# [EM] Blake's margins arguments

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Feb 18 00:22:30 PST 2003

Blake has recently recommended his margins arguments to us, and so
for that reason I'd like to reply to them here. I realize that all of
these arguments have already been replied to here more than once.

Because Blake's arguments are very long, I'd like to copy part of
my reply to the beginning of this message:

Before re-answering the remaining arguments, let me show an example
of how wv & margins treat majorities differently:

101: A
50: BAC
100: CBA

About 60% of the voters have indicated that they'd rather elect
B than A. And so margins elects A.

WV counts, keeps, & honors the B>A majority. A has a majority defeat that wv
doesn't lose or erase. With margins, what happens to that majority against
A? Margins erases it.

With wv, I should add that B wins whether or not the B voters vote
a 2nd choice.

If one wants a majority to count, then one doesn't want margins.

Blake said:

Margins vs. Winning-Votes in Condorcet Criterion Methods

Some time ago, I had a long-running argument on the Election-Methods
list
I can
in the space I allowed myself. Please email me if you want proofs of
the
various factual assertions I make throughout this essay.

By the way, when I speak of a pairwise majority decision in this essay,
I am
referring to a majority of those expressing a preference between the
two
candidates, which is not necessarily the same as a majority of those
voting,
or a majority of those eligible to vote. Some people would prefer to
reserve
the word majority for one of these other cases, and my opponents in
this
argument would reserve it for the second.

You can define majority any way you want to, but the definition that's
actually in use says that an electoral majority is a set of voters
consisting of more than half of everyone voting in that race.

Such a set of voters is an important one, since they have the power
to get their way. The question is, though, what do they need to do
in order to get their way? With most methods they'll sometimes have
to reverse a sincere preference, for instance. We've chosen the winning
votes (wv) Condocet methods because they minimize the need for
a majority group of voters to misrepresent their preferences in order
to protect a majority preference. Margins Condorcet has no such
properties.

However, it's understandable that Blake would want to use a different
definition of majority, considering how poorly his method does for
majorities as the term is usually defined.

[I've deleted parts of Blake's arguments page that don't make
arguments]

Blake continued:

Of course, we could avoid the issue by forcing voters to give complete
rankings (which is what I believe Condorcet expected). So, if their
actual
preference is:

A>B=C

They could vote either:

A>B>C

or

A>C>B

The voter would just choose between these alternatives randomly. What
then
will be the effect? The people choosing randomly between B and C will
end up
split somewhat evenly between the two factions. On average, for each
voter
holding B and C equal, there will be about half a vote placing B over
C, and
half a vote placing C over B.

So, instead of forcing the voter to randomly choose between filling in
B>C
and C>B, we might place half a vote for each side.

Excuse me, but when I don't indicate a preference between Smith &
Jones, I'm not voting half of a preference for Smith over Jones and
half a preference for Jones over Smith. I'm voting no preference either
way. Of course whether or not those falsified half-vote have an effect
on the outcome, and what kind of an outcome it has, depends on how
defeat strength is measured.

Blake continued:

This system of giving half a vote to each side is mathematically
equivalent
to using the margin of victory to gauge strength, which is the method I
will
be advocating. For subtle statistical reasons, in these methods, a
voter is
slightly better off on average filling in their ballot randomly than
leaving
lower candidates unranked. More on that later.

Blake's unstated assumption, when making the above statement, is
that the election is a 0-info election. Actually, our public political
elections are never 0-info.

Blake continued:

I think it reasonable to expect that generally, the more people there
are
who favour a proposition, the more likely it is to be true. Similarly,
the
more who oppose it, the less likely it is to be true. The obvious
conclusion
is that if we have a majority vote, we have justification for siding
with
the majority. Of course, the majority may well be wrong. Sometimes
majorities will actually come into conflict with each other, in which
case
we usually choose the greater ones because by this reasoning, they are
more
likely to be true.

Here Blake is expressing his belief that there's such a thing
as an objectively true proposition (pairwise defeat). As I've pointed
out before, it's meaningless to talk about an objectively true
proposition unless one can give an operational definition of it.
A definition that provides a test for determining if a proposition
is objectively true. Blake is in the minority with his belief that
pairwise propositions that say one candidate is better than another
have objective truth or falsity.

In some other areas of discussion, people talk about how the truth
or falsity of one set of statements can be proved to affect the
truth or falsity of other statements, or they name a set of
initial statements by which other statements are proven true or false.

In these areas, it's meaningful to talk about truth or falsity, since
methods are available for proving them. That can't be said of Blake's
"true pairwise proposition" or "best candidate".

Blake could say that, with no information about who the electorate
are, the margin of the AB defeat is a measure of the probability that
Blake would consider A better than B. Maybe, but it's questionable
how much that means under the conditions that actually exist. If
Blake is a Republican and the other voters are Greens, then Blake's
assumption will prove very wrong.

Besides, the whole probability justification depends on the assumption
of sincere voting. But with margins' strategy problems, sincere voting
can't really be assumed. We may have had sincere voting in some of
our polls, but there was one in which order-reversal apparently
occurred
(probably without strategic intent). In our most recent poll
someone tried to vote anonymously, probably because he wanted to vote
in a way that contradicted his previously-expressed preferences. The
ballot was disallowed, because our rules explicitly forbade anonymous
ballots.

But if we could assume sincere voting, then of course Borda would
be the best rank-count. And in fact CR's high social utility potential
would be achieved, and there'd be little reason to use a method other
than CR.

Maybe you,
and maybe I, are sure that such a candidate proposition is true or
false, but in publicly-accepted reality, that's just your opinion
or mine. Blake has called me a postmodernist, because, I believe,
which of 2 candididates is better than the other really is, publicly,
a matter of opinion.

And Blake's advocacy of margins is based mostly on that fallacious
notion.

Blake continues:

We would not expect a vote of 51 to 49 to be stronger that 50 to 0, in
the
sense of being more likely right. To do so, one would have to entirely
discard the information provided by the presence of the votes on the
losing
side. However, if we take every "yes" vote as an evidence for a
proposition,
and every "no" vote as evidence against, subtraction seems a natural
choice.

The alternative is to argue that 51 to 49 is stronger than 50 to 0, but
a
single changed vote can make this 50 to 50, a neutral decision. Another
single vote changes this to 49 to 51, now stronger than 50 to 0, but in
the
other direction. I find this hard to justify.

But Blake isn't just saying that 50 to 0 is stronger than 51 to 50.
He's also saying that 3 to 1 is stronger than 50 to 49.

For good reason, most organizations won't even count a vote that
doesn't have some minimum number of voters, called a quorum. They'd
disagree with Blake on which of those 2 above defeats means more.

But all this is about intuitive emotional plausibility. I'm more
interested in the standards of majority rule and getting rid of
the lesser-of-2-evils problem. As I said, those standards are
the most popular ones among single-winner reform advocates, and
those are the things that we hear voters expressing concern about.

If certain standards are important to you, then choose a method that
does well by those standards, rather than such issues as which
defeats look more emotionally plausible--unless you consider that
itself to be an important standard.

Like the IRVists, Blake doesn't consider majority rule & LO2E to
be the important goals. Fine. Blake isn't wrong. His standards are
merely different from those of most of us who want better voting
systems. I don't set out to show that Blake is wrong about which
defeat measure is better. I merely intend to show that his does
very poorly by the popular standards that I named above.

Blake continued:

Majoritarianism

One argument made on behalf of winning-votes is an appeal to a
precisely
defined majoritarianism. The argument is that a majority comprising all
the
voters (as opposed to a majority of those eligible to vote, or a
majority of
those who expressed a preference) is the only true majority.

Nonsense. As I said, "majority" can mean, for Blake, whateve he
wants it to mean.  He can talk about any kind of majority he likes,
and I won't say it isn't a true majority. Even if it's something
quite different from what others mean when they speak of an
electoral majority in an election with more than 2 candidates.

Blake continues:

So, for 100 voters, a vote of 51 to 49 must take precedence over a vote
of
49 to 2, as the first is a true majority and the second is not. Of
course,
winning votes goes far beyond this. For 100 voters, it says that a vote
of
52 to 48 is stronger than 51 to 1, even though both are true majorities
by
their definition.

Only Blake has used the term "true majority".

Contrary to what Blake says above, wv advocates aren't saying that
one of those defeats is stronger than the other. They're merely
_defining_ it so--defining defeat strength in that way. That's very
different from asserting that one defeat is stronger in some
objective way that we could debate. We define defeat-strength as we
do in order to gain compliance with criteria that measure for standards
that
we and many others consider important. Also, there are ethical
reasons why wv is fairer, and I'll get to those later in
this message, though they've already been posted here.

Before re-answering the remaining arguments, let me show an example
of how wv & margins treat majorities differently:

101: A
50: BAC
100: CBA

About 60% of the voters have indicated that they'd rather elect
B than A. And so margins elects A.

WV counts and keeps the B>A majority. A has a majority defeat that
wv doesn't lose or erase. With margins, what happens to that majority
against A? Margins erases it.

With wv, I should add that B wins whether or not the B voters vote
a 2nd choice.

If one wants a majority to count, then one doesn't want margins.

Blake continued:

There's a big problem with viewing a majority of voters as a special
kind of
majority. Voters could have made the 49 to 2 vote into this kind of
majority
unranked.

It isn't clear what Blake is talking about here. That people have
the power to falsify preferences, making an insincere majority vote?
Sincerity can't be legislated, but that is hardly a justification for
erasing a voted majority preference.

Blake continued:

Another problem with this argument is that it assumes that we believe
in
majority rule dogmatically, and only argue about how it should be
"correctly" defined. Such an argument can go nowhere.

What? Neither I nor anyone else said that you or anyone should
believe in majority rule. In fact, I've repeatedly said that you
aren't wrong when your standards are different from those of other
people.

For instance, no one is saying that you should value majority rule
because so many others do.

But because so many people do value that standard, it's worthwhile
pointing out how poorly your method does by that standard,
as it is understood by everyone but you, with "majority" defined as
people other than you define it.

Additionally, majority rule failure results in strategy problems.
One reason to honor majority rule is to minimize need for defensive
strategy, as measured in criteria such as SFC, GSFC, WDSC, & SDSC.

And no, Blake, no one is saying that you should believe in the
importance of minimizing the need for defensive strategy. I merely
say that if majority rule and minimizing defensive strategy need
are important to someone, then your method is not what they want.

Blake has a longstanding habit of misquoting people with whom he
disagrees, and his website is no exception.

It's like people
who
take "democracy" as given but have a very specific definition that
supports
all their own ideas. In effect, they are taking their own views as
axiomatic.

I'm sorry to say this, but that's really an asinine statement;
I've been constantly repeating that Blake isn't wrong if he has
different standards from those of others. It's as if Blake is
conducting debates with himself, speaking for us with statements that
he'd llke to hear and refute.

Again, no one says that "majority" has to be defined one way instead
of another. But hopefully Blake can forgive me if I mention the usual
meaning of electoral majority in multicandidate elections. I'm not
saying that's the only possible meaning, and Blake may define anything
in any way that he wishes to.

Blake continued:

To understand why using margins has been called into question you have
to
consider that many people are greatly concerned that if a new electoral
method was adopted, people would not express all their preferences.
Sometimes this can actually cause the voter's favourite to win, as in
the
following example:

Group
I 49 A -- Actually prefer A > B > C
II 11 B > A > C
III 40 C > B > A

[...]

way
that partial rankings cannot have so much effect.

Only if you consider majority rule &/or the goal of minimizing
the need for defensive strategy to be important, then yes let's
tablulate votes in a way that won't violate those standards.

Yes, truncation examples are a way in which that happens in margins.

Blake likes to say that if we make it so that truncation won't do
that, then people will just resort to offensive order-reversal
instead. But offensive order-reversal is much less likely to happen
spontaneously when people vote. People will vote short rankings because
they're in a hurry, because they aren't interested in the differences
among all the candidates, etc. Nonstrategic truncation. That's very
different from strategically voting your last choice over a middle CW.

Not only is offensive order-reversal much less likely spontaneously,
but it's also much more for a strategist to ask of voters. The request
would sound ridiculous.

Also, Blake doesn't understand, though it's
been frequently explained to him, that offensive order-reversal differs
from truncation in another way too: It's risky in wv. It only works
inkling of your intent to do order-reversal against them, and they
don't co-operate with their own victimization, then your attempted
offensive strategy will backfire badly against you.

It's also been pointed out to Blake, futilely apparently, that
a campaign to organize offensive order-reversal couldn't be kept
secret from its intended victims, and it's a sure thing that they'd
withdraw their help from the reversers' candidate, and the offensive
order-reversal would backfire, and the reversers would regret their
strategy.

Blake continues:

Recall the example above:

Group I 49 A -- Actually prefer A > B > C
II 11 B > A > C
III 40 C > B > A

Using winning-votes, the winner is B. Of course, if group I had just
randomly filled out their ballots instead of leaving candidates
unranked,
their votes would not have been diminished in this way. The advocates
of
winning-votes hope the voters won't understand the method well enough
to do
this.

Again, Blake takes it upon himself to speak for us, in this
case telling you what we hope.

Guessing about that might make some sense if it weren't for the
fact that we've repeatedly explained to Blake that order-reversal
will be deterred in wv. We never said that wv's success depends on
people not understanding that there's an offensive strategy of
offensive preference-falsification. But we've told why that strategy
is deterred, and why its perpetrators are unlikely to get away with
it, because it's impossible to oganize it secretly.

If one group of voters understands the strategy of offensvie
order-reversal
well enough to try to use it, surely other voters can be
assumed to understand it too, and to understand the simple
counterstrategy
that that will make the reversers sorry for their
strategy attempt: Don't help the reversers' candidate.

I 25 A > B > C
I 25 A > C > B -- Actually prefer A > B > C
II 11 B > A > C
III 40 C > B > A

[I've already replied to Blake's random-ranking arguments that he
brought up earlier. I sometimes don't reply to arguments that I've

Blake continued:

In fact, in winning-votes it is never justifiable, even for
strategic reasons, to leave candidates unranked, as long as your goal
is to
elect the best possible candidate from your perspective.

Is that supposed to be a problem?

Blake continued:

Partial Rankings as a way to Punish Strategizers
So, if voters are punished for leaving candidates unranked, what use is
even
allowing them the opportunity?

Blake thinks that a voter is punished for voting a short ranking
because wv doesn't let that short ranking take victory away from
a CW whom a majority have voted over the truncator's candidate.

Blake continues:

One idea is that instead of being used
to
represent absence of opinion, partial rankings could be used as part of
a
strategy to get the sincere Condorcet winner elected. Now, I must admit
to a
certain suspicion with this kind of argument. Presumably, we could have
all
kinds of check boxes and special markings on the ballot which would
only be
used for strategy.

Maybe Blake is proposing that, but we never have.

Blake continues:

Partial rankings, once shown not viable for sincere
use
is resurrected as useful as one of these kinds of tricks. I doubt that
anything of this kind is useful, but am willing to argue on a case by
case
basis.

Here is an example brought up to show the punishment use of partial
rankings:

Group I 40 A C B -- actual preference A B C
II 30 B
-- actual preference B A C III 25 C B A

Here, group I is using strategy to defeat "B", and group II is using a
strategy to punish them.

Using winning-votes, the winner is "C", which is group I's sincere last
choice. Using margins, the winner is "A", so their order-reversal paid
off.
of
punishing group I for their strategy. Of course, it does not give a
better
result from group II's perspective. In this case, they are punished as
well.

Not as much. C isn't as bad for B voters as he is for A voters.
The A voters know that, and the B voters know that the A voters know
it.
If you regard it as a game of chicken, the B voters have tremendous
advantage, because victory by A isnt as bad for them, and because
B is the CW, the rightful winner, and it's the A voters who are
attempting something that obviously amounts to stealing the election
from a rightful winner.

The defensive strategy of refusing to rank A is intended to deter
order-reverssal by A voters, and that deterrent strategy is
a "dominated strategy", meaning that there's a configuration of
other people's votes in which it can worsen one's outcome, but
there isn't a configuration of other people's votes in which it
can improve one's outcome.

But dominarted deterrent strategies are common in legal systems
and the animal kingdom. They're used so universally because they work.

The fact that defensive truncation, to deter offensive order-reversal,
is a dominated strategy isn't a meaningful argument against it.

Blake continues:

However, the same can be done in Margins if the B 1-st voters use the
strategy of ranking "A" last.

I 40 A C B
II 30 B C A
III 25 C B A

Now, "C" wins. It has been claimed that this strategy of punishment
ranking
is dangerous for group II. After all, if the "A" voters relent, could
not
the C voters take advantage of being raised by group II to use order
reversing themselves? In fact, the arithmetic does not allow it. It is
always safe to drop a candidate who could effectively use strategy
behind
candidates who could not.

Now Blake is assuming that the B voters know who could use offensive
order-reversal against them. With good enough knowledge of the
other voters' numbers, Blake says, the B voters could counter the
offensive order-reversal in margins. Yes, and with good enough knowledge
about the other voters' preferences and numbers, even Plurality would
always elect the CW. I suggest that a defensive strategy that depends
on having a good knowledge about the factions' numbers isn't very
useful. If voters have that kind of knowledge, we don't need Condorcet
anyway.

What Blake is offering to you is a defensive strategy for B voters
that consists of order-reversal. Note that Blake's defensive strategy
requires the B voters to order-reverse, while wv's defensive strategy
for B voters merely requires them to refuse to vote for the candidate
of the likely offensive order-reversers.

Blake continues:

The partial-ballot punishment strategy is never expected to improve the
result from the punishers perspective. It may be good to convince
others
that you will use this strategy (though no better than my suggested
order-reversal strategy). It does not make sense, however, to actually
do
it. It is really a bluff.

Wrong. It makes sense for the B voters to carry out the threat, to
publicly advise eachother to use the counterstrategy. It's more than
a bluff if the B voters actually refuse to rank A.

Again, Blake is missing the fact that dominated deterrent strategys
are in wide use, in the legal system and in the animal kingdom.

Their goal is an equilibrium in which the deterred act doesn't happen.

We have a law providing that the state will have to support you for
a long time if you rob a bank. But that's to your disadvantage too.
So you don't rob the bank, and the state doesn't pay for supporting
you for 20 years. Neither player could improve on his outcome by
unilaterally changing his strategy.  The state would gain nothing by
repealing the deterrent law when you don't rob the bank. You only
lose if you rob the bank.

Sure, if you do rob the bank, then not only do we lose the money
you've spent or hidden before getting caught, but the state also
loses the money that it costs to support you for 20 years. No matter
what you do, the state can't get a better outcome by having that
deterrent law--the state can only lose more money by having that law.

And yet they do have that law, and lots of others like it, as do
all legal systems. Because dominated deterrent strategy still deters,
and when it does, it doesn't cost anything.

The cat who threatens to attack a cat who intrudes on its territory
risks getting all scratched up if the intruder calls his bluff.
The risk of that fight is worse than having the intruder in his yard.
But the intruder knows that he means it, because it is his yard,
and the would-be intruder doesn't want to get hurt either. So he
doesn't intrude, and no one gets hurt, and the defender's yard isn't
intruded. That's an equilibrium where neither side could gain by
changing strategy.

Blake continued:

might
have large numbers of voters putting in incomplete ballots in the
belief
that their favourite candidate was the true public choice, and that
others
were likely to conspire against them. If too many people do this,
elections
could end up like plurality.

Don't vote for anyone whose voters are talking about offensively
order-reversing against your candidate, if you belive that your
candidate has a chance of being CW. In general, if it's a
devious offensive-prone electorate, don't extend your ranking any
farther than the candidate whom you expect to be the CW.

It would be ridiculous for everyone to vote for only their favorite,
and it's a little ridiculous to suggest that outcome.

Blake continues:

So, there's no need to confuse the method to enable a strategy that
isn't
even practical.

The criteria SFC, GSFC, WDSC, & SDSC tell why I like wv. The example
that I posted shows why too.

It isn't only about defensive truncation. Often a majority group
won't need any defensive strategy, where they would in margins.

Check those criteria at our websites:

http://www.electionmethods.org
(at the technical evaluation page)

and

http://www.barnsdle.demon.co.uk/vote/sing.html

Blake continues:

Conclusion
So, I hope this explains why I support Margins. I have not tried to
counter
every possible argument or example in favour of winning-votes. However,
I
have given some reason to believe that the perceived advantages of
Winning-votes are in no sense free. When there is no Condorcet winner,
it
makes the result much less plausible.

It offers all the guarantees named in the majority defensive
strategy criteria, and demonstrated in the simple, plausible example
that I included in this reply.

Blake continued:

it
prevents incomplete ballots from having a disruptive influence, this
effect
is easily circumvented if the voters have even a modest understanding
of the
method.

I've told why offensive order-reversal isn't as likely as
truncation, which may or may not be offensively intended. But
the majority defensive strategy criteria don't say anything about
truncation. They merely described how the need for defensive strategy
is minimized by complying methods. And note that in my example
in this letter, it isn't necessary that the A voters are using
offensive truncation strategy. Maybe they just don't hava preference
between B & C. Either way majority rule is violated by margins but
not by wv.

Blake continued:

Although its advocates believe that it provides an extra
strategy
which will be useful in supporting sincere Condorcet winners, I have
given
reason to believe that this strategy is not particularly useful,

Strategies like it are universally used because they are useful &
effective in deterring what they seek to deter.

Blake continued:

is
redundant

Blake offers us, instead, a strategy that involves defensive
order-reversal, instead of defensive truncation, and which requires
a knowledge of the factions' numbers.

Blake continued:

, and may be disruptive as well.

???

Blake continued:

It seems then that there is
no
reason to abandon the more intuitive Margins method.

Except that it avoidably violates majority rule and increases the
need for drastic defensive strategy--if you care about those things,
that is. Blake doesn't, and that's fine. But Blake is dogmatically
claiming that others' standards are wrong and his are right, and that's
where he's wrong.

Mike Ossipoff

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