[EM] FWD: Borda Count by Paul Dumais

[Bart Ingles]

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.

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."

> 
> 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.  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.

Bart



> 
> Another related point is that Ratings is often advocated as an
> attempt to maximize utility.  Actually, this is an error because
> people will be affected by the outcome of an election by different
> amounts.  By having each persons lowest candidate rated 0 and highest
> 100, we ensure that true utility is not being measured.  Of course,
> Path Voting isn't based on maximizing utility either.
> 
> > In the first example, 45% of the voters prefer A over all other
> > candidates.  15% prefer B, and 40% prefer C.  The full ratings are as
> > follows:
> >
> >
> > EXAMPLE 1:  Voters' private suitability ratings
> >
> >       Rating:
> >       100    80    60    40    20    0
> >       ----------------------------------
> > 45     A                          B  C
> > 15     B  C                          A
> > 40     C                          B  A
> > ---
> > 100 votes total
> >
> >
> > Average sincere ratings:
> >
> > Candidate A = (45% x 100)              = 45.0 points
> > Candidate B = (15% x 100) + (85% x 10) = 23.5 points
> > Candidate C = (15% x 90) + (40% x 100) = 53.5 points
> >
> >
> > Borda Count:
> >
> > Candidate A = 90 points
> > Candidate B = 115 points
> > Candidate C = 95 points
> >
> >
> > Borda picks B as the winner based on rankings, although B has only half
> > the rating of the other two candidates.
> 
> This first example assumes that highest average rating is the best
> possible goal.  Since I disagree with this, I am unconcerned with the
> result of this example (which also apply to Condorcet and PV, if
> anyone is wondering why I'm defending Borda).
>