't elect at least two seats, quickly, I'd say that the
community needs some professional assistance, it's divided and contentious....

The missing seat can be filled if the electors can all agree, in
which case representation is complete. But short of complete
representation, two seats can adequately make decisions, and can
consult the remaining electors, at their discretion. Even with the
remaining seat filled, it still requires two votes to make a decision!

The goal of doing this whole process is to produce a result which is
widely perceived as fair, so the committee, I'm sure, will be
motivated to ensure that all concerns are heard, but control over the
process is in their hands for efficiency, so that it isn't discussed
forever, which is, itself, quite undesirable.

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