At 12:56 AM 12/21/2008, Kevin Venzke wrote:
--- En date de : Ven 19.12.08, Abd ul-Rahman
Lomax <[email protected]> a écrit :
[starts with Venzke, then my response, then his]
> > 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!
I can't understand what you're criticizing. It is the zero-info strategy.
You seem to be attacking this strategy by attacking the voters who would
have to use it. That doesn't mean that those voters wouldn't have to use
it.
Yes, that is *a* zero-knowledge strategy that
misses something. A voter with no knowledge about
other voters is a very strange and unusual
animal. I'm saying that the *strategy* is a
stupid one, and that real voters are much smarter
than that. Voters have knowledge of each other,
generally. Positing that they have sufficient
knowledge of the candidates to have sufficient
preference to even vote -- I don't vote if I
don't recognize any of the candidates or
knowledge of whom to prefer -- but they don't
have *any* knowledge of the likely response of
others to those candidates, is positing a
practically impossible situation. Yet this is the
"zero-knowledge" assumption. In this sense,
"zero-knowledge" doesn't exist, it's an oxymoron.
I'm a human being. My response to a collection of
candidates is a human response. My response will
*resemble* that of other voters if we live in the
same society. It won't be the same, but, I'm
contending, assuming that my response is
more-or-less typical is a very good starting
position. In other words, one of the things that
I should consider in a zero-knowledge situation,
in any voting situation, is what will happen if
everyone thinks like me! This enables me to avoid
Saari's "mediocre" election, for starters. Now,
take this to an extreme, how will I vote? I will
vote in a manner that will do no harm if everyone
thinks like me, so, if the method is Range, I
will express a significant preference if that's
possible. I *won't* vote as if the other voters
were random robots picking from among the
candidates randomly. However, I will also assume
that there is *some* variation between my opinion and that of other voters.
Most voters, in fact, have a fairly accurate
knowledge of the rough response of the overall
electorate to a set of candidates, provided they
know the candidates. Those on the left know that
they are on the left, and that the "average
voter" is therefore to their right. And vice
versa. Those near the middle think of themselves
as, again, in the middle somewhere.
We know this *generically*, we don't have to look
at polls, and we will mistrust polls which
strongly violate our assumptions. Essentially, we
can't be fooled quite as easily as that.
The most common Approval Vote will be a bullet
vote. How much "knowledge" does that take?
This is why runoff voting is so important, why
the need for runoffs doesn't disappear by using
an advanced voting system in the primary. What
happens when voters don't have sufficient
knowledge to make compromises is that they don't.
They bullet vote. And if enough of them do this,
and there are enough candidates attracting these
votes, there will be majority failure. No matter
what the system, as long as the system insists on
a majority to award the win. Better informed
voters, which means that they know more about the
candidates *and* they know more about the social
preference order and the preference strengths
involved, will cause them to make more
compromises. "Strategic voting." Very functional,
very helpful strategic voting, essential to democratic process.
If the method is Approval, they will lower their
approval cutoff as necessary, as they see
appropriate, so we would start to see additional
approvals. Bucklin in a runoff would allow them
to maintain their sincere preferences, but also
open the door to compromise. Bucklin, indeed, is
more likely to find a majority, probably, than
IRV, in a nonpartisan election, because it does count all the votes.
> 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?
I don't know of anyone who said that voters would follow this strategy
in a public election.
It's been implied that the scenario is somehow
realistic. If there is no possibility that a
scenario could occur in a real election, then
considering it as a criticism of the method is ivory-tower thinking.
Mean utility of the candidates strategy has been
proposed by Approval supporters, but unless the
utilities are modified by expectations, it's a
terrible strategy, bullet voting is better, probably.
But even better is to make some assumptions about
the overall voter responses to the candidates,
based on one's own -- I'm still assuming a
"relatively zero knowledge" situation -- and vote
accordingly. If my preference for A over B is
small, I might assume that variation between my
position and that of the majority could mean that
the social preference order is reversed from
mine. The real issue comes up like this, in a 3-candidate election:
I prefer A>B>C. B is in the middle, in terms of
my own satisfaction. This is Saari's "mediocre
candidate." What is the risk that C, whom I really don't like, could win?
This is where I need to have *some* idea of the
other voters. But in most situations, with B in
the middle, even if B is a little above middle
utility (thus "mean strategy" would indicate that
I vote for both A and B), for most voters, it's
unlikely that C could win. Only if I recognize
that my own position is idiosyncratic does this
additional knowledge suggest that the risk is
real and worrisome. This is the situation where
I'd also approve B. This isn't true for most
voters; if a voter is "average," the voter's
personal opinion is a quite clear indication of
the result. If an average voter has those
utilities, for C to win requires overcoming two
preference reversals. It doesn't happen beyond
very, very rarely (with a good method).
With IRV, not a particularly good method, the
third candidate in first preference votes *never*
makes it to win after transfers. (There might
have been a very few exceptions in Australian
elections, I'm not sure if I remember that there
were none, or none since something like sixty
years ago.) Now, that's a two--party situation,
really. So it might be distorted some, the more
general case, it might happen. (It *should*
happen with a good system, that third candidate could be the Condorcet winner.)
As my preference strength between A and B
decreases, the likelihood that I will approve
both increases. At some point, I really don't
care significantly which one wins and I *will*
approve both. Many voters making this decision,
with various levels of knowledge and preference
strengths, will tend to average out to a closer
estimate of social preference order than any
individual estimate is likely to show.
> > "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.
Ok, but I have never done that. "Better than expectation" strategy
does not really depend on ignorance of other voters' intentions.
"Better than expectation strategy" is sound.
"Better than mean of the candidates" isn't. But
this is inherently a "strategy."
Nevertheless, one point should be totally clear:
every preference expressed in Approval and in
Range can be taken as sincere, and this
information, which *optionally* includes some
kind of expressed preference strength information
-- in Range only -- allows the determination of a
social order that satisfies basic voting systems
criteria. Never does it, under realistic
conditions, involve reversing preference,
indicating a preference where the reverse is
true. All that happens is that some preferences
are more strongly expressed than others. We
cannot assume that expressed preferences are
linear, unless we use some kind of auction
system. Range, however, with any resolution (this
includes Approval) places a constraint on the
preference strengths expressed: they must add up
to 1 full vote. One full *vote*, not one full
range of possible sincere utilities. The votes
are *choices*, not necessarily raw utilities.
Dhillon and Mertens consider them as investments
in lotteries, if I've got it right. From those
investments we extract certain information, and
it happens that the extraction is simple: count
all the votes and add them up....
> 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.
But when this argument is accepted, the situation isn't zero-knowledge
anymore.
That's right. Zero-knowledge is, in effect, an
oxymoron, since the voter is a voter and therefore a sample of the electorate.
I don't agree with myself, by the way. The bullet
vote is not the only rational vote, I didn't give
the exception: when preference strength is
sufficiently low, combined with strong preference
against another candidate, or the voter
anticipates that the voter's own position is
idiosyncratic in a way known to the voter, the
voter may approve an additional candidate, or may
even vote antiplurality. But that isn't the norm.
Note that we can have, say, two-thirds of the
voters in IRV bullet voting *and we will never
know* -- unless we inspect the actual ballots or
images of them. Bullet voting is normal if one
supports a frontrunner, which in most elections, the average voter will do.
Basic rule for Approval: don't approve a
candidate if you'd be displeased if your vote
elected that candidate! And demand that voting
systems require a majority. That protects you in
most situations; then, fallback rule: if your
preference strength between your favorite and the
second best is low, you would *still* be *quite
pleased* to see this second-best candidate win,
then also approve that candidate. You are unlikely to regret it *much*!
But Bucklin lets you have your cake and eat it
too. Your lower preference won't prevent your
first preference vote from helping your favorite
win, unless there is majority failure. Then your
second preference vote becomes an additional
approval. Thus if a majority of voters think like
you, your favorite will win. Your second
preference vote has done no harm. Whether or not
you need to add it, though, depends on what's
there besides the two. If there is a third
candidate you judge has some possibility of
winning, but is much less preferred, then the
second preference vote becomes reasonable insurance.
I've been realizing that Bucklin allowed three
ranks, and one could reserve the insurance for
the third round. The risk in that is that the
worst candidate gains a majority in the second
round, and that your vote would have caused a tie
in that round, and thus a 50% chance of winning.
(Ultimately, I'd want to see Range incorporated
in a Bucklin method.... and Range roughly doubles
the expectation that a vote will improve the
result. A single vote in Range can move a loss to
a win, it takes two votes or a coin flip in full-vote methods.;
According to "better than expectation" strategy, if e.g. the two
frontrunners are expected to have 50% odds of winning each, then for
the middle candidates, you must approve those who are better than the
average utility of the two frontrunners.
Voters don't like being told what they "must" do.....
There are other considerations for voting that
don't have to do with winning the election. Votes
for non-frontrunners are generally moot, so they
would tend to be some simple expression of
feeling about those candidates. The voter can
sensibly place the approval cutoff anywhere in
the middle, in this case. Do you want to
encourage that candidate or a party involved?
Vote for the candidate. If not, don't.
I wouldn't even *think* of some kind of average.
> 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.
I don't think "mean strategy" overlooks that factor (unless you just
mean that real voters won't stick to effective strategy). I would rather
say that the numbers have been filled in incorrectly, when the result
doesn't agree with one's gut. (This is subject to the assumption that
the voter is trying to vote optimally.)
"Effective strategy" refers to strategy focused
on optimal results from the election. But voters
have other considerations that are important to
them. Sincerity, for example. I've spent a lot of
words arguing that "sincerity" is a problematic
concept, but in the ordinary sense it has a great
deal of meaning. Other things being equal, voters
will vote as some kind of sincere expression. And
votes for non-frontrunners are quite free, there
need be little or no "strategy" to consider, all
the necessary strategy has been managed in
determining who the frontrunners are. If one
cares. Otherwise, vote for the favorite, and
anyone else considered almost as good, maybe, and leave it at that....
Again, with real runoffs, a final decision is
left for the runoff, when the voter will have far
better information about the candidates *and* the
position of the rest of the electorate. The
French voters knew pretty well what Le Pen's real
support was, though they *worried* that they
might be wrong, and they wanted to make very,
very sure that Le Pen wasn't elected or that,
even, he might get a large chunk of the vote,
which they felt would reflect poorly on France.
Essentially, if you look at the runoff results,
Le Pen got his core support, period. And all the
other voters united against him. They had no
option to vote for Jospin, whom they almost
certainly preferred by a large margin, because
write-in votes are an American practice, not used
elsewhere much (at all?). The language in the
French press was that they voted "with a clothespin on their noses."
Strong preference motivates high turnout in any
election. Most runoffs have low turnout because
the preference involved isn't strong, usually.
Those were the top two candidates! Only in a
Center Squeeze situation, where an extremist
candidate might make it into second place, is it
different. That created high preference in the
runoff. Never would have happened with, say,
Bucklin in the primary. In this case, IRV would
*probably* have prevented it as well. However,
with a less extreme candidate, IRV could have failed as well.
I never said that the zero-info case was an existent situation. I am
saying that the strategy of approving above the simple mean, is the
zero-info strategy, not the generally recommended strategy.
That is, essentially, a moot strategy, to be
applied in only a highly artificial setting,
where the choice among the candidates is random.
I've done a zero information study, to be sure,
where the voter doesn't know which of the various
possible vote patterns will occur, but that was,
in fact, not realistic, it was a purely
theoretical exercise, I was showing that in the
special case of true zero information, three
candidates, Range 2, the "fully sincere Range
votes" would be 1, 0.5, 0, the "strategy" of the
sincere vote had the same expectation as the
strategy of Approval Voting, and the two
reasonable Approval votes had *almost* the same
utility, the difference between (1,0,0) (greater)
and (1,1,0) vanishing with an increased number of
voters. This contradicted the conventional wisdom
that Approval style voting was the best strategy in all cases.
However, Approval Voting is simple; further, the
*variation* was greater with Approval style.
I.e., with the sincere vote, one was somewhat
lessening the possibility, for example, that the
favorite wins, but was simultaneously decreasing
the possibility that the worst candidate wins.
Voting Approval style (say 1,0,0) gave more
utility from the favorite winning, balanced by
less utility from the worst winning, i.e., the worst possible outcome.
My own conclusion: if range resolution is
adequate that the "fully sincere" vote can be
accurately expressed, voting that fully sincere
vote is quite reasonable strategically, it's not
actually worse than the supposed strategic
approval-style vote. It's less likely to make the
favorite win, but it's more likely to prevent the
worst from winning. However, that's
zero-knowledge. With knowledge, it's possible to
more effectively increase the expected utility,
but not in all situations. My sense is that one
would never seriously regret a fully sincere
vote, in a real situation. But there is nothing
wrong with modifying it based on a reasonable
sense of outcome probabilities. Get those
probabilities wrong, though, the possibility of
serious regret arises. It's a choice that the
voter makes, quite properly, and we do wrong in
trying to prevent voters from being able to make
these kinds of choices by disallowing fractional votes.
Bucklin had a Range implementation! Oklahoma.
Second preference votes had a 1/2 value, and
third preference was 1/3. In other words, folks,
Range was attempted in the U.S. It was a
descending "runoff" form of Range, but it was
Range, because of the fractional votes. It was
found unconstitutional, and for some reason I
always though that it was because of the
fractional votes, and I even agreed that this was
proper. I was wrong on both counts. The reason
was compulsory ranking! In fact, there was a
dissent that agreed with the majority that
compulsory full ranking -- i.e., using all three
ranks -- was unconstitutional, but that the court
shouldn't have invalidated the whole law, just
the compulsory ranking feature that didn't count
votes without the full ranking. (Australian
influence? An example of why not to make too many
changes at once! Full ranking can *seem* like a
good idea, makes systems perform better,
supposedly, but, in fact, it simply introduces
noise and results in more spoiled ballots. The
big reason for full ranking? It won't actually
work with three ranks, but supposedly it
guarantees a majority. That claim was repeated
about Bucklin in a lot of what I've been reading,
it's false with Bucklin just as it is with IRV.
You need *full* ranking to "guarantee" a
majority, and it's a majority that's been created
out of, too often, donkey votes. Noise.
Fortunately, I suppose, with Robson Rotation,
those votes don't normally shift results, but
it's a pretend majority, in fact. With U.S. RCV,
it's not really any kind of ordinary majority at all....)
> So the "oscillation," the lack of stability, will
> only take place when the choice isn't terribly important
> to most voters.
I don't think I understand this argument.
Voters with strong preference won't alter their votes much based on polls.
So for the oscillation to take place, preference
strength must be weak. A poll may cause one to
adjust an approval cutoff, but not drastically.
And there is a certain distrust for polls.
Quite simply, it won't happen.
Note that the problem gets real when, indeed,
there are small preferences, and this is most
likely to arise when there is an attempt to
replace pre-election process so that a primary
and election, with multiple Democrats and
Republicans and who knows what else, all on the
same ballot, with the winner to be determined in
a single stage. This intrinsically sets up a far
more difficult situation. The preselection by
party simplifies voter choices; there are
certainly problems with it, but I don't think
that eliminating independent party process makes
things any better. The Lizard v. Wizard election
was the result of Louisiana's open primary;
Center Squeeze, then, shut out the probable
Condorcet winner, a Democrat, in favor of the
other Democrat, the Lizard as he's known. Thus we
had the situation of a thoroughly corrupt and
largely rejected Democrat -- but still with some
strong "core support" -- facing a Republican who
was a former Grand Wizard of the Ku Klux Klan --
who had also beat out, because of some strong
core support, the moderate Republican. The voters
turned out, again, in large numbers, to defeat
David Duke, the Wizard. Clothespins on their
noses. Better primary election method, *much*
better result, possible no runoff needed. IRV,
again, would *possibly* have come up with a
better result, but isn't so reliable, still
suffering from Center Squeeze. In this case, IRV
might easily have elected the Lizard also, just without the runoff.
A simple example of what I mean would be where there is a preference
cycle of A>B>C>A. Imagine that everyone likes their top two choices
better than midrange. Then, when polls predict that the frontrunners
are A and B, for instance, this causes the electorate to plan to vote
in such a way that B will actually place third. When polls pick up on
this and report that the frontrunners are actually A and C, then A can
be expected to place third. And this could go on, in theory,
indefinitely.
The scenario presumes a very balanced situation
*and* voters highly responsive to polls. Both are
very unlikely, especially the second. Lots of voters don't even look at them.
Note that if a situation is very balanced, and
with weak preference strengths such that votes
would flip as described, it's probably true that
one could pick any of the candidates randomly and
Bayesian regret would not increase significantly over the best.
Really, Kevin, you are worrying about something
purely theoretical, and actually unlikely, and if
it did happen, harmless. So what if the polls
oscillate? Does it tear the bridge apart? Or do
voters decide to simply vote with some kind of
rational sincerity, forget the polls. Maybe
bullet vote, which is generally a reasonable
strategy in a three-frontrunner situation, which
this must be, though that depends on preference
strengths. (In this case, probabilities are equal
for all the candidates, so what controls the
maximum strategic vote is pure utilities. The
oscillating polls would show this, in fact. *It's close!*)
> > > 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.
But that isn't inherently good. That means a compromise choice without
many sincere first preferences can only win by unexpected accident.
The compromise choice would be much more likely to win if he were
identified as a frontrunner.
Half of the following is nonsense. There were
aspects of this situation, clearly, that I need
to examine more. But I don't have time tonight to
review it, and this is a discussion, not polemic. Now, to what I wrote:
Perhaps. What's a "frontrunner"? If the polls
are based on bullet voting, and there is a risk
that C, the voter's worst fear, will win, the
voter is more likely to vote for B, the
compromise choice. Only if A and B are the
frontrunners will the A voters not approve B, but
the C voter will. You vote for a second-choice
candidate if you fear that the candidate *won't*
win. If the candidate is a frontrunner, and you
prefer someone else, who is also a frontrunner,
you *don't* vote for that non-preferred
candidate. But this could be a three-frontrunner
situation, where all bets are off. (As far as simple frontrunner strategy).
Thus the compromise choice is *less* likely to
win if identified as a frontrunner. People who
prefer someone else will not vote for this
candidate, seeing him as the main rival. Unless
their own candidate doesn't have a chance, and
they prefer this candidate to the third
possibility, *then* they will vote for the frontrunner.
Standard Approval strategy: vote for your
favorite, the preferred frontrunner, and any
candidate you prefer to the preferred
frontrunner. This strategy breaks down if there
are three frontrunners. Are there? Being in third
place doesn't mean that one is not a frontrunner.
Now, the compromise candidate isn't going to lose
core support votes no matter what the polls. But
core support could be quite small, though if it
is very small, it requires, pretty much, that the
absolute preference strength for most voters is
low over the entire set of the top three.
1/3 electorate A>B>C
1/6 electorate B>A>C
1/6 electorate B>C>A
1/3 electorate C>B>A
Classic center squeeze, on the edge (i.e., take
one vote away from B, B, everyone's second
choice, is history with IRV. Even though in a
faceoff with B, either of A or C would lose by a vote of 2:1.
Poll result shows B in third place. Now, *How
far* in third place? Small. Won't affect the next
poll, I'd say. Also won't affect chances of
winning. If everybody bullet votes, we have a
three-way tie, a tossup. But not everyone will
bullet vote, and B will win, with Approval,
though this could vary depending on preference
strengths not expressed above. Still, the B
voters are less likely to add approvals for A or
C, whereas the A or C voters are more likely to
add approvals for B, since they see each other's
candidates as much worse. (B voters may be closer
to A or C, but see them as both *roughly* equally undesirable.)
(Imagine linear issue space, spanning -1 to +1, A
is at -5/6, B at 0, and C at +5/6.)
What happens if the voters think B is trailing?
It depends on who is leading. If voters think B
has no chance, it's moot. They won't vote for B,
except for the B voters, since the other voters
have a favorite, who is, by the definitions of
the problem, a frontrunner. Vote for your
favorite frontrunner, plus anyone you prefer to your favorite.
But there is a rather clear exception to this
strategy. If the *worst* frontunner is reasonably
likely to win -- perhaps he's leading, even --
then you'd want to know who has the best chance
of beating him. You'd want to know who could
accomplish that, should your own candidate fail.
You'd want to figure out who a compromise
candidate might be. I.e., you'd want better
information than you would get in a plurality
poll. I'd want to have Range data, the more
detailed the better. With Range data, one would
get a sense of preference strengths. The MSNBC
polls, which were Range 2, default vote 1 for
candidates not rated, would be much better than
pure approval polls, though pure approval would be better than plurality.
Higher res Range would be even better.
1/3 of the electorate votes for B, for sure. B
only needs a little more, 1/6 of the electorate,
to win. Where do these votes come from?
If the polls are reasonably accurate, the A
voters know that C has a 1/3 chance of winning,
roughly. The A voters have quite a good reason to
fear that C will indeed win. They strongly prefer
B to C. Some of them will add an approval for B.
Some of them have, in fact, only a weak
preference for A over B. That's about 1/12 of the
electorate, say. (This is the B-ward quarter of
the A voters). The same is true on the other
side, with the C voters. There is the 50% of the
vote needed to get a majority, but this situation
may result in only a plurality. B will get 1/3 of
the vote, minimum. Additional approvals from B
voters will tend to balance, and there won't be
many of them. On the other hand, additional
approvals from A and C voters, and there will be
more of them, will all go to B.
Bucklin, not really much of a problem. I vote for
my favorite, then B in second place if B isn't my
favorite. Some voters wouldn't do this, but I'd
think this would be confined to the outer 1/3 of
the electorate at most (1/6 on the A side, away
from B, the same on the C side).
B would win in the second round with 2/3 of the
vote. The B voters may truncate, not add any
additional preferences, but if they do, they
split on the candidate they add. It's a wash. We
have 1/3 of the voters, the supporters of A and
C, to the extremes, truncating. So we see roughly
1/3 of the 1st preference vote in the second rank
votes. That's roughly what I've seen in municipal Bucklin elections.
Further, consider what happens if it is Bucklin
and a majority is required. I understand center
squeeze. I want to make sure that the compromise
candidate, my second choice, gets into the
runoff, at least. Exactly how I will vote will
depend on my position, on the preference
strengths, but the motive becomes fairly high to
add a second preference vote and not merely
bullet vote. My second preference vote won't
cause my favorite to be eliminated, and if the
runoff allows write-ins, I could still consider
that vote there, I'll want to know the first
round election results before I decide. If the
compromise candidate is eliminated in the
primary, then what happens depends, again, on
preference strengths and the overall numbers.
Strong preference for a majority of voters: a
write-in campaign, with those voters marking, in
second rank, their second choice. If B is a true
Condorcet winner, with significant preference, B
could actually win, and Bucklin in the runoff prevents the spoiler effect.
Running a write-in campaign, the organizers and
voters must understand the risk. The runoff isn't
going to require a majority, that protection is
gone, so I'd think they would suggest voters vote
for the write-in, in first or second rank,
period, plus their favorite; if they prefer their
favorite, then first rank. But the additional
vote will be there, this time. B might win with
2/3 of the vote. (The best of A or C might get
50%, if that, depends on how many of the B
supporters add 2nd rank votes for the nearest of
A or C. A double majority is unlikely, but
possible in this situation. Barely. B will win,
as a write-in *if the preference strength is sufficient. It might not be.
Imagine that the position of A in that -1 to +1
spectrum is -0.1, B is 0, and A is +0.1. B's core
support has shrunk to a span of 0.1 (5% of the
voters). -- Yes, yes, I'm assuming a linear
distribution. So sue me. It's just for
illustration. The absolute difference in position
between A and C has shrunk from 5/3 to 1/5.
Prediction: no write-in campaign, and low turnout
in the runoff. The B voters, almost entirely,
won't show up, but also many of the A and C
voters. The result will actually depend far more
on the *campaign* between A and C. And no strategic complications.
[...]]
> > 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?
Not necessarily, because requiring a majority would alter the strategy
of the method, possibly in a bad way.
Actually, there are very strong reasons for
requiring a majority, hang the strategy issues.
Lack of a majority means that the electorate
hasn't made a collective decision, except through
plurality rules which are known to be
unsatisfactory, these are never accepted when
other options are available, it's only when
repeated balloting isn't practical that plurality rules are even considered.
What a majority requirement does in a primary is
encourage bullet voting. Bullet voting is fully
sincere! A bullet vote, in an Approval method,
indicates that the voter prefers the candidate
over all other candidates. If the voter actually
had no preference for that candidate over one of
the others, presumably the voter would also
approve that other candidate, all strategic
considerations disappear in Approval that would
lead to bullet voting when the favorite has a true clone.
The problem arises, though, when the runoff
itself terminates with plurality, and when there
are eliminations involved. It's not a totally
solvable problem within the restriction to two
ballots, hence Asset solutions, that could make
what is effectively further balloting practical.
(And even a first runoff isn't necessary then.)
Now, we can ask voters to add additional
preferences until we are blue in the face, and
many won't. They don't with IRV, many of them. I
really should look at those ballot images, San
Francisco doesn't compile truncation data, only
exhaustion data, which doesn't cover the
candidates left standing in the final round.
(They stop eliminations when a candidate has
found a majority of remaining ballots).
So pretending that, say, Condorcet methods will
somehow collect all that preference data is
living in a fantasy. They will only collect the
data that the voters express, it's true for all
methods. That is, there is always going to be a
lot of bottom-equal ranking. Even if ballots
allow full ranking, which they won't, in the U.S.
There is going to be a lot of bullet voting. Most voters, even. (Probable.)
What I'm saying is that I view it as bad if large numbers of Approval
voters are failing to participate in the most important contest, or
failing to even identify such a contest.
If they care, they will participate. So what's
the problem? However, I'm *not* proposing
Approval except as a quick and dirty immediate
no-cost reform, a first step. How much it will
help, I don't know. It will *ameliorate* -- not
solve completely -- the spoiler effect. (But it
will probably eliminate 90% of it, my guess.)
Bucklin requires a more complex ballot, but
canvassing is still quite simple, existing
equipment is no problem. Bucklin, though, allows
that important first preference vote and makes a
second preference vote not obscure the first
preference. A first preference of a majority is
certain to win (only if that preference is weak
and if the method allows multiple votes in first
rank would this not be true; classical Bucklin
didn't allow multiple votes until the third rank.
I'd allow multiple votes in any rank simply
because if a voter doesn't have a significant
preference, the voter should be allowed to equal
rank. There may be some situations where there
would be a strategic motive to equal rank, but I
consider this harmless. A voter is not going to
do it in the presence of a strong preference,
it's too easy to just vote sincerely to express
that preference. And I don't like considering
ballots spoiled when they contain decent information from the voter.)
> 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.
I am not disputing that the candidate with the most Approval is the best
candidate to win an Approval election. Same as I wouldn't dispute that
if we run out of food we should resort to cannibalism rather than starve.
I'm saying it's bad if we do something that is prone to leading us in this
direction.
Isn't the metaphor a tad extreme? Just how likely
is it that the most-approved candidate was
actually not preferred by a majority. It's
possible, but actually not likely at all. And how
much damage is done in this case? It's hardly
likely to be a bad outcome, but the lower that X
is, the more the likelihood increases. I dislike
Approval without a majority requirement, at least
in a primary round. I'd prefer to maintain that
without restriction as to number of rounds. If
wishes were horses. Actually, I prefer Asset. I
don't want to keep voting, I want to be able to
designate someone I trust to do it for me and for others similarly inclined.
> > > 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 would have thought IRV would be squarely in the category that fails
by electing a mediocre candidate, and rarely by electing a terrible
one.
Actually IRV can elect a quite poor candidate,
rejected with significant preference strength by
a large majority. Center Squeeze. How often? To
my knowledge, the simulations haven't dealt with
the variability, i.e., how bad it can get, but only with the averages.
> 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.
Well, if voters tend to bullet vote under Approval, I guess it really
won't be much different from FPP or IRV.
I'm calling Approval "Open Voting," because the
voting really isn't about "approval," it's about
"consent," or a "decision to support," a
different animal. Most voters will bullet vote,
probably roughly 90% or more. Where Open Voting
makes a difference is with those who support
minor candidates. At practically no additional
public expense, they now have an option that
allows them to express support for their
candidate plus a favored fruntrunner. It's not
the ideal method, though it's quite good
considering how simple it is. Range and hybrid
Range methods are better, significantly better.
Range with runoff has, in the limited work that
has been done, lower Bayesian regret than pure
Range. (Pure Range would be ideal if voters could
vote absolute utilities and all did it, but that
is not going to happen; for starters, voters will
much more commonly vote, and we still call it
"fully sincere," normalized utilities, normalized
typically to the ballot candidates or maybe one
write-in. And the will vote VNM utilities,
generally, not pure linear ones. Still, Range is
best, according to the known measures. And it's
possible to test those preference strengths if
it's needed: when it's needed is when preference
analysis shows a candidate who beats the Range
winner pairwise by preference. This is a
situation where there is a possible majority
criterion failure or certainly a condorcet criterion failure.
If we incorporate an approval cutoff in the Range
method, which might be as simple as defining
midrange or the next increment above midrange as
"approval," i.e., acceptance, an "approval vote,"
and we require majority approval, then we've set
up a majority test. If we include in such a test
the situation where there is a pairwise victor
not the Range winner, we can hold a runoff, I
won't give the full description, nor have I fully
worked it out. But the bottom line is that when
it is not clear that a majority of voters have
accepted the Range winner, there is a runoff
between the Range winner and the best alternative
(definitely including a Condorcet winner by the
votes), and runoff elections test sincere
absolute preference strength. If the Range winner
legitimately is this, he or she has a great
advantage in a runoff. But the majority has the
right to decide! Awarding the victory
automatically to the Condorcet winner deprives
the majority of its basic democratic rights, one
of which is to decide on greater overall good
than simple majority first preference. If the
Condorcet preference is weak, those voters won't
show up to vote in a runoff; further, if it is
weak, some of those voters will decide to respect
the Range vote, plus, of course, more will come
out in the runoff campaign. In the end, the
majority of those voting will decide.
> (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.)
If you listen to Warren Smith, Condorcet methods are prone to
catastrophic failure because voters have incentive (real or instinctive)
to attempt burial strategy against the worse frontrunner. When
too many voters do this, and there's no majority favorite, the result
will be the election of a candidate that nobody cared about, who was
just being used as a pawn.
Right. That strategy could quite possibly be
common. It's easy to think that way.
This makes it odd that he has seemed to prefer Condorcet to IRV,
seeing as IRV can't have such disastrous failures.
It certainly can. With sincere votes. That's the problem, Kevin.
Center Squeeze. I gave an example above. With
IRV, the compromise candidate is eliminated, and
the result is a winner who is opposed by
two-thirds of the electorate, and a majority of
this has quite strong preference strength behind
it. This is the kind of election result that can spark rebellion and violence.
That's with every voter voting sincerely.
Supposedly one advantage of IRV is that it
encourages voters to vote sincerely. I think it
probably does that, though it probably, also,
doesn't do it to any great extent beyond that
which happens with Bucklin. The problem is what
it does with those sincere votes. It doesn't
count most of them, for starters, usually. We
don't really know -- precisely because the votes
aren't counted or reported. Sequential
elimination, because of its superficial
resemblance to runoff voting, seems simple, seems
to make sense. But people don't realize,
generally, the complications this brings. Most
people don't notice the implications of
elimination, and what this means to the voter who
votes sincerely for their favorite, who is
eliminated even if that candidate is everyone's
second choice. There really has been a lot of
deceptive and just plain wrong information
disseminated about IRV, by people who should know better.
I'm an American. Why don't we try, in America,
"American preferential voting," which is what it
was called in a number of the sources. Or just
the "American system." It's ironic to see San
Jose vote for IRV, then wait ten years because
it's too complicated to canvass, now they think
that they may be ready, maybe next election. They
could have done Bucklin immediately, "American
preferential voting," and the results will almost
always be the same, except in *some* of those
cases where IRV misses a compromise candidate
that Bucklin might catch. IRV is definitely
damaging the best voting system we have, top two
runoff, replacing it in nonpartisan municipal
elections, almost always on a cost argument. And
with the claim that it will still require a
majority (San Francisco) or even explicitly "the
winner must get a vote from a majority of
ballots" (Steve Chessin writing the ballot
argument in San Jose). If they actually did
continue to require a majority, that would be far
better. But IRV fails in this, rather badly. So
did Bucklin, by the way, though probably not
quite as often. Bucklin was oversold as a way to
ensure a majority, just as IRV is now. It's not
correct, but Bucklin doesn't pretend to find a
false majority, like IRV does. It just counts all the votes and adds them up.
Bucklin really should be suggested to TTR
communities as a primary method, and in ones that
allow write-ins (default in California), as a
runoff method as well (only two ranks needed).
Cheap. Easy to understand. (The claims are in the
early literature that Bucklin was very popular
with voters.) Used as a primary method, it will
avoid maybe half of the runoffs, which is pretty
good for a no-cost method. IRV avoids very few
runoffs, if used as a primary method -- plus it
can pick the wrong top two, because of Center
Squeeze. Bucklin *could* make the same mistake,
if nearly everyone bullet votes, but it won't
happen with significant use of additional
preferences. The problem with IRV is that it can
happen with sincere votes and even with full
ranking. It would never happen with Bucklin with full ranking....
> 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.
There are two possibilities. If the voter really didn't have a preference
between the two frontrunners, then it doesn't matter. But if they did,
then by not voting for one of them, they vote "suboptimally" because
they fail to vote in a way that maximizes their expectation. And it is
suboptimal overall, because the wrong frontrunner will be elected.
However, with the consent of that voter, who, by
voting that way, has indicated that gaining the
additional utility of a better winner is relatively unimportant.
Now, of course, the problem here is that
Plurality doesn't allow the expression of
additional preferences. The voter has a Hobson's
choice. However, that's terribly easy to fix.
Just Count All the Votes. Open Voting. Approval.
No cost. And then we can make it better cheaply,
allowing ranked expression of preferences.
Bucklin. With Bucklin-ER, you have a full
integration of Approval and a ranked method that
runs in rounds like IRV, but without the
eliminations, which are where the big problems
come in, the eliminations and vote transfers make
precinct summation useless. Bucklin can be
counted in rounds, but each round is independent.
Just count all the votes. (The only problem is
that votes for the same candidate in the next
rounds must be locked out, not counted again.
Otherwise it would be totally simple. Count the
marks. Classical Bucklin also considered multiple
votes in the first and second rounds to void
those rounds and all subsequent ones -- similar
to what's done with IRV. I'd just drop that -- I'd drop it with IRV as well.)
> 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?
I don't understand what you're saying here. If the frontrunners are
Gore and Bush, then I'm calling "suboptimal" all votes that don't favor
one over the other, when the voter actually had a preference.
Suboptimal from whose point of view? The voter
decides not to vote in the "real election." The
voter could equally well decide to stay home. For
whatever reason, the value to the voter of the
Nader vote exceeded the value of the Gore vote.
Or Bush vote, we too easily assume that all these
voters would vote for Gore. I suspect that with
IRV, maybe half, maybe more, of them would have
voted for Gore. The rest would have truncated.
Another way of putting this is that the voter
doesn't like either Gore or Bush. The voter may
have a preference, but the strength is low. If it
were a runoff between Gore and Bush, the voter
might well stay home. Now, if the voter's
preference strength is low, what is the value of
a Gore > Bush vote? It actually doesn't change
the overall social utility much. It overstates
the voter's true preference strength.
You may not think this voter's vote to be
optimal, and I certainly don't either. But the
voter apparently thought differently. The real
problem in the U.S. was that Bush and Gore were
running neck and neck. It looks like the true
popular vote margin in the U.S. was maybe 500,000
votes (more for Gore), but that still means that
were were divided, and neither gained a majority,
as I recall. In Florida, as well, neither gained
a majority. We have a quirky system, to be sure,
a corruption of the original intent, which was to
make the electoral college a true representative
body, not a rubber stamp for each state's
majority. In a deliberative environment, the two
leaders running neck and neck and neither gaining
a majority is a fairly strong indication that the
best result might be neither of them. Only Asset
Voting, of all the systems I know that might be
seriously proposed, would allow this situation to be fixed.
> 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.
But under Plurality it is hardly ever a concern, because the polls are
sufficiently stable that voters who wish to cast a meaningful vote have
no difficulty in doing so.
Sure. And that won't change should we implement
Open Voting. First preference is really the most
important poll to know, but it's better to have
more detailed data; Range allows margins to be
assessed to more accurately predict how votes
might change. Weak preference strength with a 10%
gap could vanish overnight. The same gap with
strong preference strength would be much more stable.
If Approval polls prove relatively unable to whittle the field down to
two frontrunners, I would expect more votes on principle and (with it)
more waste of votes.
Kevin Venzke
Compared to what? The proper comparison of Open
Voting is with standard vote-for-one Plurality,
and then possibly with IRV, as an example. It's
got lower Bayesian regret than IRV, apparently,
even with all it's problem. Sure, if all voters
bullet vote, it's simply Plurality. Except that
won't happen. There will be additional approvals,
possibly 10% or so. That's enough to greatly
improve results. It probably would have given
Florida to Gore, but that's tricky, we don't know
what additional approvals Bush would have gotten
from the supporters of other minor candidates.
However, the big deal with Open Voting is that
it's free. Just Count All the Votes. It's easy to
vote, for the large majority of people, and those
who need to consider additional votes can pretty
easily understand it. The candidate with the most
votes wins. That's not terribly complicated!
Approval isn't going to radically change the
overall political picture. And voters simply
aren't going to pay that much attention to polls.
They will bullet vote, most of them, we know that
from applications, but there will also be
significant numbers of voters who add additional
approvals without any poll data at all. This
simply means that they have low preference, they
decide that they really don't mind if the winner
is A or B, and it's simpler to vote for both rather than nail it down.
And then when there is frontrunner information,
they will, some of them, add compromise votes for
frontrunners. Those who support a frontrunner as
first preference, with significant preference
strength, have no inceintive to add additional
approvals, and there really is little reason to
think they should. It's probably moot, you know.
Bucklin simply makes it easier to make the choice
to add additional approvals, since one does
express a preference and it does make a difference in the first round.
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