At 12:34 AM 12/3/2008, Juho Laatu wrote:
--- On Mon, 1/12/08, Abd ul-Rahman Lomax <[EMAIL PROTECTED]> wrote:
> > One approach to sincerity is to compare voter
> behaviour to the requested behaviour. In Approval if the
> request is to mark all candidates that one approves then
> placing the cutoff between two main candidates is often
> insincere..
("Insincerely" is not the best word here since
that carries a meaning "morally wrong". I could
have said e.g. "Not based on the sincere opinion
only".)
The problem here, Juho, is that "sincere opinion" is not the basis
for voting, which is an action with, in fact, moral consequences.
Vote for Adolf Hitler because you like his moustache ....
Or fail to vote to prevent the election of W.
(Now, if your sincere opinion is that there was no difference between
G. and W., the vote cannot be faulted, only the stupidity of the
opinion, and I would have no intelligence test for voters, voters
have the right to determine, themselves, if they are qualified to
vote or should, alternatively, leave it to others. In fact, what I'd
like to do is allow them to *choose* the other or others who
represent them when they do not vote themselves, but to the maximum
extent possible, I'd leave the power to decide whether they vote
directly or not in their hands. Instead of deciding, as many have,
that we cannot trust the people to know enough to vote intelligently,
hence we need a republican system, I'd leave the decision of whether
or not a person knows enough to vote to the person, and I'd allow
them to transfer their voting power to someone they trust, without
coercing or interfering with that in any way.)
> Approval is a special method from this point of
> view since it is often described as requiring the voter to
> plan what is the best strategic vote (where to put the
> cutoff).
>
> It requires no such thing. Voters, however, will maximize
> their expected outcome if they vote optimally.
"Optimally" means something like "following the
best strategy" here.
Or close. Which is actually pretty easy, and is what most voters are
quite accustomed to doing. For most voters, should Approval be
implemented in the current contest, the best strategy is simply to
vote for their Favorite. But they now have an additional option or
options, and some might wish to use it, and, in particular, those
whose Favorite is unlikely to win the election. It gets tricky only
in the situation that there are three frontrunners.
> And they vote
> optimally by making a sincere expression
"Sincere expression" is obviously meant to be
different than "sincere opinion".
Ballots do not ask for the voter's sincere opinion. They ask voters
to make a choice or choices.
"Sincere expression" here means, "expressing some preferences
sincerely, and expressing no preferences insincerely." It means no
preference reversal.
"Sincere opinion," here, must imply the idea that there is some
absolute state called "Approval," such that all the voter need do is
to transfer this to the ballot in order to vote with "sincere
opinion." And that is the myth. There is no such absolute as applies
to voter choices.
There are some absolutes; we could assume that a voter feels
attraction or repulsion with respect to each candidate. (or some
neutrality, so it would actually be easiest to vote based on this
phenomenon with Range 2, so the voter has a middle category.) But
this is not the meaning of "approval" in a voting context. It means
"accept." In a business context, what I will "accept" certainly isn't
what I prefer, normally. (It can be, but that's another matter.) It's
usually less, and, sometimes, I'm not even happy with it, I'm averse.
But I have concluded that I won't do better.
Do we want voters to vote "sincere opinion," in this sense? Perhaps.
We might see a lot of majority failure, but that's not necessarily a
problem, as long as we do the follow-up.
This is the equivalent to voting fully sincere Range. It improves
outcomes. But it is also not our ordinary decision-making procedure,
when we have information about the context. It's quite reasonable
when we have zero knowledge. But voting zero-knowledge can be
*tough*. It's tough with Plurality, even though, zero-knowledge, it
should be obvious to vote for your preference. But we never have
zero-knowledge. We know ourselves and we are people and, on average,
we are either like others or we know that we aren't and we have some
knowledge of what other people would like or accept. The radical
leftist isn't terribly surprised when a conservative wins an
election! He knows that his opinions are not mainstream.
It's an interesting assumption: if we are average, which most of us
must be considered to be, then Plurality works quite well if people
vote sincerely! Most likely, the way preferences are distributed, the
candidate with the highest first preference will usually be the
Condorcet winner. And, for that matter, the sincere Range winner.
All I need is clear definitions and terms for
various levels of strategic behaviour. A
generally used term for the starting point is
"sincere opinion". That refers to the
independent internal preferences of the
voters. After that there are different levels
of strategic/optimized/... behaviour.
Sincere opinion isn't very expressive. However, we could take it to
mean absolute utilities. That does automatically translate into
preferences, if you know the utilities, the preferences should
follow, so we can then talk about "sincere preferences," and we can
assume that they are transitive (that's a whole issue of its own; my
sense is that Condorcet cycles internally are quite unlikely, we
don't use rank to determine preference order, we use something like a
Range technique.)
1) Sincere opinion
2) Sincere opinion modified as requested (e.g.
normalize ratings to full scale so that all
voters will have roughly the same weight)
No ballot requests this. It's been proposed, sometimes, that ballots
automatically be normalized. Bad Idea, I'd say (though there is a
method, DSV, which does automatic optimization in a more
sophisticated way, and the voter can opt in or opt out of optimization.)
However, the ballot only allows a certain maximim "opinion" to be
expressed. It's actually a maximal weight, a choice, not an opinion.
One may infer some opinions from a Range Vote, but not necessarily
others. We may assume that any candidate rated above another is
preferred to the other, but we cannot assume that any candidates
rated the same are not differently preferred, and we cannot assume
that the differences in rating between various candidate pairs
correlate with difference in preference strengths, except that we
can, from some Range votes, infer limited information about
preference strengths. I gave an example in another post today.
3) Optimize vote as requested (e.g. place the
approval cutoff between some of the front runners)
Again, no request. This is important. I might suggest to you, I might
request of you, I might yell and scream and demand that you also
approve Gore, but the ballot isn't going to do that, the system is
not going to do that, you are going to decide, and I would not
presume to challenge this as insincere. Quite simply, sincerity is
irrelevant. Your decision is going to be faced on two factors:
sincere opinion, i.e, underlying ratings, comparatively for all the
candidates, and your judgment of what to accept, what candidates to
help win. It is your choice, your decision, and your responsibility.
There is no "request." Not from the system.
I wouldn't start with "sincere opinion," it's far too difficult. I'd
start with the frontrunners, with the set of candidates who might
win. (By the way, in proportional representation systems, where
representative power is increased by votes and there isn't a single
winner, all bets are off, there are still strategic considerations
unless we go to the max and use Asset Voting, but it's quite different.)
Usually there are just two frontrunners, so, in Approval, I'd simply
start with them as if they were the only names on the ballot. Indeed,
I'd start this way if there are more than two. I vote for my favorite
among them and definitely not for the worst. If there are some in the
middle, this gets tricky, but that is rare. I'd complete my
consideration of this before deciding any other votes. With two, it's
easy, and maximal strategy is obvious and, in fact, sincere among
this set. It never involves preference reversal which is why Approval
was originally called "strategy-free." However, some authors
"improved" the definition of strategic voting to include, it's a
little unclear to me, however one sets an approval cutoff. It's
strategic in the sense that one does it better if one knows and uses
expected outcome for the election.
And once I have decided on frontrunner votes, I can vote for my
favorite if my favorite is outside this set, and most people would
want to do that, under those conditions. Even if my favorite is one
of the frontrunners, I might want to encourage another candidate, but
I really shouldn't do this if I'd be horrified to see that this
candidate actually won!
4) Optimize vote as well as possible but within
generally accepted limits (e.g. exaggerate in
Range as much as you can)
Actually, that's not optimization, necessarily. And what is
exaggerated is apparent preference strength, not a single vote
itself. In fact, these are just votes, choices as to how much weight
to put in each pan. It's only when we assume that they are "supposed
to be" sincere ratings, whatever that is, that we can even talk about
"exaggeration."
5) Optimize vote beyond generally accepted limits
(e.g. try to bury in Condorcet)
Again, no such limit exists. It's not illegal. It's a choice, and
voters make that choice in an attempt to optimize the outcome. Please
notice this: they will only do this if their preference is strong, so
this can be seen as an attempt to shift the outcome toward a Range
result, which is, overall, socially beneficial. It's not even
reprehensible. If that's the voting system, it's allowed.
Our concept that it is reprehensible is defective. Strategic voting,
in general, is voting to improve the outcome over what one expects if
one votes "sincerely." It is not a bad thing, and with some methods
it is a quite good thing, as with Plurality. It represents making and
accepting necessary compromise, so that the method works best.
6) Optimize results beyond what is allowed (e.g.
vote twice)
Hadn't thought of that. Since it's illegal, it would indicate very
strong absolute preference. My suggestion: toss the offender in the
clink, but count the vote. It will probably improve results.... (For
this to work, it has to remain illegal, for only if it is illegal
would it represent true strong preference, deserving of the extra
vote. Nice paradox, eh?)
I'm only partially kidding. We really need to start thinking about
preference strength, for failure to do this has led us into a lot of
traps, such as the idea that low voter turnout is a bad thing and
leads to bad results. That's true if the low turnout is due to
differential difficulty, where one class of voters is impeded, but if
access to voting is equal, low turnout means that the voters
generally have low preference strength among the candidates, and this
has other implications than what we have usually assumed.
I'm quite used to use term "strategic" to refer
to all technical changes in the vote that make
the vote different to one's sincere opinion. Term
"sincere" is often used to refer (technically) to
the "sincere opinion" or resulting "sincere vote".
Yes, it's being used that way. But it used to refer only to
preference reversal. There was no question of "exaggeration."
Consider this: Range voting is equivalent to giving every voter 100
ballots, say. Now the voter votes, one vote at a time, across the
candidate set. "Vote," here, means complete an approval ballot. Each
ballot is sincere, i.e., the candidates, on each ballot, are divided
into two sets, with every member of one set being preferred to every
member of the other. We can, then, reasonably call each ballot "sincere."
This is not "sincere opinion," which implies some absolute approval
status for each candidate. There is no such status, it is the voter's
option where to set the approval cutoff.
Now, the voter does this 100 times. But the voter sets the approval
cutoff in different places -- or does not. We now have a collection
of 100 sincere votes from the voter. Each one represents a sincere
opinion as described, an opinion that every candidate in the
voted-for set is better than every candidate in the other set.
Does an opinion become insincere by being repeated? Or by not being repeated?
Here is what we can derive from this manner of looking at Range
Votes. On every one of the ballots, we'd expect to see the Favorite
getting a vote. And we would expect to see the worst candidate,
sincere opinion, get no vote on any ballot. But what happens in
between is a *choice* of the voter, and never is this choice insincere.
The voter might toss dice to determine where to place the approval
cutoffs -- this would work -- or the voter could step down the
preference list repeatedly, which would produce a Borda-like vote --
also not bad, as long as the voter pays attention to clines and
simply considers them as one candidate, rated the same -- or the
voter could leave it with a bullet vote -- 100 votes for the
Favorite, or the voter could decide which pairwise races are most
important and make sure that most or all votes discriminate between
those candidates.
It is *all* sincere with Approval and Range, and that's why Brams was
not crazy to assert that Approval was strategy-free,.
But we can define something called "fully sincere," or we've been
calling this vote "accurate," and it has a few possible meanings, it
is much more restricted than ordinary sincerity, which usually means
that whatever information that is disclosed or implied is true. An
accurate vote only takes on meaning with Range; this vote expresses
preference strength accurately, and this has entirely new
implications which most, quite simply, have not adequately considered.
With certain means, it even becomes possible to encourage the voting
of accurate utilities, and we can go beyond accurate relative
utilities, indeed it may be easier to go to absolute utilities.
That's what a Clarke tax does, if I'm correct. Votes are *prices*.
This isn't necessarily plutocracy, but that is another matter.
As an example, though, of a way to avoid plutocracy, the votes might
be *relative* prices. The tax might be a percentage of wealth instead
of an absolute value. So it would be progressive, not absolute. It
could be a *bracket*, so it wouldn't even necessarily be linear. This
is way beyond what I've studied, it's just pointing out that the idea
of voting absolute utilities, which is what truly maximizes
satisfaction, isn't preposterous.
Money certainly isn't everything, but, I can tell you, I'd have been
happier with the election of Bush in 2004 if I'd gotten $10,000 as
compensation for losing. (Not enough, by the way, but you might get
the idea. How much would be enough? That, if actually done, would be
a measure of my true utilities. What does it take to buy me off.
Offer me enough, I can undo some of the damage -- maybe all of it --
done by the election making an otherwise bad choice. Or I can head to
the Bahamas and hope that the fallout doesn't go there, more than can
be handled. Frankly, though, they couldn't afford what it would have
taken to do this with the public. The idea that this would be
plutocracy misses the point. There are many people with little money
and only a few with a lot; a situation where the bulk of wealth is
controlled by very few is unstable and isn't actually what we have.
We have high concentration, yes, but the overall financial power is
actually with people with much nore modest resources, individually,
but there are many more of them.
The problem is that the many are not organized, whereas the wealth of
the few is more naturally organized. One wealthy person can spend
that money with a single decision, it's much tricker to amalagamate
and use the power of the many. When the wealthy buy elections, they
do so efficiently. If they had to *really* buy elections, by actually
paying the voters, it would be much more difficult.
How much would you need to be paid to vote for a candidate you
thought would do a bad job governing the place where you live? If you
are an average voter, multiply that by the number of voters and ...
it would be a WholeBoatLoadoCash, to use a technical term. A Big BoatLoad.
Any terms are ok as long as there is a common
understanding of their meaning. Neutral and
descriptive terms are better than confusing ones
and ones with hidden meanings (or ones that are
planned to present some particular viewpoint in
better or worse light than others).
That's right. The problem with "sincere" is that it is a totally loaded term.
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