[EM] Ratings as a standard

[Bart Ingles]

[Blake Cretney wrote:]
> > > 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.
> >
[Bart Ingles]
> > 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.
> 
[BC]
> 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.

[BI]
Fair enough, but in that case all you're claiming is that using
preference orders is slightly (your term) better than random selection
in choosing a correct proposition.  Not a terribly strong claim.

I'm not convinced we should even be thinking in terms of correctness,
even though I tend to think of my own views as "correct" and conflicting
views as "incorrect".  It might be better to think more in terms of
competing interests.  Even in a simple two-way election, the group
which prevails is not necessarily correct, just bigger.  I don't believe
elections are a good way to determine correctness, even if they are
slightly better than a random guess.

[BC]
> 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.

[BI]
I'm certainly not going to defend the average reading, but suppose some
of the gauges have readings which are improbably similar?  This might
make more sense with more than 5 gauges -- suppose you have 10, and four
of them read exactly 32 degrees, while the rest have widely scattered
readings all above 32.  Is the median still a better guess?  It seems
here that similarity in readings could indicate agreement between
gauges, just as similarity in ratings would indicate indifference on the
part of a voter.

[BC]
> 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.

[BI]
If you think in terms of conflicting interests instead of correctness,
you no longer a need to assume that the winning faction is "correct", or
that the losing faction is somehow incompetent to gauge the strengths of
its own preferences.

You could think of degree of support as a measure of the amount of
"consent of the governed."  This is not necessarily binary, while the
terms "correct" and "incorrect" are, at least as applied here.

[BC]
> 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.

[BI]
Again, I don't see how you can infer "correctness" from any election. 
That's not the purpose of democracy, as I see it.  It's often more
important for a solution to be workable, than to be correct in the way
you seem to mean it (correct = optimal?).

In any case, it would be hard to argue against a strong consensus
candidate that both sides substantially agree on.

[BI]
> > 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?

[BC]
> Strategy is irrelevant if we are choosing a standard based on sincere
> opinion.

[BI]
How about party strategy?  Wouldn't a voter with weak preferences be
more likely cave in to rumor mongering or other manipulation?  The
voters preferences would still be sincere.

[BC]
> 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.

[BI]
As for your concern that a voter swayed by frivolous information might
exaggerate its importance, wouldn't that mean that the voter is likely
to change his rank order as well?  If the voter himself exaggerates the
importance of an issue, I wouldn't call it frivolous, at least from the
viewpoint of that voter (I suppose you could say that the *voter* is the
beholder I had in mind).  What I meant by 'frivolous' was that the voter
himself doesn't care, and chooses between two candidates in an offhand
way.

Such truly frivolous choices may cancel if averaged across many election
cycles, but I wouldn't want to count on it during a given election. 
Suppose only one party is engaging in a disinformation campaign?  Or
suppose only one faction happens to have weak preferences that can be
manipulated in that way?

[Side note -- Anyone forced to make an either/or choice without
meaningful information should use a coin toss or something similarly
random in order to rule out subtle, possibly subconscious, manipulation. 
This would help to insure that frivolous choices actually do cancel
during a given election, not just over many election cycles.]


> > [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.

[BC]
> 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.

[BI]
I said *Average* ratings isn't the point.  The "ratings as a standard"
heading, or something similar to it, is one that you originated about a
year ago when replying to one of my messages.

I don't consider average ratings to be the ultimate standard, but a
useful gauge of voter satisfaction and indifference when used in sincere
voter examples.  My original reason for using averages was to point out
why I believe the CW is also not the ultimate standard.  That said, I
believe that average (or total) ratings is probably at least as good as
the CW as measure of a candidate's overall acceptability, when applied
to sincere examples with a full candidate field and with the utility
ranges reasonably defined.

It wouldn't matter if I had proposed one particular standard using
ratings as a component, since refuting it wouldn't necessarily discredit
all such standards using ratings.

[BC]
> > > 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.
> > 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.

[BC]
> I agree for 100, but why zero.  Might not the nominating process
> eliminate truly terrible candidates.

[BI]
I suppose you could use it that way, if you are concerned that a
particular voting system might not be able to do so on its own.  The
nominating process is often used to weed out possible spoiler candidates
as well, especially when FPP is the voting system.

The problem here is that the voters who would have supported those
pre-rejected candidates now feel cheated before the election is even
held.  And who decides which candidates are truly terrible?

I see the role of the nominating process (in theory at least) as
selecting a minimal field of candidates which is representative of the
voters.  This is especially true of example elections, where the object
is to challenge voting systems.  I could see excluding candidates
because they are not viable or who have no mathematical chance of
winning, but not because they are 'evil' or somehow undesirable.

[BC]
> 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.

[BI]
Based on an election between the two remaining candidates, I agree.  On
the other hand, I don't see anyone rioting if A wins.

If the third candidate is non-viable and doesn't represent any voters,
and for that reason doesn't deserve to be nominated, then he shouldn't
play a part in defining the range of voter ratings either.  In that
case, the 40 voters' rating for A should really be zero.

Bart