[EM] Ratings as a standard

[Blake Cretney]

Bart Ingles wrote:

> [BC]
> > I assume that voters have a slightly greater probability of backing
> > correct propositions than incorrect ones.  It follows that B is most
> > likely better than A because more voters said this than said the
> > opposite, and there are no contradictory majority decisions.
> 
> [BI]
> I take it that you also assume that this "slightly greater probability"
> is equal regardless of the degree of preference?  If not, then your
> conclusion does not follow.  

There's a subtle point here.  If I decide not to use degree of
preference, then my argument follows.  In the same way, I don't really
believe that every voter is equally likely to make good decisions, but
if I decide to use a neutral method, I can still conclude that a given
proposition is more probably true, based on their vote.  If I used
additional information, provided by who voted, or how strongly they
felt, I might be more confident in my result.  However, this doesn't
mean I can't use valid probabilistic arguments ignoring this
information.

So, I'm not really arguing that the slightly greater probability is
equal regardless of degree of preference, qualifications of voter,
alcohol blood level, or time of the year.  I'm just not using this
information.  So, the resulting decision may not be the best possible,
but it may be the best result possible using specific valid
information.

Of course, you would argue that in degree of preference is additional
information I should use.  I disagree.  Let's say you have 5
temperature gauges, that may or may not be working properly.  Which
would be better, their average reading, or their median reading? 
Well, malfunctioning meters might greatly skew the average, so it
seems like the median is a safer system.

My view of elections is similar.  I see it as a useful goal to
minimize the effect of the "bad meters".  If most people say that A
and B are very similar, but that A is better, but a few say that B is
greatly better than A, I don't assume that the smaller group has some
kind of special insight.  Instead, I suspect that this is a bad meter
situation, and that if they can be wrong about their relative
preference, they can also be wrong about their degree of preference.

In fact there are lots of reasonable scenarios where degree of
preference seems invalid.  For example, let's say that there are two
major political parties.  You strongly favour party A over B, but you
still have preferences between the candidates of your favourite party.
 Someone else only likes one candidate from your favourite party, and
considers all other candidates from both parties to be about equal.

Now, I don't know who is right, but I see no reason to believe that
your selection between the candidates in your party is less likely to
be correct than that of the other voter.

> You don't explain why a nearly indifferent
> voter is as likely to be right as a moderately concerned voter. 
> Wouldn't an indifferent voter be easily swayed by frivolous information,
> or by strategy? 

Strategy is irrelevant if we are choosing a standard based on sincere
opinion.

As for indifference, remember that the voter need only be indifferent
relative to his preference between other potential candidates.  The
preference may still be firmly held.  As well consider that
frivolousness is in the eye of the beholder.  My concern is that a
voter who is swayed by frivolous information is also likely to
exaggerate its importance.  So, a small difference expressed by the
voter may not correspond to one based on frivolous grounds.  As well,
truly frivolous choices are likely to be near random, and therefore
will tend to cancel each other out.

> [BC]
> > Note that the only reason given for rejecting B in this situation is
> > that B scores too low on average ratings.  I have never expected that
> > you would reject a ratings result simply because it was too different
> > from Condorcet, but you expect me to reject a Condorcet result simply
> > because it is too different from ratings.
> 
> [BI]
> Average ratings is not really the point -- my reason for rejecting B is
> that almost all voters consider B to be almost as bad as the worst
> possible choice, while an actual majority of voters consider A to be
> acceptable.

It isn't the point?!  The whole debate, as shown by the subject
heading, is whether ratings is defensible as a standard.  Now, you
seem to be quietly dropping it in favour of some new standard that is
too vaguely defined to be disputed.

> It has been argued that pairwise methods make no assumptions about
> strengths of preferences between pairings, but in fact pairwise systems
> do assume that all such pairings are equally relevant, as you indicate
> above.

I think I have clarified this point.

> Given only rankings, the only assumptions we can safely make about a
> voters' preferences are that the voter substantially prefers his first
> choice over his last choice, otherwise he would not bother to vote
> (unless you make voting mandatory).  There is no way to know what a
> ranking between first and last signifies, if anything.  In other words,
> we don't know whether the voter strongly approves or strongly
> disapproves of a middle candidate, or something in between.  Where the
> middle candidate stands in relation to the known first and last choice
> is arguably more important than where that candidate stands in relation
> to another middle choice of unknown significance.

What your saying is that we can't extrapolate much about ratings from
rankings.  Since I don't want to use ratings, this doesn't concern me.

> > > If you contend that the outcome is a result of extremist voting, then
> > > which voters are the extremists?  Since only three voters strongly
favor
> > > B, they would seem to be the most suspect.  Does this mean that
> > > Condorcet favors the extreme voters in this case?  If not, then since
> > > they also favor A, how could the 499 A voters be considered extremist?
> > 
> > Consider a vote on how much money will be spent on an upcoming
> > project.  Voters have a range of opinion between $0 and $1000, and
> > favour amounts closest to their first choice over amounts further
> > away.  Let's assume that the median view is $500, which is represented
> > by candidate B, and supported only by 1 voter.  A will represent a
> > lower amount, C a greater amount.
> > 
> > Now, B's plurality support is largely dependent on the placement of A
> > and C.  If A and C represent $499.99 and $500.01, then B will only
> > receive one vote.  If A and C are chosen for $0 and $1000, B will
> > likely receive lots of plurality support.  This is why I do not agree
> > with the argument, "Since only three voters strongly favor B, they
> > would seem to be the most suspect."
> > 
> > Now, even though the A-1st and C-1st voters sincerely rate their
> > favourite at a great distance from the next candidate (B), this may
> > simply be a result of a personality trait.  The B-1st voters may be
> > more willing to compromise than either the A-1st or the C-1st.  Of
> > course this doesn't mean that any of them are extremists, in the sense
> > of the word you intend.
> 
> [BI]
> I don't know what you're trying to show here, or how it relates my
> question.  In your scenario, there is only one policy dimension, and all
> candidates are equidistant.  Since B is the median voter, he is by
> definition not an extremist.  This is different from the example on
> which my question was based.  

My example was one possible explanation for the results shown in your
example.

> Whether B receives lots of plurality
> support in your example has no bearing on whether there is an extremist
> in mine.  And why would they vote differently with 499.99/500.01 than
> with 0/1000?  Under what voting system?

Under every voting system.  Let's say that you personally favour the
$400 figure.  Now, lets say that the candidates represent:
A $0
B $500
C $1000

You might decide to vote for B as your first choice, since this is
the closest to your ideal result.  Of course, you might also decide to
vote for A, if you would rather go down than up, but let's assume you
vote B.

Now, if instead A was chosen to represent $450, then you would
clearly vote for A as your first choice.  You might do this even at
$350.  That is, as A and C move inwards towards B, they will pick up
more and more plurality support at B's expense.

In some methods, we can expect that the "low" and "high" could end up
positioned to squeeze out the middle, but this can happen long before
either actually represents the middle.

This is why politics is so frequently polarized.

> > What do you mean then by talking about "absolute" ratings.
> 
> [BI]
> Take a universe of potential candidates, containing all candidates who
> are eligible and willing to run under reasonable circumstances, and are
> the favorite of at least one voter.  You can peg each voter's favorite
> at 100, and his least favorite at zero.
> 
> "Absolute" may not be the correct word, since this scale is relative to
> the best and worst potential candidate for each voter, but it is
> certainly not relative in the sense that it depends on who is actually
> in the race.  You could probably say this scale is "relative" if
> interpreted as Von Neumann-Morganstern utilities, but it is not relative
> to some arbitrary subset of candidates.
> 
> If the nominating process is fair and provides a field of candidates
> representative of the "ideal" field of candidates, then most voters
> should have an actual candidate who rates reasonably close to 100, and a
> candidate rated reasonably close to zero.  If the field is sufficiently
> representative, you should be able to use 100 and 0 as approximations of
> absolute ratings.
> 
> Turning this around, if you have a good nominating process, then you
> should be able to use 100 and zero as the range for actual candidates.

I agree for 100, but why zero.  Might not the nominating process
eliminate truly terrible candidates.
 
> If this is off too far, the nominating process is at fault; if off only
> a little, the actual ratings should still be more representative of
> "ideal" ratings than rankings would be.

So, perhaps a better example would be this:

1  voter   A 100 B 0
40 voters  A 99  B 100

Here, the 40 voters are voting in response to a really terrible
candidate who was eliminated by the nominating process.  Perhaps
someone who favoured exterminating their ethnic group.  Next to him, A
and B look pretty similar, as a Republican and Democratic candidate
might look next to a Nazi.  The 1 voter may not have seen as much
wrong with this candidate, so he still has his full range available. 
Of course, we can't tell that this is the scenario, just by looking at
the ballots, but it seems plausible.  I still think that B is the more
reasonable choice based on the ballots.

---
Blake Cretney