[EM] Why I think IRV isn't a serious alternative 2

[Abd ul-Rahman Lomax]

At 12:56 AM 12/21/2008, Kevin Venzke wrote:
>--- En date de : Ven 19.12.08, Abd ul-Rahman 
>Lomax <abd at lomaxdesign.com> 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.