[EM] Ratings as a standard
Blake Cretney
bcretney at postmark.net
Mon Jan 31 17:59:42 PST 2000
Bart Ingles wrote:
> [BC]
> > Here's the way I see the discussion so far. You came out with a
> > theory, which was that if you get a sincere absolute rating from each
> > voter on each candidate, than the proper winner would be the candidate
> > with the highest total rating. I was skeptical, and suggested a
>
> [BI]
> That was never my "theory". I never claimed that the winner should
> necessarily be the candidate with the highest total rating. My focus
> was at the opposite end of the scale -- that an election whose winner
> has an extremely low rating, when other candidates have much higher
> ratings, is absurd and indicative of a breakdown in the election method
> used.
But, if we elected B in the following example, wouldn't that be "an
election whose winner has an extremely low rating, when other
candidates have much higher ratings." Even if you abandon average
ratings as a standard, but still require that methods not be too
different from it, you run into the same problem.
1 voter A 500 B 0
40 voters A 0 B 2
> [BC]
> > So, I await either an explanation of why absolute ratings is right in
> > this situation
> >
> > > > 1 voter A 500 B 0
> > > > 40 voters A 5 B 9
> >
> > or a new theory to improve on absolute ratings.
>
> [BI]
> And I have already done so. My initial examples assumed a 0-100 scale,
> and that all voters had favorites rated 100, and least favorites rated
> 0. Given that subset of possible scenarios, I showed that it is
> possible for a Condorcet winner with an average utility of nearly zero
> to defeat a near first-choice majority candidate with an average utility
> of over 50. I argued that this outcome was absurd. Rather than defend
> the outcome in that example, you raised examples which were not in the
> range of scenarios I was considering.
My defense is simple. I argue that rated "average utility" is
irrelevant. I back this up with an example where average utility
clearly leads in the wrong direction. If your current argument is
that average ratings doesn't make sense, but that for some reason
candidates should not win if their ratings get too low, then my new
example holds against that theory as well. But as I say, once average
utility is discredited, I don't see why we should be worried about
straying too far from it. I also don't see why, if a standard is
valid, it should only hold for the scenarios you present.
> Again, here is the kind of example I was concerned with:
>
> Voter utility
> 100 99.9 99.8 0.2 0.1 0.0
> ---------------------/\/-- --/\/-----------------------
> 499 A B C
> 3 B A C
> 498 C B A
>
> Condorcet Winner: B
> Avg. utility: A=50.1997 B=0.3997
>
> It seems to me that your other examples are irrelevant. If your
> hypothesis is that the Condorcet winner is always desirable, and I give
> an example like the one above, your choices are to either explain why B
> is a better candidate than A _in_this_example_ or else reject your
> hypothesis.
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.
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.
> 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.
> [BC]
> > Why should there be a maximum range? Presumably you could always
> > come across someone who felt even more strongly than allowed by the
> > bounds given.
>
> [BI]
> Because utility rating systems, such as Von Neumann-Morgenstern
> utilities, use fixed ranges.
What do you mean then by talking about "absolute" ratings. Do you
mean that a rating of 7 from voter X should correspond to the same
perceived utility as a rating of 7 from voter Y? Do you mean that a
rating of 7 from voter X in one election should have the same
perceived utility as a rating of 7 from voter X in a different
election? Do you mean that a rating of 7 should have some external
meaning outside its relative strength to other ratings in a given
example?
The reason I ask, is that it is clear that Von Neumann-Morgenstern
are only interested in the relative value of ratings, so they are free
to scale them to whatever bounds they choose. Do you mean to use
utility ratings in this way?
If so, then unbounded ranges are not necessary. If one voter
perceives a difference in utility 1000x that of another voter, we can
simply scale the ratings so they still fall neatly between 0 and 100.
So, if you have 99 people who think a pair of presidential candidates
have significant, but not tremendous differences, and you have one
person who believes that one of the candidates is the literal
embodiment of the Anti-Christ, you can properly scale the result so
that the 1 outweighs the 99.
> Because an open-ended, emotion-based
> "feeling" scale is not what I was advocating, and has nothing to do with
> my point.
Perhaps instead of "felt even more strongly," I should have said
"perceived an even greater utility." That perception could be the
result of correct or incorrect reasoning instead of intuition or
emotion.
> > > Of course, this is an odd example where the vast majority of voters are
> > > almost completely indifferent.
Don't you mean indifferent relative to the other voter. If votes are
scaled, then we cannot tell whether these voters are indifferent, or
the lone voter perceives a tremendous difference.
> > > It also seems to imply a very bad
> > > nominating process, since the majority of voters don't like either
> > > candidate.
>
> [BC]
> > Maybe they're saving the upper range for some kind of truly great,
> > heroic candidate. It may mean that they're just optimistic.
> > Presumably the lone voter feels he has found such a candidate.
>
> [BI]
> In order for the 40 "reasonable" voters to reserve their top rating for
> this heroic potential candidate, the potential candidate must exist. If
> he exists, but is not in the race, there must be something terribly
> wrong with the nominating process. If he doesn't exist, then the voters
> must not be reasonable after all.
Lets say that one year, you really like one candidate. You give him
a 100 rating. In the next election, there is no equal candidate in
the race. Your favourite candidate has died or retired. The best
candidate in this race, you consider only a quarter as good. Your top
rating must then be 25.
Or do you mean that each voter should have his ratings scaled so that
their highest rating is always 100 and lowest is always 0?
---
Blake Cretney
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