[EM] FWD: Borda Count by Paul Dumais

[Bart Ingles]

Blake Cretney wrote:
> 
> Bart Ingles wrote:
> 
> > Blake Cretney wrote:
> > >
> > > Bart Ingles wrote:
> > >
> > > > The following are examples of failures in the Borda Count voting
> > > > method.  The first example shows a failure mode common (in some form)
> to
> > > > most if not all popular election methods that use ranked ballots, and
> > > > the second shows a failure that appears to be peculiar to Borda.
> > > >
> > > > The examples show voters' suitability ratings of the candidates on a
> > > > scale of 0-100.  I am assuming that each voter has the right to give a
> > > > maximum score (100) to his/her first choice, and minimum score (0) to
> > > > his last choice, and that the voter has the right to place middle
> > > > candidates at any position along that scale.  I use average ratings to
> > > > score the overall suitability of a candidate.
> > > >
> > > > While voters' sincere ratings are probably not measurable, I believe it
> > > > is a mistake to pretend they do not exist.  Even though we may not be
> > > > able to use ratings directly in an actual election, we can set up
> > > > examples based on sets of voter ratings and see how various election
> > > > methods behave.
> > >
> > > Just because I don't choose to rely on ratings doesn't mean I pretend
> > > they don't exist.  However, I don't view the goal of the election to
> > > be to find the highest average rated candidate.  Instead, I see the
> > > goal as finding the most likely best candidate based on the ballots.
> > > From this perspective, average ratings would still make sense if you
> > > believe that a voter's rating is a good measure of the likelihood of
> > > accuracy.  That is, if the voter says that A is MUCH better than B, we
> > > would think that this increases the probability that A is in fact
> > > better than B.  I, however, view allowing people to self-rate the
> > > certainty of their opinions as misguided.  Often the strangest
> > > opinions are the most strongly held.  The same errors in reasoning
> > > that result in a faulty preference can also cause the strength of the
> > > preference to be exaggerated.
> >
> > 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.  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.


> 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.


> > The nice thing about thought experiments is that you can stipulate that
> > the voters' rating are correct based on their internal opinions -- in
> > other words I, as the hypothetical observer, am reading the voters'
> > minds and determining the proper ratings to assign to each candidate.
> > Nowhere do I suggest that the voters actually vote these ratings.  Put
> > more simply, I am merely saying in the examples, "if you have these
> > correct conditions, then here are the results."
> 
> I tend to use the phrase "correct" to describe a vote which is best
> for global interest as opposed to one representing self interest or
> confusion.  So, I mean something different when I talk about a correct
> vote than you do.  That's just a difference of definition.

Difference of usage, not definition.  I was using the term "correct
conditions" to mean "accurately reflecting the voter's views" and "able
to correctly predict how the subject will vote under various election
methods", not whether the voter's motivation was proper.

As far as global interest vs. self interest, I am all for supporting the
greater good.  I don't think any particular election method is better
than another at distinguishing between the two, however.


> > > 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.


> > 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?


> 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.