[EM] Professorial Office Picking

[Juho]

On Jan 25, 2010, at 11:07 PM, Abd ul-Rahman Lomax wrote:

> 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"!

I might vote A=100 B=100 C=100 D=0 E=0 F=0 G=0 if I believe that  
otherwise I might end up in room D or E. If others give more evenly  
spread ratings my strategy could be very efficient (and if they  
exaggerate my sincere vote might be too weak against their opinions).

>
>> 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.

(I already gave up the sincere ratings (4,3,3,3,0) when I used the  
Borda utilities. (Equal ratings in Borda style could be counted as  
4,3,3,3,2 or 4,2,2,2,0.))

(If rooms B, C and D are equal to the voter then giving B the highest  
points (and getting room B instead of C or D) is not a problem. In  
some cases the voter might lose all of those rooms when voting B>C>D,  
or might win B thanks to this, but maybe this is just minor random  
noise.)

>
>> 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?

As I said, no problem to allow equal voting if it causes no extra  
problems. Simple voting is also a nice property and makes voting  
easier to the voters. Not having equal rankings is not just forcing  
voters to something they don't want.

>
>> 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.

Sincere ratings would give noiseless utilities, but I excluded them  
for other reasons.

>
>> 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.

Ok, that's one way to do it. If I interpreted you right you didn't  
claim that this type of iterative methods would be more accurate or  
more efficient than the "exact target definition + approximate  
algorithm to find it" approach that I proposed.

If you want to include more choices and parameters to the equation  
than what the simple Borda ratings offer then I refer to the other  
method that I proposed.
 > 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))).

Juho