[EM] FWD: Borda Count by Paul Dumais

[Blake Cretney]

Bart Ingles wrote:
> > > I used Average Ratings as a means of showing overall support (as in
> > > strength times breadth), and not as a "gold standard" for election
> > > methods.  I had considered including Median Ratings as an additional
way
> > > of quantifying support, but didn't want to unnecessarily clutter the
> > > examples.  It wouldn't have made much difference in these examples
> > > anyway.
> > 
> > > Nobody is suggesting that the voters "self-rate the certainty of their
> > > opinions".  They are rating the suitability of the candidates to hold
> > > office.  If a voter's assessment that "candidate B is much worse than
A,
> > > but only slightly better than C" cannot be trusted, then neither can a
> > > ranking that shows B somewhere between A and C.
> > 
> > This is the result of a fundamental difference between the way you
> > and I are approaching the issue.  You seem to be approaching the
> > problem as one of
> > 
> > "Which candidate creates the greatest over-all satisfaction?"
> > 
> > where I usually ask
> > 
> > "Which candidate is most likely the best?"
> >
> > If you look at the issue from my perspective, the problem is that
> > people often will make wrong decisions, but are at least slightly more
> > likely to make right ones.  So, when a person says that
> > A>B
> > you can use this as evidence that A is in fact better than B.  Note
> > that the assumption here is that people are attempting to find the
> > best candidate from a global perspective, but may get the answer
> > wrong, due to self-interest or ignorance.  From this perspective, if
> > you give one person's
> > A>B
> > equal weight to ten persons'
> > B>A
> > this is only justified if you place ten times as much certainty on
> > the A>B.  Of course, since in Average Ratings this is caused by the
> > A>B person giving ten times the difference between A and B as the B>A
> > people, I give the interpretation that people are in effect
> > self-rating their certainty level.
> 
> I guess it depends what you mean by "certainty level".  A person might
> rate A as 100% suitable to hold a given office, B as 10% suitable, and C
> totally unsuitable, and still be absolutely certain that B is better
> than C.  

True, but then, what you want to know is not "how much is B preferred
to C," but "is B better than C".
I was trying to interpret the ratings in a way that would make them
relevant to this question.

> I don't see how you can improve accuracy by discarding that
> information.
> 
> On the other hand, I am not that caught up with Average Ratings.  Median
> Ratings would answer your objection, and still make my point.  Of
> course, I don't advocate either as election methods, but only use them
> as tools to quantify sincere-rated examples.

Average ratings matches well with our concepts of finding the
candidate with the most support and finding the candidate to maximize
[normalized] utility.  So, I understood why you would view it as a
standard, and I felt it was necessary to criticize it.

Median Ratings, however, is just another method.  Why should I care
if one method is closer to it than another?

> > The "satisfaction maximization" method by which you are interpreting
> > the results is as follows.  Each person states their satisfaction with
> > each potential result on a 0 to 100 scale.  From this point of view
> > the only incorrect vote is one that does not accurately describe the
> > voters perceived self-interest.  This perspective assumes people will
> > not vote altruistically.
> 
> Not at all.  A voter is just as likely to have the good of the community
> in mind when rating candidates as when ranking.  I suppose an outcome
> beneficial to the community would provide most voters some satisfaction,
> though, even if not based on self-interest.
> 
> Just to be clear, my scale wasn't based on personal satisfaction, but on
> the individual's assessment of suitability for the office, where 100 is
> completely adequate, and 0 is completely useless.

Consider the following situation.  Candidates A, B, and C are running
for office.  Their ratings, based purely on self-interest are
group  votes     A    B    C
I      60      100   90    0
II     40       90  100    0

A 96
B 94
C 0

So, the winner is A.  From the Average-Ratings point of view this is
also the candidate that provides the greatest average satisfaction.

Now, if the group I voters decide to vote based on community
interests instead of self-interest, they would use these average
ratings as their individual ratings, normalizing them of course.  So
we get

A 96 * 100/96=100
B 94 * 100/96=97.9 approx 98
C 0 * 100/96=0

So, if group I is voting with community interest the votes are

group  votes     A    B    C
I      60      100   98    0
II     40       90  100    0

A 96
B 98.8
C 0

So, B is the winner.  So, group I not only hurt themselves, but hurt
the community as a whole by their community interest.  I think it's
clear from this that Ratings assumes people vote for their
self-interest, or it won't work properly.

--snip--
> > > > In particular, if 10 people say that A is better than B, do you
> > > > really think that should be equaled by one person saying that B is
> > > > better than A, even if that person feels 10 times as strongly about
> > > > it?
> > >
> > > Again, the scales do not show "strength of feeling", but "assessment of
> > > fitness to hold office".  These are not open-ended scales, so extreme
> > > views would be clipped or compressed to fit the 0-100 scale.  The only
> > > way 91% of the voters would rank two candidates only ten points apart
> > > would be if there is at least one other candidate who is either much
> > > better or much worse than the first two.
> > 
> > If both candidates are reasonable then there will probably be lots
> > that are a lot worse.
> 
> That is why I am more interested in eliminating candidates that are much
> worse, than in worrying about which of two good candidates win.
> 

I think this statement refers to an earlier posting where you made
the claim that Approval keeps out bad candidates, while other methods,
if enough people use misguided strategy, can elect them.  I think it
is unfair, however, to give Approval examples that assume everyone
uses perfect strategy, and Borda examples that assume the opposite. 
Anyway, here is an example where bad strategy can cause problems in
Approval.

group  votes    A    B    C    D
I         24   100  95   95    0
II        24   95  100   95    0
III       24   95   95  100    0
IV        28   0    0     0  100

What should happen is that some of group I, II, III should approve of
multiple candidates, thereby sacrificing their favourite but
preventing D.  If no one does this, however, the result could be.
               A    B    C    D
I        24    X              
II       24         X         
III      24              X
IV       28                   X

D wins.

> > > So yes, if the large group of
> > > voters are more concerned with supporting or rejecting some third
> > > candidate, I have no problem with a smaller group of voters having more
> > > influence in deciding between the first two candidates.  In return, the
> > > smaller group gives up some power in deciding between the third
> > > candidate and at least one of the original two.
> > 
> > But is that the best bargain for society?  For example, you might
> > have ten fairly rational people giving similar ratings to two similar
> > candidates, keeping them both well away from the lunatics they are
> > rating the lowest.  The decision of these ten people could be
> > overturned by one person who makes the decision based on the national
> > origins of the two candidates, and feels so strongly about it he would
> > place them at opposite ends of the ballot.  Note that I am not
> > assuming strategy, just extremist thinking.
> 
> The real bargain is in eliminating the low-rated lunatics.  If you can't
> do that, does it really matter how you decide between two good
> candidates?

I think in realistic cases, ranked methods do this at least as well
as approval.

> 
> 
> > Obviously, one can always come up with examples where a method
> > behaves badly because of bad voters.  However, Average Ratings seems
> > to greatly exaggerate the influence of small numbers of people who
> > think in extreme terms and have single over-riding issues.  So, I
> > reject this method as a standard by which other methods may be judged.
> 
> Then use Medians.
> > 
> > >From a probabilistic point of view, each person is a potential source
> > of error.  By giving every pair-wise decision the same weight, the
> > ability of one person's error to affect the result is minimized.
> 
> Then use Medians.  You can eliminate errors caused by extreme
> individuals, without having to add the error of assuming all pairings
> are equal.

I assume that all pair-wise decisions are equally likely to be true
(independent of how much difference would be placed between them in
ratings).  But you yourself say that the ratings are not indicators of
certainty:

> I guess it depends what you mean by "certainty level".  A person might
> rate A as 100% suitable to hold a given office, B as 10% suitable, and C
> totally unsuitable, and still be absolutely certain that B is better
> than C.  

So, why should I treat them as such?  And why should I assume that
Medians is worthy of being a standard?

---
Blake Cretney
See the EM Resource:  http://www.fortunecity.com/meltingpot/harrow/124