[EM] Professorial Office Picking

[Abd ul-Rahman Lomax]

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.