At 05:03 PM 8/10/2007, Juho wrote:
>In the light of this example it doesn't matter how the "sincere"
>votes are derived or where they come from. Any method and logic is
>ok. It could be based on terms "sincere" and "utilities", or not. The
>only criterion is technical by nature, i.e. that the voter uses the
>values in some other way than using mostly min and max values.
In other words, even if your vote of max for one and min for another,
and no intermediate values for anyone (maybe they are also max or
min, or you left them blank) is an accurate reflection of your
preferences, i.e., it is sincere, then your vote is "strategic."
> > So how is this a "bad result"?
>In the example the idea of Range electing the candidate that has best
>utility from the society point of view failed. In the example the
>votes were 50% - 50% but Range could ignore also a clear majority
>opinion.
Wait a minute, the is the very crux of the matter! Range does not
"ignore" a majority opinion, but it *can* pass over it, *if* the
majoriy expresses a weak opinion. That is, strong preferences are
given greater weight in Range than weak preferences.
This is *necessary* if any method is to elect the candidate with the
"best utility." It is the very foundation of how Range operates. If
you want to cast strong votes, you cast them. Weak votes, you cast
them. If you cast a weak vote, big surprise, somebody else casting a
strong vote *in that pairwise election* has, in it, more power.
Once again, Juho has not stated what the "bad result" is. When he
says that the votes were 50-50, he means what? The example has been
lost. I've been asking for an example of a bad result, and Juho keeps
repeating himself. So, of course, I'm repeating myself too. I ask for
an example, and he says he gave one. But it was not, at least not to
me, a "bad example, and he has not explained why.
I think this is the example we were talking about. It was not
described in detail.
> One could e.g. translate utility values 1
>A=90, B=80 and 1 B=90, A=70 to actual votes 1 A=100, B=0 and 1 B=90,
>A=70.
So this is two voters. Thus it is 50-50 as far as first preference is
concerned. (And we can imagine that this is two whole sets of voters
voting identically.) Fine. If I'm correct, Juho is asserting that, if
the votes are translated as stated, the outcome is "bad."
Yet what method is going to do better than Range in this example?
First of all, Juho has ignored all that was written about utilities.
There is only one way that I can think of to make utilities
interpersonally commensurable, and that is to fix the scales in some
way, to something common. What I did was to fix them at "absolute
best possible outcome" and "absolute worst outcome possible." We
could equivalently state this as "as satisfied as possible" and "as
dissatisfied as possible."
If voters vote sincere utilities, and the method has sufficient
resolution, we know that true social utility (or at least
"satisfaction" is maximized. But this is not at all how we expect
people will vote. Rather, they will treat a Range election as they
have been treating elections for centuries, as a *choice* between a
set of realistic alternatives. They will *usually* ignore possible
write-ins except in quite unusual conditions.
With ranked methods, starting with Plurality, you make a *choice.*
You vote that choice simply, maximum strength, one full vote.
Approval starts to allow you some more flexibility, but there is
still the fact that by making one choice strong, you are making
another maximally weak. Pure ranked methods allow you to make
maximally strong choices among an entire set of candidates, but this
leads to some contradictions and other problems, plus "maximally
strong choice" is not an accurate picture of real preferences, and so
ranked methods can make some spectacularly poor choices (though
usually they don't).
Now, if the voters described vote their supposed "sincere" utilities
-- which were completely undefined by Juho -- Then we have a total of
180:150, A wins. Any ranked method, though, will give us a tie,
because the two voters have reversed preferences.
The problem with what was stated by Juho is that voters make a choice
from a set. And if there are only two candidates in the set, there is
no basis for voting less than one full vote. If you actually care. If
you don't care about the outcome, then ignoring your vote (i.e.,
treating it as you stated it, weak) is *not* a bad outcome, it should
certainly be fine with you, and it was the preference of the other
voter, so where's the beef?
Juho stated utilities of:
A B
1 90 80
2 70 90
And then said that this could be translated to
A B
1 100 0
2 70 90
Wbich it certainly could. If we assume that the utilities are
"sincere" -- passing over for the moment the problem of what that
actually means -- then what we see here is two voters who vote in two
different ways. One takes the election as a choice, as being asked
"Which is better." Since there are only two candidates, "How much
better," which Range is good at considering, is *moot*.
There is no clear standard for comparing utilities for two
candidates. When you get a larger set of candidates, the candidate
set becomes the anchor. It's pretty simple: with 3 ormore candidates,
the best is 100, the worst is 0, and then you can set the remaining
ones in between. There is only one reason you would not do this.
If you really don't care which candidate wins the election.
If we assume that some unstated factor makes sense of the utilities,
such as two more candidates who are actually worth considering (i.e.,
might win the election, so the voters will take their utility for
that candidate into account when voting), then what we have is a
statement from one voter that A is very good.
Compared to what? Why isn't A 100 in the first place? Is A the best
candidate on the ballot? So why, then, didn't the A supporter have a
utility of 100 for A in the first place? Apparently, Juho is using
unnormalized utilities.
If we look at the first voter, the A/B preference is shown as 9/8.
The second shows this preference as 9/7.
Now, suppose this is a simulation. The stated utilities are absolute
utilities (that is, subject only to the "first normalization"). That
is, they have nothing to do with the candidate set, each utility is
related only to the voter's opinion of the candidate.
Voter 1 is saying, by the vote, "I want A and I don't want B." Voter
2 is saying "I don't care very much." So Range gives the election,
with the translation, to A. How is this "bad"?
Now, we already know that if voters vote absolute utilities and do
not normalize, we get true maximization. But absolute utilities we
will *never* know. What we know is what voters tell us. This is a
democracy. We *trust* what voters tell us!
They tell us that they strongly prefer A to B, we will trust that
they do. If they tell us that they don't care about the choice
between A and B, we will trust that as well.
Often overlooked in all this discussion of strategic voting is that
if the voter votes max for A and min for B and C, the voter is
abstaining from the B/C pair. If it turns out that this is the
critical pair, *the voter is abstaining fully from influencing the outcome.*
Bottom line: no harm has been shown from the use of Range in the
circumstance described. Yet Juho proposed this as an example of the
"mess" that Range allegedly creates.
We have seen this over and over again. A critic of Range claims that
evil strategic voters will harm the innocent, sincere voters, but no
scenario is shown that is both reasonably realistic, does not involve
assuming contradictions, and that shows significant harm that the
sincere voters did not indicate, by their vote, was acceptable to them.