At 02:58 PM 11/25/2008, Michael Poole wrote:
Your definition is wrong. A strategic vote is one that is not
representative of the voter's honest views or ideal outcome. When
using strictly ranked systems (where no ties are allowed), the only
possible form of insincerity is order reversal. When using approval
and range voting, preferences may be insincerely magnified or diluted,
in addition to being reversed.
Mr. Poole, I think you should look at the old definitions. Take a
look, also, at James Arymtage-Green's efforts to consider whether or
not Approval Voting satisfies the Majority Criterion. He has to stand
on his head to come up with a definition of "sincere" that makes Approval fail.
"Insincerely magnified or diluted" implies that there is a "sincere
expression," which is then not expressed. Preference reversal is
certainly possible in Approval and Range, but provides no advantage
to the voter.
How did it come to be that a political scientist like Brams would
claim, in his early publications, that Approval was strategy free? He
claimed that within the context of the time, simply. It was free of
what was called strategic voting at the time. But what I'm pointing
out here is that it is *still* free, if we are careful about what we
mean by "strategic voting," which, it turns out, must mean preference
reversal. Otherwise what the voter has done is to consider a
preference of no importance, either because it is small in absolute
terms, or because one of the options is unlikely and the voter does
not want to waste voting power expressing a moot difference.
(Note that it is possible to design a ballot and method where full
and accurate preferences are expressed without loss of voting power;
I've suggested how to do this many times; it's pretty simple. One
method would be a preferential ballot where one ranks the candidates,
equal ranking allowed (that means no preference, true indifference),
*and* rates them. It would probably be sufficient if there were a
"plus" indicator, as in the voting method A+ that I proposed years
ago. I.e., you mark a candidate Plus if you have rated another
candidate the same, to express that you prefer this candidate over
the other. Yes. That would only allow two ranks at any rating, but
that is quite likely to be adequate for public elections. Plus could
be a necessity in some places where laws allocate ballot position
with an assumption that voters have voted only for their favorite.
Bucklin, with equal ranking allowed, would be similar to Plus, for
most practical purposes. (Bucklin won't find a supermajority winner
if there is a majority one, unless equal ranking is allowed; it could
still fail.)
What Approval sincerely represents from a voter is a *decision* as to
where to place an Approval cutoff. Once the Approval cutoff is
determined, the vote then follows from preferences in comparison to
the Approval cutoff. It is easiest to understand this with Approval,
without the complications of Range. What I've seen from those who've
written on this, as Mr. Poole wrote above, is that they do not define
"magnified or diluted." How do we determine if a vote has been
"magnified or diluted?" Is there any absolute Approval cutoff, so
that we could know if a voter has either voted for a candidate that
the voter really does not approve of (diluted) or has not voted for a
candidate who the voter actually approves (magnified)?
As a thought experiment, consider the case where I would score three
candidates as 100, 50 and 0 on a uniform scale.
Would under what conditions? That's the whole point I made! Did you
read the quoted material? Those are, perhaps, absolute utilities?
Which aren't commensurable, by the way. Okay, I'll assume that they
are absolute utilities normalized to the same scale, perhaps a scale
of 0 to 100. But what about probability assessment? Voting is a
real-world collective decision-making method, and to expect it to
ignore expected probabilities is to ignore how intelligent creatures
operate. We pay no attention, for the most part, to irrelevant
alternatives, we don't invest in them, would be a more accurate way
of saying it.
I'm not convinced that it is useful to discuss this until the
underlying problem is recognized. Where did these 0, 50, 100 scores
come from? What is that scoring sincere and 0, 1, 100, or 1, 99, 100
is not? The latter might be von Neuman-Morganstern utilities. They've
been adjusted according to outcome probabilities. von
Neuman-Morganstern utilities, if I'm correct, preserve full
preference order unless a probability goes to zero. I still prefer
the million dollar tax credit over the $100 one, but I'm only going
to put miniscule voting power into it, and my assessment of the
likelihood that the option is a meaningful one is so low that it
probably would not be expressed in any practical voting system. I'd
vote 100% for $100 and also for $1,000,000. But if I can vote the
accurate utilities, it might be $100, 99.999% and $1,000,000, 100%.
If I know that the
first two candidates are close in the polls, I may vote for them as
100, 10 and 0 so that my preferred candidate's chance of winning is
increased. This is a strategic vote in the usual sense. You attempt
to redefine "strategy" so that it is not called one.
That is not a strategic vote in the original sense. Please translate
this into Approval and look at it. And lets make the supposed sincere
utilities be 100, 90, 0. Note, as well, that these utilities are
truncated and normalized, almost certainly. Are there other possible
candidates with utilities outside that range? With VNM utilities, it
doesn't matter. A zero probability of election, and infinite
resolution on the utilities, means that a new candidate with very
small probability can be inserted without significant shift to the others.
Now, how would an Approval voter vote? Where do we put the Approval
cutoff? There is no absolute reason to set it at 50%. Nor is
"sincerity" any guidance. What if the voter was a strong supporter of
someone who didn't make it through the primaries, so the utilities of
the candidates in the election, on the ballot, are really 50, 45, 0.
How do we decide to "accept" an offer, or to "approve" an outcome? We
compare the offer with what we think we can get! I.e., we consider
probabilities. In Approval Voting, we are casting a vote accepting
the outcome of an election of any one of a set of voters. How do we
choose which candidates to include in this set?
Surely it depends on who is running, and our perception of what the
electorate may realistically approve. If I have a choice between the
absolute best candidate in the world, in terms of my personal
expectation, and someone who is merely good, better than average,
etc., or maybe even better than anyone who has ever been elected to
the office, and I think that if I can get the best, I'll vote for the
best. If I might get something worse than the good candidate, if I
don't approve of him or her, then I'll vote for both the best and the
good. And in a good method, I can say that I prefer the best and, at
the same time, not risk failing to elect the good by giving the good
insufficient votes. (Pure Range, quite simply, doesn't do this, nor
does pure Approval, but it's easy to add: the question is whether or
not that additional preference information is sufficiently valuable
to be worth the trouble. I think it is, actually, though with
high-resolution Range, it's probably moot. (I consider 0-100 to be
high-res.) I'd sacrifice 1/100 of a vote in order to express a
significant preference, and the probability of this causing a poor
outcome is truly minute, not worth worrying about.
Rambling about ideal abstractions,
Moi? Ramble? I'm looking for constructive criticism, not personal insult. Ahem.
(Comment added later: I dish some back.)
inevitable voter knowledge, and so
forth does not change that it is a distortion of my honest ratings
based on desired outcome and beliefs about other ballots. Strategic
voting works *only* in the case of (believed) knowledge about how a
significant number of other voters vote.
Consider a vote as if it were a bid. You have so much to spend. You
can split your money between campaigns. The campaign that collects
the most money wins. Now, who in the world is going to say that your
"vote" is insincere?
You've posited sincere utilities that can be simply translated into
votes. That's a myth. Smith uses, in his simulations, utilities that
are generated according to models; these, then, can be used to
predict voter behavior. In some models, voters know who the
frontrunners are and they vote depending on this information. Such
models are far more realistic than models which assume fixed
utilities, unmodified by probability information.
Yes. "Strategy" is required, i.e., smart voting. A voter who isn't
smart may waste his or her vote. That, actually, might be a good
thing, it may improve overall outcomes. Remember, we are talking
about voter expectations, but some voters know more about what
candidate will be good, overall, and some don't. Many vote contrary
to their own real interests, being deceived by propaganda, or are
simply ignorant. In no way would I suggest that such voters should be
deprived of power. But neither should I take it as tragic that such a
voter, with plurality, votes for a candidate with no chance of winning!
But "strategy" is not the same thing as strategic voting as was used
in the study of voting systems. The concept of "exaggeration" of
preference strengths didn't exist, and that's what Mr. Poole has
presented as an example. His example did not distort preferences, but
Range allowed the voter to decide what choices, what pairwise
elections within the voters' preference list, were more important than others.
If you delude yourself into thinking otherwise, and on that basis
convince yourself that range voting does not suffer from -- or even
permit -- strategic voting, you will only undermine your own
credibility.
Horseshit.
Does this writer from Trollus.org imagine that I'm going to conceal
what I think and know because he imagines I'm deluded and threatens
me with loss of credibility? Who, indeed, is deluded?
Here is what I'd suggest to him. He should read what I wrote, read
about von-Neumann Morganstern utilities and the work of the authors I
cited, and also do a little research into the history of Approval
Voting and strategic voting. And try to understand these before
imagining that he can truly criticize them. Dhillon is going to be
tough, Smith wrote that the paper used "notation from hell." I don't
expect readers to understand the details of Dhillon, and Dhillon's
claim that Relative Utilitarianism (which we might as well call Range
Voting) is a unique solution to a modified set of Arrovian conditions
has not necessarily been verified, and I certainly can't follow their
proof. But what von-Neumann Morganstern utilities are is not so
difficult, and the claim is, and it seems to be widely accepted, is
that summing these is a mathematical simulation of how we (and
presumably other intelligent creatures) make decisions, individually.
We do not use pure preference lists; rather we use, as Smith has
claimed many times, something like Range Voting, and the "votes" are
modified by probabilities, we do not invest our resources in
preferable outcomes that are improbable, even if we maintain an
awareness that they are preferable. Pure VNM utilities do maintain
preference distinctions.
Then, if we normalize these utilities, following the democratic
principle of one person, one vote, we can make collective decisions
in the same way. Not perfect, because of that normalization,
actually, and also because of defects in how we estimate
probabilities. But probably as good as we can get.
Look, suppose a society says to a person, it's up to you, which do
you prefer, A or B? This is the situation in every election where
your vote will turn the election. (In a Range election, one vote can
actually turn the election, whereas in most whole-vote methods
(including Approval), one person can't change a winner from one to
the other, but only from one to a tie, or a tie to the other.) In a
close Range election -- the only one where your vote counts,
actually! -- society is essentially saying, "We are, overall,
indifferent between A and B. So you choose." Now, what is a "sincere
vote" under those conditions? Because the issue of probabilities is
removed, we get pure choice. Which is *not* pure utilities. The voter
will vote to produce the outcome that the voter desires.
Our voting systems work because every voter may be in that situation,
which is most likely if they are voting in a certain way. And
standard Range and Approval strategy encourage them to do exactly
this: assume that your vote counts, and vote that way. This means,
quite simply, voting 100% for one frontrunner and 0% for the other,
almost no matter what your supposed "sincere utilities" were for
them. Unless they truly are equal, and both acceptable, in which case
you can thank your lucky stars that you were facing such an election,
I've never seen one in my life.
So some voter who votes, for two frontrunners, 100% and 99% --
FairVote posits a whole electorate of 99 voters who vote like that,
except for one, who votes that nasty strategic vote of 0% and 100% --
is saying, well, we have a "slight" preference for one. But, really,
we don't care enough to make a strong vote for that. The "strategic
voter" is faced with a choice, and makes it. And thus, supposedly,
the decision is made by that last voter who, the critics posit, was
really the same as the others, having a very slight difference in
preference, only reversed. The whole thing is preposterous. If those
are really some kind of sincere, absolute utilities, *it does not
matter which candidate wins,* it is almost the same. If you care,
vote strongly. If you don't care, you can vote however you like!
Also, if a candidate has little or no chance of winning, and this
candidate is neither the best nor the worst, you can vote however you
like. But -- don't vote so that if you were wrong, and the candidate
wins, you will regret it, and try not to vote so that if someone
worse than that candidate wins, and this candidate would have won if
you voted more strongly, you will regret it.
(If an election has two candidates, and Range Voting is allowed,
which means fractional votes are allowed, and voters decide to vote
fractional votes in the election, they are making partial
abstentions, they are saying, to some degree or other, "We don't
care." So if they say that, presumably, they will not complain if
someone who *does* care makes the decision.)
I'm approaching this from a theoretical standpoint, on the one hand,
and from a practical point of view, with respect to how people make
decisions, on the other. Smith has approached the study of voting
systems from another, using simulations. Generally, the results
agree. The work of Dhillon and Martens is known, and has seen some
quotation in the literature, almost entirely in the field of
economics, as far as I know.
It's true that if voters could vote what Smith has called "fully
sincere" utilities, that this would maximize overall "sincere
utility." Voting "strategically," where every voter shifts the
utilities to maximize their personal expectation, must, therefore,
lower overall satisfaction with the result.
Note that for this to be fully true, the utilities must be
commensurable and absolute (or all modified by the same factor from
absolute). This would be utterly insane and probably impossible in
real elections. The assumption is made, instead, that the possible
range of satisfaction of every voter is the same as for every other
voter, the utilities are normalized to fit into one full vote and,
usually, they are also truncated to the election set before being normalized.
By the kind of arguments Poole has presented -- and he's certainly
not alone -- I would be required, if I added the name of an obscure
candidate whom I personally consider to be the absolute best by far,
to lower the utilities of all the other candidates (except for the
worst, of course). And then, at the other end, I could dredge up a
truly bad, awful, horrible candidate, and thus would be forced, to
maintain my vote as sincere, to raise the votes of all the others.
Since these candidates aren't realistic possibilities, what I've done
is to, for no good reason except making a statement irrelevant to the
outcome of the election, weaken my vote.
As I've said, perhaps people who weaken their votes in that way
should be allowed to do just that, society can benefit from this. But
the ballot instructions will not say, "Vote sincerely." They will say, "Vote."
(It's simple with Approval, "Vote for any candidate you choose to
support for election. The candidate with the most votes will win."
But for various reasons, we may need more than pure Approval; people
want to express first preference, for example. Hence Bucklin may,
indeed be a way to go, or some other hybrid.)
Approval probably will function in public elections well enough that
the difference with higher resolution Range is academic.
----
Election-Methods mailing list - see http://electorama.com/em for list info
