Ratings as a Standard

[Blake Cretney]

Bart Ingles wrote:

> Blake Cretney wrote:
> > 
> > Bart Ingles wrote:
> > 
> > > In an earlier post, Blake Cretney wrote:
> > >
> > > It occurs to me that extremist voting problems should be excluded from
> > > the question of rating-based standards, just as strategy considerations
> > > are.  An actual election method would need to deal with both, but the
> > > standards are only dealing with hypothetical situations.  We can then
> > > relate these standards to actual methods in two steps:
> > 
> > The purpose of a standard method, as we were using the term, was to
> > be able to judge when practical methods were arriving at the proper
> > conclusion, based on the sincere preferences of voters.  So, it made
> > no sense to criticize a method as a potential standard because of
> > strategy problems.
> > 
> > The plan to hypothesize away extremist voters is a different matter,
> > but I can still see some merit in it.  It may, however, be difficult
> > to define exactly what constitutes an extremist voter.
> > 
> > For example, imagine that one issue confronting voters is Proposal X.
> >  Most voters dislike Proposal X, but only as one of many issues.  A
> > smaller percentage of voters love proposal X with a zeal that causes
> > them to rate exclusively on this basis.  Under these circumstances,
> > support for proposal X would tend to help a candidate (in any method).
> >  However, this is particularly the case in methods based on ratings,
> > where the supporters will have an effect far above what their numbers
> > might suggest.  So, my question is, [1] are the Proposal X supporters the
> > kind of voters that you will hypothesize do not exist.  If not, [2] is
the
> > likely result using ratings a problem.  [3] Ratings would seem to suggest
> > that Proposal X is overwhelmingly likely to be right. Do you agree
> > with this?
> 
> [1] I was thinking more in terms of assuming all examples have
> candidates rated between 0 and 100, where 100 is fully qualified for the
> position, and 0 is lacking any particular qualifications.  I wouldn't
> necessarily exclude the X supporters in your example, but would make
> sure that their ratings were bounded reasonably.
> 
> [2] I don't think the problem is as bad here as with ranking in
> unfavorable ranked examples.  In the above case, the X advocates will

The ranked examples that precipitated this discussion occurred when a
majority of voters voted strategically, and the strategy back-fired. 
Since they involved strategy, they should not be considered for
determining which method makes the best standard as we are defining
it.  Do you have bad Condorcet or Path Voting examples where everyone
votes sincerely?

> win only if the multi-issue voters can't find a candidate with whom they
> agree on most issues, or if they are split so that the X voters can act
> as the tiebreaker.  

             A anti   B  pro    C  pro
90  I anti   100      90        0
10  II pro   0        100       100
Total        9000     9100      1000

Group I may agree totally with A (after all they rate A at 100), but
B still wins.  Is this what you want?  Are group II reasonably bounded
when their votes of B over A carry ten times the weight of A's A over
B votes?

> At the very least, you can still say that the larger
> the majority, the more ambivalent they can be and still cancel out a
> strident minority.

That's true, although not very reassuring.

> At worst, this kind of problem is merely the opposite of the problems
> you have when ignoring ratings completely.  You could avoid either
> extreme by using ratings, but by giving less weight to the ratings than
> Average Ratings would, or by limiting the rating value that can come
> from a single issue (say to 50 points or so).
> 
> [3] I don't believe that ratings (or rankings) necessarily mean that the
> voters are correct.  This question comes up later in this message.

I didn't say, "which side is correct?"  I said:

> > [3] Ratings would seem to suggest
> > that Proposal X is overwhelmingly likely to be right. Do you agree
> > with this?

"LIKELY to be right," not, "right."  I was talking about probability,
not certainty.

--snip--

> I would use raw ratings for comparing various real methods, but use
> whatever form of normalization is appropriate (if any) when applying a
> particular benchmark method.
> 
> If using Averages as a benchmark, raw ratings would not work for obvious
> reasons, but neither would linear normalization.  

We are in agreement on both counts.

--snip--

> > > Why wouldn't you want an accurate representation of the voters'
> > > thinking?
> > 
> > I'm not sure what you mean by this.  If I understand you correctly,
> > you are questioning me for advocating deliberately throwing away
> > information in choosing rankings over ratings.  However, to get the
> > most information possible about voters thinking, we would use
> > unbounded utility ratings, with each candidate rated from negative to
> > positive infinity.  If we could ensure sincere votes, this would
> > result in government by the most passionate, which is clearly not a
> > good idea.  Therefore, I think we can conclude that at least in some
> > cases, throwing away information can be a good thing.
> 
> And of course I am advocating clipped ratings :-)
> 
> But if ratings above 100 and below 0 are the product of extremist
> thinking or emotionalism, then we have good reason for excluding this
> information.  We could even go farther and say that no two candidates
> can be more than 50 points apart (or some other number), without having
> to discard ratings information entirely.

How are the 100 and 0 ratings defined?  This seems to imply that
absolute levels of support are defined.  How do you decide how much
someone has to like a candidate for it to be 100 support, or how much
dislike results in 0.  This decision could alter the outcome
prescribed by the standard.

> 
> Just to be clear, I'm not that hung up on Average Ratings per se.  I
> have used it because it's easy to understand and it takes both number of
> voters and rating values into account.  It gives as much weight to
> ratings as to number of voters, which may be viewed as an extreme (I
> can't imagine why I would want to give more weight to ratings). 
> Condorcet would be at the opposite extreme, not using ratings at all.

It seems that the reason you are not "hung up" on any particular
Average Ratings method as a standard is that they all have
demonstrable flaws.  And yet Condorcet is criticized for not being
enough like these methods.

If you would give a specific, defined standard then I could argue
whether it is better or worse than Condorcet.  Right now, you seem to
have a huge group of widely different possible standards.  It seems to
me that the purpose of this discussion is to come to some agreement
(or at least debate) a standard for judging the proper winner based on
sincere preferences.  Then we could decide which method will come the
closest to this method when votes are not necessarily sincere.  I
don't see how such a large and vaguely defined mass of potential
methods as you are proposing can be said to be more or less like any
other method.

--snip--
> 
> Interesting.  If you break the votes into separate decisions on each
> issue, then one wrong decision on the part of each of the A>B voters
> should have the same effect as an equal number of wrong decisions
> allocated among the B>A voters.  It might be easier for a small group to
> make a wrong decision than for the large, but they would have to make
> more wrong decisions to have the same impact, so it sort of balances
> out.

Except that
1) The small group may not be making more wrong decisions, they may
just be making one that they feel particularly strongly about.
2) The decisions an individual makes are not made independently from
each other.  A wrong decision is likely based on incorrect principles
that will lead to other wrong decisions.  

> 
> This assumes that the likelihood of a wrong decision is inversely
> proportional to the size of the group.  

Right.

> Offhand I would guess that this
> would be the case if the errors were "random".  Errors caused by
> extremism on the part of the voters might be more likely than average in
> a small group.  On the other hand, if the errors were not the fault of
> the voters, but rather the result of a political operative supplying bad
> information on one issue, then the large group could more easily be the
> cause of a wrong election outcome.

I still don't see why a large group would be easier to fool than a
small group.

--snip-- 
--cutting my example about Average ratings and altruism--
> 
> I don't know how else to respond to this, other than to say that I don't
> agree with your definition of altruistic voting.  The idea that in order
> to vote altrustically, a group should average their sincere preferences
> with the likely vote of the opposing side, makes no sense to me.

Since this example is about normalized ratings, and you don't appear
to be advocating this as a standard, I have lost interest in
explaining it.

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