[EM] James--wv & order-reversal. Ways of thwarting order-reversal.

[MIKE OSSIPOFF]

Somehow the format of the lines got scrambled. I've tried to unscramble it 
by cutting & pasting the message back into the e-mail, and by copying it and 
pasting it again, but without success. I even tried Microsoft Word, checking 
its format options, hoping there'd be one that would get rid of linebreaks, 
making it into one big block, to which I could then add paragraphs. Sorry 
about the mess.


Subject :  To James, order-reversal in Condorcet wv

James:

You wrote:

	My most general reply is this: You give a number of
reasons why
offensive
order reversal is unlikely to succeed in a public
Condorcet election,
and
why a sort of chicken-car crash scenario is unlikely
to occur in a
public
Condorcet election. For the most part, I agree that
these things are
reasonably unlikely. However, as I wrote before, I
think that if they
do
happen, then it is a real disaster, and will utterly
undermine the
credibility of the system.

I reply:

Let me repeat something that I said:

Let's put this in perspective: Without offensive
order-reversal, wv has
no
need
for defensive strategy. That's a remarkable and rare
property. The only
other
methods that have that property are SMA, NES, and
probably DSV.

And, when there's offensive order-reversal, or a
substantial risk of
it,
then wv
begins to have a defensive strategy need that's
roughly comparable to
the
problem that other methods have all the time. Did I
say "roughly
comparable"?
Very roughly. Because wv can thrwart the offensive
order-reversal by
mere
defensive truncation, or defensive equal-ranking. But
Plurality & IRV
need
defensive favorite-burial--and that's without anyone
doing offensive
strategy.

So offensive order-reversal in wv isn't going to harm
wv's credibility.
If
people's standards were that high, they'd have
rejected Plurality a
long
time
ago.

In fact they'd be pretty much out of luck, because the
only methods
without
an order-reversal problem are methods that have even
worse problems.

The only way to meet the majority defensive strategy
criteria is to
look at
pairwise preferences. Otherwise the method can't know
what majorities
are
saying and who is CW. (But it needn't be a
pairwise-count method). And
when
pairwise preferences are the important thing,
offensive order-reversal
can
make a symmetrical cycle of public pairwise results,
which means that
there's
no way for the count rule to distinguish the
reversers' candidate from
the
CW. The reversers then will win if they've chosen the
right time to
order-reverse, when the faction-size numbers are in
their favor.

You continued:


	The question then becomes a matter of *how* unlikely
these scenarios
are
in a public election.

I reply:

To the extent that there's any perceived danger of
offensive
order-reversal,
defensive truncation will be employed as a
countermeasure. If offensive
order-reversal ever started looking like a problem, it
would quickly
become
a
poor backfiring strategy.

You're assuming that the reversers are sophisticated
enough to reverse
(or
emotionally-inclined to do so because they feel like
it).

If so, then the intended victims will be sophisticated
enough to easily
counter
the order-reversal, or could be emotionally-inclined to do so.  And not 
ranking a 2nd choice is a
much more natural
strategy
than reversing a preference, something that
emotionallly makes sense,
especially
when people hear that it prevents successful
order-reversal.

You continued:

Are they astronomically improbable (say, one in a
million)? If so, then I would be willing to let it
slide and back
Condorcet without any backup mechanism. Are they
improbable on the
order
of one in a hundred? If so, then I would start to get
somewhat
uncomfortable with the raw, unprotected Condorcet
being used for a
serious, high-stakes public election.

I reply:

Again, you're holding Condorcet up to a standard that
no other
1-balloting
method could pass, least of all Plurality, which is
what Condorcet
would be
replacing.

You continued:

The cost of a backup mechanism
begins to be less important to me that the risk of one
of these
scenarios.

I reply:

Each public balloting costs a lot of money. Sure,
strategy can be made
easier by
a 2nd balloting, and I've described proposals to use a
2nd balloting
with
Condorcet. But Condorcet has so little problem, even
in its 1-balloting
form,
that I suggest that the goal of further reducing that
problem doesn't
justify
the doubling of the balloting cost, by holding a 2nd
balloting.

And your proposal involves more than just 2
ballotings. For a public
method,
people would never
accept a method that requires more than 2 ballotings.

I've suggested a range of anti-order-reversal options
that could be
allowed
with
1-balloting wv if there were a perception of an
order-reversal problem.

You continued:

If it is more like one in fifty, then this continues
to increase my
concern. And so on. At a certain point, I will refuse
to back Condorcet
at
all without some backup mechanism.

I reply:

As I said, even if order-reversal were a genuine
problem, with a
completely
devious electorate, the problem is controlled by the
deterrence of
defensive
truncation. The defensive strategy situation with wv,
even with a
completely
devious electorate, is less than the one that
Plurality has all the
time,
and
that IRV has much of the time. And, even under the
worst conditions,
wv's
defensive strategy consists only of truncation (or
defensive
equal-ranking
could
be used too, but, because equal ranking isn't a
deterrent, the
truncation
would
be a better defense in a devious electorate).

You continued:

Mike Ossipoff wrote:

I'd said:

>That's the subject of the criterion SFC. GSFC
generalizes SFC to
situations
where there's no CW. When defeats are measured by wv,
then SSD and
Ranked-Pairs
meet the powerful GSFC. Plain Condorcet (PC) meets
SFC.
>In fact, SFC and GSFC describe plausible conditions
under which, with
>complying
methods (Condorcet wv), the majority who don't want X
can be
>sure X won't win, _without having to do anything
other than vote
sincerel_.

	I don't understand what you mean by this. Could you
clarify?

You mean the last sentence?

To explain why that's so, I have to define SFC & GSFC:

SFC:

If no one falsifies a preference, and if a majority of
all the voters
prefer
the
CW to candidate Y, and vote sincerely, then candidate
Y shouldn't win.

[end of SFC definition]

Sincere voting definition:

A voter votes sincerely if s/he doesn't falsify a
preference or fail to
vote
a
sincere preference that the balloting system in use
would have allowed
him/her
to vote in addition to the preferences that s/he
actually did vote.

[end of sincere voting definition]

Richard's definition of voting X over Y:

A voter votes X over Y if s/he votes in such a way
that if we count
only
his/her
ballot, with all the candidates but X & Y deleted from
it, X is the
unique
winner.

[end of definition of voting X over Y]

A voter votes a sincere preference if he votes X over
Y and prefers X
to Y.

A voter falsifies a preference if he votes X over Y
when he doesn't
prefer X
to
Y.

GSFC:

If no one falsifies a preference, and if X is a member
of the sincere
Smith
set,
and if Y is not, and if a majority of al the voters
prefer X to Y and
vote
sincerely, then Y shouldn't win.

[end of GSFC defnitiion]

Now, here's the sentenced that you asked the meaning
of:

>In fact, SFC and GSFC describe plausible conditions
under which, with
>complying
methods (Condorcet wv), the majority who don't want X
can be
>sure X won't win, _without having to do anything
other than vote
sincerel_.

The conditions I refer to in that sentence are the
premise conditions
of SFC
&
GSFC.

Under those premise conditions, the majority who
prefer the CW to Y
(with
SFC)
or X to Y (with GSFC) need only vote sincerelly to
ensure that Y won't
win.
That's what the criteria's requirements say. So, if a
method meets
those
criteria, the majority who prefer X to Y won't have to
do anything
other
than
vote sincerely in order to ensure that Y won't win.
That follows
directly
from
the criteria's premise and requirement and the
assumption that a method
meets
those criteria.

What that means in an actual election: Say you know
that no significant
number
of people are going to try offensive order-reversal
against your
candidate.
Not
enough offensive order-reversers to change the
outcome.  Then, to avoid
the
kind of majority rule violation described in the
criteria, you don't
need to
do other than rank the candidates in sincere order. No
strategy needed.

That's what compliance with SFC & GSFC guarantees.

You continued:
	The problem with this is the way most public
elections are staggered
several years apart. This makes it hard for the threat
of retaliation
in
the next election to have much effect on people's
strategies in the
current election.

That depends on how forgetful people are when the
election was stolen
from
them,
made possible becsause they were trying to help the
people who stole it
from
them.

You continued:

	Also, in a high-stakes election, victory might matter
more than the
reputation of the candidate. For example, Bush stopped
at nothing to
steal
the 2000 election.

I reply:

Fine, but don't expect it to work more than once.

You continued:

It is clear to many people that the result was unfair,
but Gore doesn't seem to be running against him in
'04. The fake winner
is
the president of the U.S., with all the power that
implies, while the
real
winner is sort of a political ghost who comes around
to haunt the media
every so often. By your logic (as far as an unfair
winner not being
able
to show his face in public) I would expect Gore to run
again and to
smash
Bush in '04. But it seems that the power that Bush
seized was able to
override the concerns of fairness in a way.

I'd said:

>As you mentioned, it's like a game of chicken, when
defensive
truncation
>is threatened against would-be offensive
order-reversers.
>But please note that the supporters of the middle CW
who is being
>protected will suffer less if no one chickens out,
compared to how
much the
>offensive order-reversers would suffer then. That's
because, in your
>example,
the C
>is farther away from the order-reversers than from
the defenders.

You replied:

	You mean in this example?:

46: A>B>C
44: B>A>C
5: C>A>B
5: C>B>A

Not necessarily. I don't know who's order-reversing in
that example. It
needs more explanation.

Say the sincere preferences are:

40: ABC
25: BAC
35: CBA

Say the A voters order-reverse, voting ACB, and that
the B voters
defensively truncate, voting  only for B:

40: ACB
25: B
35: CBA

C wins. The B voters have made the A voters regret
their offensive
strategy.
For whom is it worse, when C wins? The B voters or the
A voters? B is
between A & C. C is worse for the A voters than for
the B voters.
That's
what I meant.

I'd said:

>Additionally, a defender has a more credible threat.
A cat defending
its
territory has a more credible threat against an
interloper than the
other
cat
has. The defender, it's understood, is more willing to
fight and risk
getting
hurt when defending what's rightfully his. This adds
to the defenders'
advantage
in the game of chicken.
>Sure, if no one chickens out, the result isn't
desirable for the
>defenders either. Defensive truncation is a dominated
strategy for
them:
>But
note
>that dominated deterrent strategies are common in
legal systrems and
in the
animal kingdom. They wouldn't be used so much if they
didn't work.


You replied:

	Interesting point. I think I agree with you, but I
would enjoy hearing
a
couple of examples.

I reply:

I probably don't know more about law or wildlife
behavior than you do,
so
what I can tell you probably won't be anything new.
Say a cat is
trespassing
on another cat's territory. The defending cat bluffs
the other cat to
make
it leave. It's saying, "If you don't leave, I'm going
to tear you up,
and
you can count on me to do that, because I'm not afraid
of getting torn
up
too." We've all heard those discussions. Now, if the
trespassing cat
calls
his bluff and makes him fight, the defending cat is
likely to get hurt.
That's probably worse than having a trespasser.
Committing himself to
fight
is a dominated strategy. The only time it makes a
difference is if the
other
cat chooses to stay and fight. Then the defending cat
is worse off than
if
he hadn't chosen that strategy. If the trespassing cat
doesn't fight,
then
the defender's choice of strategy doesn't do good or
harm. Whatever
happens,
the defender can onlly be worse off because of meaning
it when he
threatened
to attack the trespasser.

Same thing when two animals are fighting over a piece
of meat. That
piece of
meat isn't worth getting seriously cut or mauled over.
In the wild, an
injury like that often means death. Whatever the rival
animal does,
each
animal  is c ommitting himself to a strategy that can
only make him
worse
off. But he does it anyway, because he knows that the
other animal
doesn't
want that either. Same with the territory-defending
cat.

Imprisonment is sometimes justified in terms of
taking the offender
out of
society so that s/he can't do any harm for a while.
But let's ignore
that
purpose, because imprisonment is mostly advocated as a
deterrent.

If the society has an inflexible law that says that if
someone commits
a
crime they get imprisoned for a long time, at great
public expense,
then,
society can only lose in that transaction. If the
person doesn't commit
the
crime, the strategy doesn't bring gain or loss. But if
the person does
commit the crime, society pays the high monetary cost
of the long
imprisonment. Society can only lose in that game. It's
a dominated
strategy.
The strategy of not doing anything about the crime
dominates the
strategy of
imprisonment. Not doing anything is just as good if
the crime isn't
committed, and is better if the crime is committed.
But that dominated
strategy is considered a deterrent because the would
be breaker of that
law
doesn't want that costly outcome either.

With the animal willing to fight if the other animal
doesn't yield the
meat,
that strategy is dominated by the strategy of not
fighting no matter
what.

The strategy of having an inflexible law to carry out
the threat to
imprison, or the strategy to fight for the meat if
necessary, is a
dominated
strategy. But, as I was saying before, dominated
deterrent strategies
wouldn't be so widely used in legal systems of in the
animal kingdom if
they
didn't work.

When the interloper cat leaves and the cat who has
coimmitted to
fighting
for his territory doesn't have to fight, that's a Nash
equilibrium.
Neither
cat could improve his outcome. If the bluff isn't called, then the defender 
wouldn't
gain by not having
a
strategy to fight if necessary. The
interloper
doesn't gain by staying and fighting. He gets hurt if
he stays when the
defender is using the fight strategy.

Dominated deterrent strategies can enforce a desired
Nash equilibrium.

_The Selfish Gene_ has some interesting parts about
animal conflict
strategy.

You wrote:

Also, again, the ability of the
"defenders" to punish the "reversers" is severely
limited if they have
to
wait another four years to cast a vote.

I reply:

But they can punish the offensive strategy in the same
election, by
defensivse truncation. But the bluff probably won't be
called,  like
when
the cat convinces the interloper that he's fully
committed to the
strategy
of fighting if the interloper doesn't leave.

It's been said that when there's a Nash equilibrium it
will usually be
found
and stuck to. They say that's usually true, though
there are also games
where one's strategy corresponding to the Nash
equilibrium is so risky
that
no one would try it.

In a completely devious electorate, if it's known
that truncation is common,
it
will also be known that offensive order-reversal
doesn't pay.
I'd said:

>
>In public elections, effective offensive
order-reversal would require
>public organizing. There' s just no way it could be
done without its
>intended
victims hearing about it and using defensive
truncation.
>So in public elections, offensive order-reversal is a
losing
proposition.

	A couple points here. One, which we will probably
agree on, is that
this
kind of strategic organizing is much easier in a
voting situation with
fewer voters, for example a vote within a legislature
or council.

I reply:

Sure, I'm talking about public elections. In
committees it's easy to
hold a
2nd balloting. That's the simplest rule to thwart
offensive
order-reversal.
Or, if it's desired to use only one balloting, then
anti-order-reversal
enhancements such as the ones that I've described coud
all but
eliminate the
problem. Of course they could be used in a public
election too if
order-reversal were perceived as a problem.

You continued:

Hence, I
think that offensive order reversal / burying would be
much more of a
problem in such situations. Also, the cost of
implementing an
anti-reversal enhancement such as the one I proposed
would be
substantially smaller in such situations, since the
voters will still
be
gathered together and in a position to vote again when
the result of
the
first vote is announced. Do you agree that my proposal
is marginally
more
relevant for use within legislatures, councils, etc.?

I reply:

Sure. And in committees, small organizations, etc.

You continued:

Since you frequently
qualify with the word 'public,' I assume that you do.
	Secondly, burial strategies don't have to be entirely
conscious. Given
ranked ballots I think you might find that many voters
will rank a
candidate last not because that candidate is their
sincere last
favorite,
but because the candidate is the main competition for
their favorite.
This
can just be a matter of instinct, and can happen
whether voters really
know how the tally system works or not.

I reply:

Yes, but, for everyone who order-reverses just because
he feels like
it, how
many will truncate just because they feel like it? As
Adam pointed out,
truncation, not ranking someone, is a lot more natural
and un-devious,
and
will be a lot more common, than order-reversal. So
those
order-reversers you
refer to are going to be doing that in an environment
of widespread
truncatioin. Surely someone will warn them how bad an
idea that is.

You continued:

With IRV, (or any system where the
burial strategy doesn't work), people doing voter ed.
can say "listen,
there's *no way* that burying your second favorite
going to help your
favorite candidate, so why mess with it." With
Condorcet,
unfortunately,
this wouldn't be true, so this impulse will not
necessarily disappear
given good voter education.

I reply:

That statrement is unworthy of you. Gibbard &
Satterthwaite have shown
that
every method has strategy incentives. We can take that
farther and say
that
every method can have defensive strategy need, as I've
defined it.
You're
pointing out that IRV doesn't have the same strategy
incentive that
Condorcet wv has. So what? IRV has worse defensive
strategy need. The
need
to bury one's favorite. Without there being any threat
of offensive
strategy.

To copy your voter ed. scenario, in IRV no one can say
"Listen, there's
*no
way* that burying your favorite is going to be
needed."

Drastically different kinds of methods are predictably
going to have
different defensive strategy needs. Ask yourself which
is worse.

>
>For all the above reasons, I don't consider offensive
order-reversal a
>problem.
Effectively, then, Condorcet wv is practically
strategy-free.
Remarkably
strategy-free. No other method of comparable
simplicity even comes
close.
>So, for that reason, I don't feel that it's necessary
to include
>enhancements
to further reduce that already near-nonexistent
problem.
>Of course, when Condorcet wv has been in use for a
long time, and if
by
>then people are discussing the order-reversal
possibility, then, at
that
>time,
the anti-reversal enhancements could be proposed.
>Even though I claim that they aren't needed in public
Condorcet wv
>proposals,
I'm going to discuss anti-reversal enhancements in a
>subsequent posting.
>Mike Ossipoff

	By the way, in my original paper I used this example:

You wrote (about an example):

	It's trickier because mutual truncation in the first
example leads to
the
sincere Condorcet winner winning anyway

I reply:

Note that, under common, plalusible conditions of the
premises of SFC &
GSFC, the wv methods don't require that truncation be
countered be
defensive
strategy.
I'd said:

>Here's what I've propsed as a 2nd ballot solution:
>If there's a circular tie all of whose members have
another member
ranked
>over
them by a majorith, then a 2nd balloting is held.
>Before the 2nd balloting, the pairwise defeats will
have been
published,
>and order-reversal, if it happened, can be noticed.
>In the 2nd balloting, the reversal can be countered.
It can be
punished
>by defensive truncation. Or, as in your example, the
C voters could
rank B
equal to C. Note that, with wv, they only need rank B
equal to C. In
>margins they'd often have to rank B _over_ C. That's
a lot more to
ask.

You replied:

	Are the results of the second balloting final?

I reply:

Yes.

You continued:

This can be a problem
because, if a burial strategy has happened in the
first balloting, then
the chicken game is already in full swing at the time
of the second
balloting. If neither voting bloc swerves, and the car
crash candidate
is
elected in the second balloting, then the result has
gone from bad to
worse. If such a result is locked in, then it'd be
bad.

I reply:

No, because in the Approval 2nd balloting the CW can
be elected. In
fact
that can happen when the 2nd balloting is another wv
election too, if,
in
that balloting, the CW is protected by defensive equal
ranking. In the
2nd
balloting, when it's known who the CW is, and where
detering the
order-reversal isn't as important (because it can be
dealt with in the
2nd
balloting), the defensive equal ranking is what makes
the most sense in
the
2nd balloting.

In the example where B is CW, and the A voters
order-reverse, the C
voters
benefit if they don't defensively equal rank B,
forcing the B voters to
truncate & elect C. It's another game of chicken, if
the C voters want
to
make it that way. The B voters can say "We won't do
defensive
truncation.
Our candidate is the CW, the rightful winner. Now that
you know that,
it's
for you to do what will elect the CW." The B voters,
again, are the
ones in
strongest position in tha game of chicken, since an A
victory will be
worse
for the C voters than for the B voters. "Suit
yourself. Let A win if
that's
what you want. Because that's what will happen if you
don't equal-rank
B."

That's a good reason to user Approval in the 2nd
balloting, to avoid
the
possibiolity of that 2nd game of chicken. But, as with
the other
chicken
game, it seems to me that it would come out right
anyway.

In 1-balloting wv, I suggest that defensive truncation
is the right
anti-order-reversal strategy because it's a deterrent.

You continued:

	In this case I'd say that the result is still highly
unstable as of
the
end of the second balloting.

I reply:

Not if the 2nd balloting is by Approval.

And even if it's another wv election, I claim that the
CW will be
stably
elected, because the C voters understand that that's
the rightful
result.
Just as the interloper cat knows that the defender is
motivated to
fight,
and so the interloper doesn't call his bluff, so the C
voters know that
the
B voters are the ones who are in the right, and will
know that they'd
just
elect A if they defect against the CW.

It's likely that the order-reversers won't even repeat
their strategy
in the
2nd balloting, because either the defensive truncation
or defensive
equal
ranking would prevent the A voters from gaining
anything, and there's a
possibility that the reversal could backfire. But that
doesn't matter,
if
the C voters equal rank B.

You continued:

The goal of the method I'm proposing is to
find a relatively stable outcome. It offers three
definitions of
stability. One is a clear Condorcet winner on the
initial balloting.
The
second definition is an outcome that the majority
votes in favor of
when
they are given the choice between that outcome and a
re-vote.

I reply:

I don't think it's necessary or desirable to require a
candidate to get
a
majority in an up/down vote.  Maybe no one has a 1st
choice majority. I
personally have nothing aganst an up/down vote,
because it would give
me a
chance to dump the Democrat. But I don't like it
because it
unnecessarily
complicates the method's rules.

You continued:

That is, a
majority perceives it as a fair outcome, a majority
doesn't think that
they can get a better outcome without risking a worse
outcome and
considering the cost of an extra election, or
whatever. The last resort
definition of stability is to pick an outcome that
reoccurs from a
certain
number of ballotings, e.g. an outcome that repeats 3
times. This last
rule
is not necessary for use within legislatures, because
deadlock on some
issues is acceptable in the legislative process. This
rule is only
necessary when an election absolutely needs to produce
a positive
result
by a certain date. A car crash candidate or a
burial-strategy
beneficiary
may still conceivably win, but not all at once and by
surprise, as can
happen when a specific round of ranked voting is
automatically locked
in.
Instead, the voters will necessarily see the result
coming and must
make
repeated conscious choices to affirm it.

I reply:

Sure, a 2nd balloting is a good way to get away from
the situation you
describe. I just don't think wv's offensive
order-reversal problem is
bad
enough to justify the monetary cost of a 2nd
balloting. The IRV people
use
1-balloting as a selling point, for instance. They
seem to think that
the
public prefers 1-balloitng, maybe because of saving
public money, maybe
because candidates needn't campaign in 2 elections,
maybe because
there's a
turnout problem in the 2nd election.

But, in any case, more than 2 ballotings is too many,
for public
elections.

You continued:

	This rule strikes me as the best way to break
deadlock, but I
mentioned a
few other possibilities before, along with their
shortcomings.
	Going back to your suggestion, I'm also not sure that
there should
automatically be a whole 'nother ranked vote in the
event of a majority
rule cycle.

I replyi:

Yes, I prefer Approval for the 2nd balloting.

By the way there are natural circular ties whose
possibility can give
incentive to equal rank all the qcceptable candiates
in 1-balloting
Condorcet. For that reason it might be good to have
the 2nd balloting
whenever there's a circular tie. It would depend on
how important it is
to
people to avoid the expense of a 2nd balloting.
Myself, maybe I'd
rather
hold a 2nd balloting whenever there's a circular tie.

Doing wv, and going to a 2nd balloting if there's an
all-majority
circular
tie has the advantages 1) That it less often brings
the expense of a
2nd
balloting; & 2) That it uses wv, which automatically
deals with
truncation.
Just looking for a BeatsAll winner, and going to a 2nd
balloting
whenever
there's a circular tie, has the adavantage that I
wouldn't have
strategic
incentive to equal rank all the acceptable candidates.
But then voters
will
have to manuallly deal with certain circular ties that
are neatly
automatically dealt with by wv.

Of course those advantages might be combined if the
1st balloting by wv
includes enhancements that get rid of that that
acceptables-equal-ranking
incentive. I'll talk about those enhancements in a
subsequent posting.
Then
we only go to a 2nd balloting if the circular tie
consists of all
majority
defeats.


You continued:

In my proposal, if a majority accepts the completed
winner as
legitimate, then there is no need for a second
balloting.

I reply:

But doesn't it require a 2nd balloting just to take
that up/down
acceptance
vote?

You continued:

I'd said:

>But another possibilit for the 2nd balloting is an
Approval balloting.
>That simpler method won't produce another cycle, and
the defense
against
>the
reversers would consist of their victimes not voting
for the reversers'
candidate. In that case the defensive truncation
elects the CW.

	I see no reason to assume that a subsequent approval
balloting will
pick
the sincere Condorcet winner if one exists, or the
sincere completion
winner. So I can't accept this as a solution.

I reply:

The published results of the 1st balloting provide the
information
needed
for people to get their best results in the 2nd
balloting by Approval,
resulting in the election of the CW if there is one.

I'd said:

>
>The 2nd balloting pretty much eliminates whatever
amount of reversal
>problem exists.
>Something similar can be used for committees. I'd
suggest it for an EM
>poll, for instance.
>To a poll, I'd add the rule that, after the result is
announced,
there's
>about
a week or half-week period during which anyone can
truncate their
ranking if
they choose to, or can uprank an alternative to 1st
place.
>(I prefer open polls in which voters post their
ballots. That's the
way
>to have proven security.
>But, as these ballots come in, reversal opportunities
could be obvious
to
>those
who haven't voted yet. The defdensive strategy option
avoids that
reversal
problem).

	I don't quite understand this. Is the second
balloting still an
approval
balloting?

I reply:

No, there's no 2nd ballotingl in that system. When
you're calling for a
poll, on EM or anywhere else, it's difficult enough to
ask people to
take
part in one balloting. You sure don't want to ask them
to take part in
2
ballotings. So it's just a 1-balloting election. But,
for, say, a week
or
half a week after the results are posted, voters have
the option of
truncating their ballots or moving additional
candidates up to 1st
place.
That's so that offensive order-reversal, if it has
taken place, can be
countered.

When everyone's votes are posted to the list, as I
prefer, would-be
reversers who haven't voted yet can spot the
conditions where reversal
could
succeed. Hence the desirability of allowing a few days
for
countermeasures.

I'd said:

>
>Either of those 2 enhanhancements, or something
similar, could be used
>for committees.
>Tom Roiund and Steve Eppley separately independently
proposed the
candidate-withdrawal option:
>After an election result, any candidate can declare
that he withdraws,
>and call for another count of the same ballots with
his name deleted
from
>them.
>That also thwarts offensive order-reversal.
>I notice that candidate-withdrawal is part of your
proposal.

You replied:


	Sort of. In the proposal I made, candidates can
withdraw in between
ballotings, but they can't order a recount of the
previous balloting
with
their name deleted. I think that candidate withdrawal
option is an
interesting idea, but it's not exactly what I proposed
here.

I reply:

With the candidate withdrawal option, there's reallly
no need for more
than
1 balloting. Offensive order-reversal can be thwarted
every time by
candidate-withdrawal in a 1-balloting election.

Candiodate withdrawal is really the simplest, easiest,
& most
effective
anti-order-reversal enhancement. It was initially
suggested for IRV,
but it
works for wv too.

I'd said:

>For 1-balloting elections, the voter could have the
option of drawing
a
>line in his ranking, to indicate that, in the event
of an
>all-majority-beaten
circular tie involving candidates above and below that
line, he wants
to
drop
the candidates below the line. Then the same ballots,
with the
candiddates
dropped, would be recounted. That would be a powerful
>deterrent to offensive order-reversal.
>I don't claim to have covered all the possible
anti-reversal
>enhancements. We've discussed a few other ones.
>For instance, a tentative possible solution involves
giving the voter
the
option to indicate that, if there's an
all-majority-beaten circular
tie,
>and if groups of voters sharing the same 1st  choices
have certain
patterns
>of unanimity and non-unanimity within those groups,
in their
subsequent
choices, that voter wants do delete certain
candidates. That may catch
be
able
to catch some offensive order-reversals. Obviously
that isn't a
complete
detailed proposal.

You replied:

	Yes, this is a crazy and fascinating direction that I
haven't
seen explored much. That is, a vote which changes in
response to the
other
votes cast! I tried to get a proposal together along
these lines in the
fall, but it is difficult stuff! With three candidates
it is perhaps
manageable, but with a lot more than that, tremendous
complexities seem
to
emerge from whatever method I consider. Still, it is
an interesting
direction to take with further discussion, even if it
ultimately turns
out
to be a goose chase.

I reply:

No, those anti-order-reversal options will work, regardless of how many 
candidates there are. The
more you alleviate
the
strategy problem, the more complicated the enhancement
gets (except for
the
simple candidate withdrawal option). Of course the
unanimity test
depends on
a 1-dimenstional political spectrum.

I've described some anti-order-reversal options in a
previous posting,
but I
intend to post another more complete message about
them.

Just to mention one kind of fancier methods, one could
use wv instead
of
Approval as the base method for NES. NES(wv).
Uncountered
order-reversal
wouldn't be a Nash equilibrium because defensive equal
ranking could
improve
the outcome for someone. The trouble is that, in the
symmetrical cycle
that
offensive order-reversal could make, all the members
of the cycle could
end
up equal ranking another cycle-member, in the outcomes
that NES finds.
That's ok though, because, the same 3 testing options
that I described
as
triggers for defensive truncation could also be used
as triggers for
refusal
to defensively equal rank someone in the wv that is
the base method for
NES.

That's an improvement, because refusing to equal-rank
someone isn't
nearly
as drastic as dropping him/her from your ranking.

NES(wv) might also be a way of getting rid of the
acceptables-equal-ranking
incentive. I'm now not so certain that NES(Approval)
or DSV(Approval)
will
accomplish that. Maybe, but maybe not.

If not, maybe NES(wv), or even NES(NES(wv)) might do it. Or maybe it's 
impossible to get rid of that incentive, when complying with the majority 
defensive strategy criteria.

Other radical oproposals that might be
interesting to
check out could include DSV(wv), as opposed to the

usually-discussed
DSV(Approval). Could DSV be the base
method for DSV? DSV(DSV(Approval), etc.?

Even
more outrageous would be combinations of these various
methods like
NES(DSV(wv)) or DSV(NES(wv)), etc. I'm not saying that
those are
feasible or of practical interest. Some of the less
extreme ones might
be.

I'm not advocating those, just enumerating
possibilities. One thing for
sure
is that none of these will get rid of vulnerability to
offensive
order-reversal. That vulnreability is built in to all
methods that
don't
have a worse problem.

Or instead of NES(wv), one could just try wv with an
automatic
equal-ranking
option, whereby the method would equal rank for you
when it's to your
advantage, subject to cancellation under specified
conditions.

I wasn't going to start those topics here.

There isn't room in this letter to really discuss
that.

Other than with the candidate-withdrawal option, it
can start getting
elaborate and complicated when one proposes options to
minimize the
order-reversal problem.

And, as I said, it isn't just Condorcet that has an
order-reversal
problem.
All the best methods have it. All the methods that
don't have a worse
problem. (IRV and Plurality are examples of methods
with a worse
problem).

You continued:

	I was working on a method with a "variable fraction
ballot" before I
threw up my hands in frustration and decided to stick
with the simpler
proposal that I made. The basic idea was that the
strength of an A>B>C
voter's vote in favor of B over C can
depend--according to some
equation
that the voter is able to determine--on the percentage
of B voters who
vote B>A>C rather than B>C>A or B>A=C. The strength
could be 1
(ordinary /
full), 0 (equivalent to truncation, or somewhere in
between. Maybe even
a
range from zero to negative one as well.
	Using this for the final binding vote was the
original deadlock
breaker
in my procedure. (Note that in the midst of deadlock
after several
rounds
of voting, voters would have a great deal of
information to base their
equations on, which is of course helpful.) But aside
from the extreme
complexity required of voters and voting machines, I
am still not sure
what kinds of equations would be effective in
situations with several
candidates.
	Of course there could be ballot options to just trust
the equation
offered by a particular candidate, party,
organization, etc., which
would
mean that not all voters would have to devise their
own equations from
scratch. But still, it's very problematic.

I reply:

A partial reduction in the strength of a pairwise preference won't give the 
guaranteed order-reversal deterrent that outright truncation gives. That, 
and the complexity of the fractional-strength preference votes suggests that 
it's better to just allow truncation and equal ranking, without the 
fractional strength preference votes.

I'd said, before I knew better:

>Methods more fancy and complicated than Condorcet are
discussed.
Though
>all methods have strategy, there's always the
possibility that one of
those
fancier methods will get rid of defensive strategy
need, as I've
defined
>it here. Or at least let defensive truncation elect
the CW, without
the use
>of a 2nd ballotiong.

Because, as I undestand it, Gibbard-Satterthwaite merely says that all 
methods have strategy, I'd hoped that doesn't mean they all can have 
defensive strategy need. But they all can.

Later I realized that no method that uses pairwise preferences can get rid 
of the order-reversal problem.

You continued:

	Of course, I would be interested in hearing about as
many of these as
possible. I would be very impressed to see a Condorcet
efficient
single-balloting method that is more strategy
resistant the winning
votes
ranked pairs & beatpath.

I reply:

Some limited impreovement is possible. For instance, some methods seem to 
make a more difficult faction-numbers requirement for successful 
order-reversal. And NES(Approval), DSV(Approval), NES(wv) or NES(NES(wv)), 
or maybe NES(NES(Approval)), or wv with an automatic equal ranking option 
(with an option to withold the equal ranking under specified test 
conditions),  might get rid of the incentive for equal ranking the 
acceptable candidates, for the person who divides candidates into acceptable 
and completely unacceptable. But I don't know if that latter improvement is 
compatible with the majority defensive strategy criteria. I'd guess 
probably, and that one of the above-named methods might do it, but I'm not 
sure.

NES & DSV could, in principle, have anything as base methods, including 
Approval, wv, SMA, themselves, or eachother.

You continued:

It seems that whichever way
you slice
Condorcet,
you end up giving voters a chance to overrule a real
majority with a
fake
majority, unless you complete with a totally different
method, which
gives
you all the strategic problems of that method.

I reply:

Exactly. To get the strategic properties we want from a rank method, it's 
necessary to use pairwise preferences. But with those a symmetrical cycle 
can be made by order-reversal, and the method has no way to tell what's 
going on.

Sure, order-reversal isn't a problem with methods that don't use pairwise 
preferences, but such methods can't have the best strategy properties that 
we want from rank methods. They have worse problems than vulnerability to 
order-reversal.

You continued:

So far,
I don't think a
really mechanistic system can weed out offensive
strategy, which is why
my
proposal relies on fairly subjective human judgement.

I agree. But that human judgement can inform a 1-balloitng method. That's 
why I suggest these 3 defensive strategy triggering tests:

1. Cycle line option:

(previously called "tie-drop-option)

The voter can designate a line in his/her ranking such that, If there's a 
circular tie, consisting of all majority defeats, and some members of the 
circular tie are above the line and some below, then that voter wants to 
employ a defensive strategy against the candiates below the line.

(With wv, that defensive strategy could be defensive truncation. With wv 
with automatic equal ranking, or with NES(wv) or NES(NES(wv)), etc., the 
defensive strategy could be the witholding of equal ranking. These are the 
defensive strategies meant when triggered defensive strategy is referred to 
in connection with the other 2 defensive strategy triggering tests too.

2. Order-estimate option:

The voter can specify a political spectrum ordering, or requirements that 
most of some candidates 1st choice voters vote a specified 2nd choice. If 
there's an all-majorities circular tie in which voting is contrary to these 
estimates,  then the voter wants to use a specified defensive strategy 
against the candidate whose voters caused the cycle by voting contrary to 
the voter's order-estimates.

3. Unanimity test:

The voter can specify that if the unanimity test that I described in detail 
in an earlie posting suggests that a candidate's voters have caused an 
all-majorities circular tie by order-reversing, then that voter wants a 
specified defensive strategy to be triggered.

[end of automatic defensive strategy triggering tests]

In these ways, the method could be instructed by the voter to act for him in 
employing a defensive strategy under conditions specified by the voter.

You continued:

Of course, if I
can
be proven wrong, that will be a good thing.

I reply:

I'm certain that you're right, though, as described above, the voter can 
optionally give information to the method, with which for it to decide when 
to employ defensive strategy for the voter.

Sorry about the scrambled lines.

Mike Ossipoff

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