At 10:36 PM 12/18/2008, Kevin Venzke wrote:
Hello,
--- En date de : Mar 16.12.08, Abd ul-Rahman
Lomax <a...@lomaxdesign.com> a écrit :
>However, in defense of Venzke, he thinks that the situations where IRV
>is non-monotonic are rare enough that it's not worth worrying about.
What I think would be rare is that such situations (or the risk of such
situations) would have any effect on voter behavior.
This is more true than false. However, this
judgment depends on voter ignorance or laziness,
when strategic voting would substantially improve
results. Further, eventually, we will see, I
predict, the norm to be that full ballot images
will be available. It's happening in San
Francisco with limited images. (The "images" are
ballot data summarized by the Opscan equipment,
so, for example, what is legally moot may have
been removed. I don't recall details, but certain
possibly interesting voting patterns have been
removed. (An example would be an overvote in a
second rank, with no third rank expressed; this
is indistinguishable, to my memory, from the same
overvote but with one of the candidates, or
another candidate, voted in the third rank. That
is a vote where a reasonable voter intention
could be deciphered, and even if the overvote
itself were not resolvable, a better estimate of
voter intentions as to the whole election could
be made. But at the least, the claim is made that
IRV leads to more ballot spoilage, or that it
presents more opportunities for voter error, at least....)
So, some big election shows monotonicity failure,
if some small set of voters had abstained, or
voted insincerely, they'd have gotten better
results. This is different from majority
criterion failure, a remote possibility and
arguably harmless possibility with approval
methods. This would, if discovered, create a
sense of illegitimacy in the election, and there
would be, in addition, two reasonably likely
outcomes: (1) the rejection of the voting reform
-- and increased suspicion regarding all voting
reform (in this situation, a majority might agree
that the result was poor) -- and (2) increased use of strategic voting.
The idea that voters won't vote strategically
misses a huge phenomenon: the use of vote cards
in Australia, where voting strategy is decided by
a political party, and then voters are advised. Many will follow this advice.
And, of course, there is truncation. And there
will be lots of truncation, unless full ranking
is required, and, not only is this unlikely to be
used in the U.S., it's been found
unconstitutional in the past. Full ranking was
required in the Oklahoma application of Bucklin,
and, contrary to what's been claimed or implied
-- the voting system aspect of it, aside from the
three-rank ballot -- wasn't an issue for the
Court rejecting the method. It was the obligatory
additional choice votes, when there where three
or more candidates. So voters cast first rank
votes, *and they weren't counted.*
>The real bite is with Center Squeeze.
I agree with this.
Thanks. You and me and nearly everyone who understands the issue.
> Highly speculative. Bucklin probably experiences about the
> same level of bullet voting due to LNH fears as IRV, not
> much more, because the "harm" only happens when a
> majority isn't found in the first round.
If methods typically won't require more than the top rank, then I guess
neither LNHarm nor monotonicity failures will be much of a problem.
With LNH, the "harm" is that the voter sees a
second preference candidate elected rather than
the first preference. In fact, in full-vote
methods (only Range is different), a single vote
never purely flips an election result, rather it
turns an election into a tie or a tie into an
election. Voter's won't be exercised about a rare
LNH failure. Most voters will bullet vote in a
situation where LNH is a real risk.
And, yes, methods in the U.S., at least, will not
require full ranking, and for very good reasons.
The Oklahoma case gave them in about 1926, as I
recall. Dove v. Ogleby. Full ranking forces
voters to vote for someone, effectively, whom
they may detest, striking at the heart of the
freedom of the voter. Democratic process only
"forces" this when there really is no
alternative, as agreed upon by a majority of
voters. They would rather see the office filled
by the Lizard than go vacant. In real democratic
process, election failure is always an option
that a majority can create -- or prevent.
Majority rule. Don't try this at home?
>In other words, Center Squeeze is a direct consequence of LNH compliance
>by IRV.
Well, MMPO satisfies LNHarm, and is nearly a Condorcet method.
I'd have to look at it. How does MMPO work? I
worry about "nearly," but, sure, if the exception
took extraordinarily rare conditions, and the
results then were merely suboptimal, not
disastrous.... I can imagine a method that
uncovers the votes and uses them to decide other
pairwise contests, but I'm suspicious of the claim.
>Interesting, eh? Top three. A Condorcet winner is almost certainly in
>there!
I think this is doubly likely if you arrange the incentives so that it's
likely that third place achieved that position better than randomly.
In other words: I want to have a TTR election where candidates risk being
spoilers if they place worse than third.
That would be a system where the candidate is
risking damage to the overall benefit of the
election. Did you mean to write it as you did? A
spoiler typically will drop the "spoiled" candidacy one rank, not two.
By the way, I'm seeing, now, some work done in
the last two decades on the Clarke tax or similar
devices to give voters "incentive" to vote
sincerely. However, it seems to me that under
this is an assumption that voters won't vote sincerely, naturally.
The trick is to consider that their votes are
some mixture of sincerity and "strategy," i.e.,
that the votes already take into account, for
some voters, what the voters sense as a
reasonable compromise. It seems that some of us
don't trust that voters are capable of doing this.
The "incentives" may be trying to fix something
that's not broken. We have *theory* that voters
will "exaggerate" and thereby cause damage, but
if we look at the simplest case, Approval, there
is no Approval vote that makes sense that is
actually "exaggeration." If two candidates are
true clones, setting one's approval cutoff
between them makes no sense, the voter would, by
definition, be equally satisfied with the
election of either and should therefore support both.
Sometimes at this point, it will be said, "But
the voter wants his or her favorite to win!" Of
course. That's a preference difference. The
candidates aren't clones, for that voter. The
voter is attached to one of them. The reason for
the attachment isn't our business!
I claim that Range is strategically the same as
Approval, simply with additional opportunities
for a deeper expression of preference strength.
We can assume, in Range, even though it may not
be exactly true, that voters who express some
preference strength in Range actually have a
preference. And that when they don't express a
preference, they do not consider the preference
significant enough to warrant wasting a vote or fraction of a vote on it.
There is some indication, from a paper in
progress by Warren Smith, that a mixture of
"fully sincere" and "strategic" voting in Range
produces less regret than either "strategy"
alone. If this is true, the whole concept of
"strategic voting" as some kind of negative must be examined.
In any case, a good voting system will not
produce poor results with "strategic voting," but
only, at most, results that have been mildly made
less than theoretically optimal. All of the
"nightmare scenarios" that I've seen presented
for "vulnerability to strategic voting" in Range
have been results where the "sincere voters" got a very, very good result!
The exception is Saari's "mediocre" election,
where the supposed "sincere voters" simply follow
a totally stupid strategy, a mindless
approval-above-the-mean strategy, when we all
know to avoid this in real life, we don't use
that strategy, unless modified by estimated probabilities.
The *theory* of oscillation or endless regression
based on feedback between polls and voter
decisions is just that, a theory. It probably
doesn't happen much, because there are other,
stronger forces. Ron Paul might have made a good
Republican candidate, but .... campaign funding
would have to be addressed! I think Paul
supporters could have overcome poll bias, the
only Range poll that I saw on this (MSNBC Range
2, with votes of -1, 0, +1, and a default vote of
0 -- nice method!) showed Paul way ahead, far
above the other Republicans. Even with
participation bias, this was impressive. Same
polls showed, at that time, Obama way ahead of
Clinton. And, as I recall, McCain was, aside from
Paul, the most approved Republican. I find that
really interesting.... I should look again.
Voters aren't going to look at every poll and
shift their voting decisions; many or most of
them will only look at a few. Did anyone need a
poll to know that the U.S. Presidential election
was between Obama and McCain? Or that, in later
Democratic primaries, it was between Clinton and Obama?
Sure, that makes us dependent on the media. So
new? So got any alternative? (I do, we should own
the media, collectively, and we could do it,
effectively. Nothing stopping us but inertia. It
would be a good investment, done right.
Alternative: we don't own the media, but we are
well advised as to which media to trust. Same
difference. I prefer the ownership, because,
then, there is no conflict of interest, we
wouldn't prefer bad advice to a small loss in
share value, except that the loss won't happen;
the more trustworthy we find the media, the more
useful it becomes, and thus the greater the value, including economic value.)
This places part of the election process outside of the election itself,
but we already do this with Plurality.
Yes. It's normal. We need to remember that voting
systems are a special solution to a special
problem: the difficulty of managing full
deliberative process when the scale is large. As
such, we should try to imitate deliberative
process, to the extent practical. Asset Voting is
a totally new idea that is actually old, but
which escaped notice, turning any election into a
deliberative process using chosen representatives
as distinct from elected ones.
Short of Asset, what Range does is to imitate
various participation strategies: strong
preferences tend to lead to strong negotiating
positions, even a pretense of "gotta have it."
I.e., bullet voting. Weaker preferences *or a
desire for overall satisfaction,* which is a
normal human behavior, to value social
satisfaction even above one's personal
satisfaction, provided the personal loss is
perceived as small compared to the overall social
gain, leads to full initial disclosure of accurate utilities.
The voting pattern reflects two things:
(1) Preference strength.
(2) How much effort the voter is willing to put
into being accurate, which is related to (1).
I.e., what we've been calling "strategic voting"
in Range may be more sincere than we realize! It
modifies the linear transformation of utilities
into votes, it becomes more sensitive to strong
preference and less sensitive to weak, but that
is not a bad result, necessarily.
And the most that's needed as a protection is a
majority approval requirement. Hence runoff forms
of Range. Voting systems theorists almost
completely missed this in the search for ideal
methods, because completing in one round was
considered essential. It's actually a severe and
unnecessary restriction; it simply has a cost,
and it's possible to keep that cost low, lower
than the value of the improved results, when runoffs are needed.
It's possible that a good Range method would so
rarely need a runoff, and would only choose
second-best in the presence of only a small
difference in social utility from that winner and
the best, that runoffs wouldn't be worth it. If
we had runoff Range operating, we could measure
this with real elections. Until then, we need more and better simulations.
We need simulations that will predict truncation.
We need simulations that will predict turnout.
The models don't have to be perfect, some
modelling is better than none. We know that, in a
runoff special election, the idea that runoff
turnout is always poor is false when voters have
a very strong preference, such as the Lizard v.
the Wizard or the similar Chirac v. Le Pen runoff
elections, where final turnout exceeded that of
the primary. The reverse should be true: low
preference strength equals low turnout in runoff
election *and that is not a bad thing.*
So many false or weak assumptions, so little time!
>From the first message:
> "Frontrunner strategy" is a common one that seems
> to help with ranked methods as well as Range ones. Make sure
> you cast a maximally effective vote for a frontrunner, and,
> where "against" matters, against the worst one.
> Usually there are only two frontrunners, so it's easy.
> "Expectation" is actually tricky if one
> doesn't have knowledge of the electorate's general
> response to the present election situation. How do you
> determine "expectation." Mean utility of the
> candidates is totally naive and non-optimal.
Mean utility is supposed to be naive, and it is optimal, if you are
"naive" about win odds.
I know that this (mean voting strategy in
Approval) has been proposed, but it's a poor
model. A voter who is "naive" about win odds is a
voter who is so out of touch with the real world
that we must wonder about the depth of the
voter's judgment of the candidates themselves!
This naive voter has no idea if the voter's own
preferences are normal, or completely isolated
from those of other voters. This is far, far from
a typical voter, and imagining that most voters
will follow this naive strategy is ... quite a stretch, don't you think?
Instead, most voters will, in fact, assume that
their own preference are reasonably normal, and
this will indicate a far different strategy to
them than mean utility. They will bullet vote, in
the presence of significant preference between
the favorite and other candidates, *and this is
known to happen*, even when voting systems give
them other options. The exception will be when
the preference is low. Making that call can be a
difficult choice. Did we claim that voters should
only be presented with easy choices?
Other voters will know that they have unusual or
idiosyncratic preferences, and they will vote accordingly.
So in Saari's example, the supposed "nutty" voter
is the only one out of 10,000 voters who votes a
reasonable strategy! -- he or she approves the
supposedly "mediocre" candidate. If this voter
had voted the "I'm normal strategy," there would
have been a tie between Best and Mediocre --
because this is how all of the 9,999 other voters
voted. Saari should have been so thoroughly
discredited by that paper, "Is Approval Voting an
Unmitigated Evil," that he'd have had trouble getting anything else published.
Smith claims that Saari is right on in many ways,
and that sometimes he writes much better. Maybe.
All I know is that in that particular paper,
which is almost entirely polemic without solid
foundation, he went way outside academic norms and standards.
"Better than expectation" is mean *weighted* utility. You weight the
utilities by the expected odds that each candidate will win. (There is
an assumption in there about these odds being proportional to the odds
that your vote can break a tie.)
Sure. That's the correct understanding of "mean
utility." It means a reasonable expectation of
the outcome. However, what's incorrect is
assuming that voters have no idea of the probably votes of others.
Being human, each voter is a sample human, and
more likely to represent the views of other
humans than not. This is a far more accurate
model of human behavior than the assumption that
candidate preferences are random, which only
would be true in a simulation that assigns the
preferences that way. Voters are members of
society, and not independent in the sense that
their choices can't be predicted, with some level
of accuracy, by those of a sample, even a sample as small as one voter.
By this argument, the rational vote,
zero-knowledge, is the bullet vote. This happens
to be the vote that has the best probability of
favorably affecting the outcome (i.e., if the
voter is the last voter). We've done it
backwards. The default vote should be a bullet
vote, and only in the presence of significant
strategic considerations should the voter deviate from that.
Now, if the voter has low preference between two
candidates, one of them the favorite, when the
preference strength is low enough, the voter may
indeed approve both of them. But this is far from
Saari's example, where the middle candidate was
equally placed between the best and worst
("mediocre"), not "almost as good as the best."
Or if the voter has some sense of the other
voters that leads the voter to conclude that the
voter's personal preferences don't reflect the
overall ones, then the voter will consider strategy to address that situation.
And for the voter's sample to be only one voter
would require that the voter doesn't discuss the
election with anyone! Indeed, because birds of a
feather flock together, voters are quite likely
to have a biased view of the overall preferences,
tending toward bullet voting, again.
So most voters, we can think, under current
conditions, will bullet vote. Fantasies that
large numbers will approve mediocre candidates
based on a stupid strategy is just that: a
fantasy, an example of how naive game theory can
fall flat on its face. Won't happen. Bullet Voting *will* happen.
"Frontrunner strategy" is just a special case of "better than
expectation," where only two candidates are expected to have any chance
of winning.
Sure. There remains the issue of how to rate a
middle candidate. I think that the "mean
strategy" overlooks other factors, including what
might be called "absolute approval." I.e., if I
absolutely disapprove of a candidate -- never
mind the other options -- in that I would not
want it to be in my history that I voted for him
or her, I won't, no matter what the math tells
me. I'll listen to my gut instead of the math,
because it's more likely, in fact, that the math
is wrong than that the gut is wrong. The "gut"
was developed over millions of years of
evolution, where making wrong decisions was life
or death, or starvation or nutrition, and the
math is how old? The "gut" does use math, in a
sense, Warren is right. But it's VNM utilities, probably, that it follows.
> But it's a complex issue. My point is that "better
> than expectation" has been taken to mean "average
> of the candidates," which is poor strategy, any wonder
> that it comes up with mediocre results?
"Average of the candidates" is the special case of "better than
expectation," where there is no information on candidates' win odds.
Which is a non-existent situation, unless you
posit radically artificial conditions. "No idea
of probable outcomes" is rare in the real world,
it mostly crops up with gambling, where random
choice is artificially created. And, indeed, we
can make bad decisions under those conditions,
assuming, as would be natural and generally
correct, dealing with nature, that we can improve
our performance the more we play the game!
What I'm pointing out is that the voter's
knowledge of himself or herself is adequate for a
better default "zero-knowledge" strategy than "mean utility of the candidates."
In Range, i.e., Range N with N>1, I'd rate,
candidates, "sincerely," i.e., with reasonable
accuracy, but with some bias towards approval
strategy, perhaps. I.e., the transform from
utilities to range votes might be linear, except
that the transformation is truncated, possibly at
the top and bottom. In particular, I'd be
unlikely to give candidates I'd not like to see
win the election, purely on their own, any positive rating at all.
But we overlook, in these analyses, that most
voters don't know enough to "sincerely rate" all
the candidates. As Carroll noticed, most voters
may know their favorite, maybe their favorite's
main opponents, and that's it. So what do you do,
how do you vote, when you don't recognize the candidate?
Naively, Warren Smith thinks you might abstain,
and he wants to see average Range rather than sum
of votes range (Sum of votes range usually treats
an abstention as a bottom rating, though it could
be, for example, midrange, as it was in the MSNBC polls.)
However, only voting for candidates I recognize
and approving the best of these and not the
worst, is a kind of frontrunner strategy, for the
best-known candidates tend to be the
frontrunners. I may only know one candidate
(Carroll's realization), my favorite. Bullet
voting is my response, as it should be.
What we have done, too often, is to study voting
systems through their theoretical performance in
preposterously rare situations. As I've written
many times, a very common objection to Approval
Voting, including among experts, is Majority
Criterion failure. Yet MC failure with Approval
is, in the vast majority of real political
elections, highly unlikely, because of the
preponderance of bullet voting, and when it
happens, it's hardly a disaster (only if the
majority were drastically misinformed about
themselves would it be a mediocre result). (By
definition, the supporters of frontrunners when
there are only two, have no incentive to add
additional approvals unless they don't mind that
these votes, by some miracle, elect a minor party
candidate. So bullet voting when the voters are
voting for a frontrunner can be expected, it
would be the norm. It's only when voters prefer a
minor party candidate that we will see an
increase in the usage of additional votes, and
this is true for optional ranked systems. I
should look at the Australian OPV data, but the
reported data doesn't show truncation in votes
for the top two. I do know that ballot exhaustion
is *common* with OPV, which would mean bullet
voters who *don't* vote for a frontrunner.
We have to realize this: many or most voters will
ordinarily vote for one candidate, and habit
isn't the only cause for this, it is probably
better strategy for the majority of voters than a
naive "mean of the candidates."
And, of course, we can then see Saari's example
as the piece of preposterousness that it is. If
two voters out of 9,999 vote this very common
strategy -- under Plurality, where it's costly if
wrong! --, which we have every reason to think
will be normal, certainly not rare, the Best wins.
> > The big concern is what happens when poll stability
> can't be achieved.
>
> Nah! Most voters won't pay that much attention to
> polls, they will just vote their gut. Polls will be used by
> those who are very seriously involved, who want to maximize
> the power of their vote. I think most of the "big
> concern" is simply imagination. There won't be big
> surprises with Approval. Little ones, sure.
I use the term "polls" loosely. It is hard to imagine that under any
election method, voters in this recent election might not have realized
that the important contest was McCain vs. Obama.
And I can't think of an exception. Probably the
closest would have been Ross Perot. Some people
may have voted for him thinking he could win. But
I think most realized exactly what they were
doing. They simply didn't have enough preference
between Bush Sr. and Clinton to make it
worthwhile to them to drop the value of the statement of a vote for Perot.
To emphasize this, we have been diverted by the
idea that "strategic voting" is a bad thing,
instead of looking at what's underneath the hood:
preference strength. If you don't have
significant preference strength involved, you
don't bother with utility maximization, you don't
care enough even if you are *certain* that it
will be A or B, you'd rather vote for C for other
reasons. In a preferential method, *some* of you
will vote for A or B. Some won't. How many of
each? *Depends on preference strength.*
The idea that preference strength was useless,
the easy rejection of it because it wasn't
"practical," the claim that "voters will
exaggerate," all this diverted us from this large
gray pachyderm in our main living space.
Preference strength drives voter behavior, and
preference strength is behind voter turnout
(particularly in special elections), and how voters choose to vote.
If voters "vote their gut" and don't consciously use any strategy, I'd
say this will be well beyond the point where polls have already taken
their toll and removed unviable candidates from the voters'
consciousness.
But it happens without polls! That a candidate
isn't "in the voter's consciousness" is the worst
nightmare of campaign managers. "Bad publicity is better than no publicity."
Consider this: in real IRV elections, nonpartisan
is important, vote transfers seem to behave,
where I've looked, as if the supporters of an
eliminated candidate are a representative sample
of all the other voters, i.e., their lower preferences will match, generally.
I was astonished to see this, in fact, it was a
totally unexpected result. But if you think about
it, it makes a great deal of sense. In
nonpartisan elections, there isn't some automatic
means for voters to connect candidates. It's easy
for a Green Party supporter to assume that a
Democrat will be a better choice than a
Republican. Take the party markers away, what's left?
The candidates themselves, and the combination of
their character as viewed by the public, to some
degree their policies, and how well they are known.
For whatever reason, the vote transfers tend to
not alter the social order among the remaining
candidates, so the first round leader wins the
election. No exception, so far, in nonpartisan
IRV elections in the U.S. -- which is the large
bulk of nonpartisan elections. It's quite
different with Top Two Runoff, where the
runner-up wins the runoff in about one-third of
elections. At this point, the sample size is
small enough that this could be some statistical
fluke. But it's actually a known effect in
Australia. "Comeback elections" remain relatively
rare, even with partisan elections (which the
Australian PV elections are), and it is
practically unknown (totally? as I recall, maybe
one or two elections in the last century?) for
the first round third place candidate to win.
Using Approval isn't going to magically increase
the voter awareness for minor candidates! The
only system I know of that gives these candidates
a real chance, except under quite unusual
circumstances, some sea change, is Top Two
Runoff, which better simulates deliberative
process. So ... we should be following that clue.
Require a majority approve a result, *at least*
for an election to be decided on the first
ballot. Use better methods for discovering a
majority if one can be found in the votes, i.e.,
use Bucklin or a Condorcet method instead of IRV,
and better methods of picking what happens in the
runoff. I've been making Range/Condorcet hybrid
proposals. Asset, though, finesses the whole
mess. One election to pick the electors, and the
electors handle the rest, and can use as many
ballots as they choose. With public voters, the
whole secret ballot/security/counting expense thing goes away.
I absolutely want voters to pay attention to polls, because if they don't,
this is probably the same as the polls being unable to stabilize around
two frontrunners. And the results of such elections would be rather
arbitrary, I would guess.
Only when preference strengths are small! Give me
a large enough preference strength, I don't give
a fig about polls! And I think that's true of most voters.
So the "oscillation," the lack of stability, will
only take place when the choice isn't terribly
important to most voters. Like most voters, I'd
guess, in this last Presidential election, what
was most important to me was that a Democrat win.
I.e., I had *intrinsic* low preference among the
major Democratic candidates, I'd have supported
any of them. I came to favor Obama, early on, but
for a combination of electability and an
assessment of him as a person. Clinton had -- as
the MSNBC polls showed -- too many negatives, not
so much personally, but as to electability.
Please don't give me an open primary, the IRV
supporters' suggestions that IRV could replace
primaries and general elections with a single
ballot is very, very dangerous. Range might do
it, but I'd *insist* on a true majority approving the winner.
> In plurality
> Approval, strategy based on polls would loom larger. Sure,
> it could oscillate. But how large would the osciallations
> be?
The only situation I'm concerned about is where, when the polls report
that A and B are the frontrunners, this causes voters to shift their
approvals so that the frontrunners change, and when the polls report
this, the voters react again, etc., etc.
Of course. Except it's not going to happen.
Voters will overstate their tendency to bullet
vote in the polls. Voters will only approve more
than one when they have lower than a certain
threshold of preference strength, and even there,
it's questionable how much they will do it unless
they really have no significant preference, it's
hard for them to state a preference between two, so they approve both.
Further, the results don't shift the way you seem
to expect. A and B are the frontrunners, a poll
shows. How do voters respond? One common response
would be no response. Then there are the
supporters of C. They get this news, they now
plan to add a vote for A or B, from their prior bullet vote for C.
There is only one class of voter who will shift
their vote: those who already preferred a
frontrunner, but who, in ignorance of this
situation, already approved both. You have to
understand that this is an unusual situation, in
itself. Most voters in early polls will bullet
vote, unless preference strength is low, and if
preference strength is low, they aren't likely to
stop approving both. But voters who did vote like
this may raise their approval cutoff to reflect
how they probably should have voted in the first place!
Sure, it could oscillate. But only if most voters
have low preference between A and B. In which
case it doesn't matter that much who wins! Sure,
the choice would then be somewhat arbitrary. This
is Approval, after all, the terminally simple
Range 1. It's like a control mechanism with only
two motor speeds: Off or Full-On. Such systems
will oscillate under some conditions,
oversteering. In Range, even Range 2, the
response is damped. If, in an initial poll, I
rated Obama 1 and Clinton 1 -- our unusual
situation, I wouldn't have done that in reality
-- I'd not drop Clinton to -1 if a poll showed
them running neck and neck, I'd have dropped her
to 0.5. Now, in reality, I did, in fact, rate
Clinton at 0 -- midrange -- in the MSNBC poll.
And finding out that they were running neck and
neck, I don't think it would have shifted my
rating at all. (Remember, I've got other
candidates rated too, some at 1 or 0.5, some at
zero, this was a "primary poll," not for the
election itself.) Allowing intermediate responses
will reduce oscillation. The idea that everyone
is going to want to go full-on for their favorite
against everyone else is just as preposterous as
the idea that everyone will add additional preferences.
Instead, even with Approval, the results are
damped, through averaging. People aren't the
same, will respond differently, so the average
Approval votes will tend toward Range results.
(Like an analog to digital converter that
collects a lot of 0s and 1s based on a comparator
output, where the voltage of interest is compared
with either a random voltage in some range or is
swept. Either way, if the random distribution is
correct, the sum of outputs of the comparator
will vary quasi-linearly with the analog voltage
being studied even though all the "votes" are binary.
In other words, when we study Approval using
limited examples that assume large numbers of
voters voting identically, and switching their
votes identically, we get a much poorer image of
the method than some simulation that imitates the
varying underlying utilities and approval
cutoffs, the latter being a process of feedback,
of interaction between absolute utilities and
their probability-modified VNM versions.
This process is part of how a participating
electorate seeks and finds compromise. It's much
better than raw voting system theory might
predict. It considers and measures preference
strength, not directly, but through the outputs, the votes.
Obviously it wouldn't be as
neat as that (in my simulation, not everyone is allowed to change their
vote at the same time; they receive random opportunities). But I guess
the result is that there would ultimately be more than two frontrunners
in the voters' consciousness.
Actually, in real elections, there may be only
one. The incumbent advantage is a real one, and
difficult to overcome, and it's not even clear
that it *should* be overcome. I prefer Asset,
though, because it bypasses the whole can of
worms. Vote for your favorite, period. Don't
trust your favorite to carry on in your place?
Why, then, are you voting for such an
untrustworthy person? The qualification for
office *generally* implies qualification for
delegating responsibility and authority. I.e.,
for choosing who will hold the office. Real
officeholders, especially major offices, must be
able to delegate authority; someone very good at
the office, as to what they *personally* do, but
who doesn't know whom to trust, can be a
disaster, vulnerable to unscrupulous staff or
associates. So the only reason that I can think
of that one would vote for someone considered
untrustworthy is a system that doesn't allow
voting for the true favorite; the "favorite" in
this case is a lesser evil, not actually trusted.
And if the voter has *nobody* whom the voter can
trust, given the vast freedom in a mature Asset
system, well, there are two responses, and, beyond that, TANSTAAFL.
(1) Adjust medication.
(2) Register as an elector and vote for yourself.
> And, in the end, the winner is the candidate accepted by
> the most voters.
But when one (such as myself, and I think also you) portrays Approval as
a strategy game, under which "sincerity" is a red herring, a statement
like the above falls very flat. What does it mean to be "accepted" by the
most voters?
It means that the voters literally "accepted" --
which is an *action*, not a sentiment, sincerity
has practically nothing to do with it -- the candidate.
It's possible to have a Range system where the
voter specifies a value that is an approval
cutoff. So the voter could vote with total
sincerity, accurately representing preferences.
The approval cutoff is a separate decision, and
that cutoff is *always* a strategic decision. You
are offered $159,000 for your house. Do you
accept? You answer will depend on what you think
you can get, you will generally approve better
than your expectation, and not approve what is
below your expectation. Expectation, not
"desire." It's pure judgment, or should be!
Approval is *partly* a strategy game, but not
entirely. The same is true for Range. We may
assume, with Range, for example, that all
expressed preferences are sincere. (Exceptions
would be rare, largely moot). So "preference
expression" is sincere in both Approval and
Range. The "game" aspect has to do with where to
set the approval cutoff. With Range, and in
particular with hi-res Range, we can treat a
rating of 100% as indicating a favorite, or a
candidate so close to the favorite that there is
no difference worth considering, because the
strategic value of voting 100 vs. 99 is so low
that we might as well forget about it. (And it's
possible to have preference markers in Range
where voters can indicate pure preference or
precedence within a rating. There are actually
some simple, practical possibilities for doing
this. I just don't think that those markers are
necessary once the range resolution is high enough.)
Kevin, you've neglected this: the votes in Range
and Approval reflect both sincerity and strategy,
a mix. You can infer certain preferences from
them, and those inferences will generally be
accurate. The strategic part has to do with what
the voter is concealing as to preference, or
simply not disclosing. We don't know if this is strategic or accurate.
Call it Later No Harm! It's the same idea,
really. The voter isn't disclosing certain
preferences, for whatever reason. Do we want
preference disclosure to be cost-free? I'd
suggest that this is not a good idea, it
introduces noise into the system more than it
increases information. Remember, the big concern
about Range is supposed to be "vulnerable to
strategy." Behind this is an assumption that
"exaggerating" is insincere, since, supposedly,
it's cost-free. But it isn't cost-free, unless it's moot!
In a three-way election, approval A and B against
C, you've just abstained from the AB election, in
favor of defeating C. There was a cost to the
"exaggeration," if that is what it was. There is
a cost either way, but .... when the number of
voters is small, it turns out, the optimal
strategy is the bullet vote. The incremental
utility gets smaller and smaller as the number of
voters increases (and this is relative utility,
with the assumption that the vote affects the
result, so this effect is compounded by the
increasing rarity of ties and near-ties), but it
never disappears. That optimal strategy is such
when the middle candidate has an exact middle
utility. I've not studied the other cases. But my
sense is that as the middle utility moves toward
A, the optimal vote moves toward double Approval.
Has to be, I'd think, because if the utility gap
goes to zero, the optimal vote is obviously
double Approval, 100% guarantee of no regret over the vote.
Another example, by the way, of how "mean
candidate" is a bad Approval zero-knowledge
strategy. It has to be probability modified, and
the voter's own preference *must* be considered
to weight the probability, since the voter is a
member of the electorate, and if all other voters
are unknown, we still have a net vote weighted,
by one vote, toward our voter's position.
If candidates were at least obtaining majority approval, I could be
content with the statement. But if no one obtains a majority, offering as
consolation that the most "accepted" candidate won is not much more
comforting under Approval than under Plurality.
This is an argument for requiring a majority,
isn't it? Sure. However, suppose there is some
other threshold than "more than half" of the
ballots approving. Set this threshold at X.
Whatever X is, that one candidate exceeds it with
a greater margin is "more comforting" *on
average* than that, say, the other candidate be
chosen. Absolutely, this might not be much
improvement. Take the California gubernatorial
election with its bizarre number of candidates.
Make it approval. (not a bad idea, actually,
certainly better than what they did!). If the
winner has 17% of the vote, whereas with
Plurality it would have been 15%, sure, not very comforting.
Plurality is an anomaly. No business may be
decided, in deliberative process, with less than
a majority, of those voting, voting for it.
"Voting for it" is "accepting it." Using Approval
Voting doesn't change that one bit. So Plurality
voting has only to do with multiple-choice
questions, and is only used where it is
impractical to use repeated balloting, and this
has been specified in the bylaws.
I consider, it should be made clear, requiring a
majority to be so important that I'd not replace
Top Two Runoff, with all its defects, with
Approval Voting. Instead, I'd suggest: use
Approval or other method, such as Bucklin or
Range with specified approval cutoff, for the
primary, reducing the need for runoffs.
And Top Two Runoff is much better than we have
thought, particularly if write-in votes are
allowed in the runoff, and it gets even better if
advanced methods are used in the primary and runoff.
Bucklin runoff with write-ins allowed, two-rank,
totally cool. Easy to count. Sure, if voters
bullet vote for the write-in, there could easily
be majority failure. No limited-ballot system is
going to be perfect, Range and hybrid methods just get as close as is possible.
But who is likely to bullet vote for a write-in
in a runoff election between the top two
candidates from the first ballot? One of those
candidates was, say, the Range winner, and one is
a Condorcet winner if different -- or there was
no Condorcet winner beating a Range winner, so
it's top two Range, nobody having gained a
majority. Bucklin would allow voters limited LNH
protection: vote for a favored write-in, then for
the favored candidate on the ballot. Wouldn't you?
(I.e., if you thought that somehow something went
wrong with the first election, the best candidate
got eliminated, which would be vanishingly rare
with a Range/Condorcet runoff system, or everyone
got low approval so a new campaign is needed, you
can still mount a write-in campaign without
spoiling the election. There haven't *really*
been any eliminations, only restricted ballot
position, thus the method gets closer to pure
deliberative process, where no possible
compromise is every ruled out until a final decision has been made.)
> It's not going to be a terrible result,
> if Approval falls flat on its face, it elects a mediocre
> candidate because the voters didn't get the strategy
> right.
Well, what is a "terrible result" after all? It seems to me you don't
have to be too picky to find methods that only fail by electing mediocre
candidates.
When ranked methods fail, they can fail
spectacularly, and with sincere votes. It gets
unusual, to be sure, with better ranked methods
(it may be as high as 10% failure with IRV, under
nonpartisan conditions, but most of those
failures will also be of minor effect.)
I really shouldn't have written "mediocre."
Rather, Approval can elect a "less controversial"
candidate, which perhaps many or even most of the
voters would judge a "more mediocre" result than
the best candidate, were all the preferences
accurately known. Saari used "mediocre" to refer
to a candidate with mean utility between the best
and worst, as seen by the vast majority of
voters. It's correct, that would be a "mediocre"
winner. Better than the worst case for ranked methods.
(Or, perhaps I should say, "some ranked methods."
Borda, for starters, looks like a ranked method
but is more accurately a ratings method with a
highly restricted way of expressing the ratings.
I'm not familiar with *how bad* Condorcet methods
can fail. Generally, with reasonable
distributions of candidates, the difference
between a Condorcet winner and a Range winner are
small. So I've had in mind a method like IRV,
where the winner could be opposed by two-thirds
of the voters, and that could be a maximally
strong preference -- they will revolt! -- and
that's with sincere votes. Strategic voting
could, indeed, improve the results.)
> What type of voter is bad for Approval? Easy compromiser or
> tough bullet voter?
The type of voter who is willing to cast a suboptimal vote due to
principle. It is harmful under Plurality and here is a situation where
it would be harmful under Approval.
What does that mean?
Here is what I get from it. The Nader voter cast
a supposedly "suboptimal vote" under Plurality.
For principle, i.e., the importance of voting for
the best candidate, in one's opinion.
Is that the meaning? But who are we to say that
this vote was suboptimal? Remember, the campaign
rhetoric, by Nader, was that it didn't matter who
won, Bush or Gore, they were both totally in the
pocket of the large corporations. So why can't we
just assume that the voter made an *optimal*
decision? From the voter's perspective.
Or does this mean the voter who supports Nader,
but who *does* have a reasonably strong
preference between Gore and Nader, and decides to vote that?
Note that these situations apply to Approval.
Both scenarios will happen with Approval just as
with Plurality. In the first situation, i.e.,
Nader is believed, there is no incentive to add a vote for Gore or Bush.
(We presume that the Nader voter would vote for
Gore, but if there is no difference, why one over
the other? And if there is a difference, why in
the world does the voter prefer Nader, who has
just tried to feed him some nonsense? A believe
that all politicians, including Nader, are going
to lie? That, my friends, is why the American
electorate voted in large numbers for Bush, when
they knew he was lying. They all lie, after all,
so why not vote for the one who tells you the
lies you want to hear, since he'll perhaps feel
some need to follow up on *some* of those
promises, more than the other guy, who if he does
what he says he will do, you won't like it.)
In Approval, the second situation doesn't create
a big conflict, that's the improvement. With
Bucklin, the remaining conflict is resolved, the
voter can vote first preference and then indicate
alternate choices. But, still, voters, including
minor party supporters, will bullet vote, some
percentage of them. And almost all those who
truly prefer a major candidate will bullet vote.
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