Margins, majority, strategy

Blake Cretney bcretney at
Tue Sep 22 16:17:32 PDT 1998

I am going to attempt to reply to some of the points Mike has made with
regard to the Margins vs. Votes-Against issue.

First, I would like to admit that Votes-Against is indeed more
truncation resistant.  In effect, it penalizes voters for insincerely
leaving candidates unranked.  It also penalizes voters for sincerely
leaving candidates unranked.  I think if you really think the harm of
truncation is so great you have to penalize all voters who leave
candidates unranked, it would be more honest to simply ban leaving
candidates unranked, as the Australians do.

> > Votes-Against fails this criterion because if your sincere preference
> > is A > B=C, it is more likely to your advantage to rate A > B > C or 
> > A > C > B.  It can back-fire, but the insincere vote is more likely
> > to get you what you want, so unless you have detailed knowledge about
> > how everyone else is voting, the insincere vote is better.
> But that isn't really what I'd call a serious strategy
> dilemma. No one is being strategically forced to do other
> than vote their favorite alone in 1st place.
> I don't like it when people have to rank a less-liked alternative
> equal to or over a more-liked one. But if I'm indifferent between
> B & C, and if I estimate that I could benefit by ranking B over
> C, then that doesn't bother me. If I'm indifferent between them
> why should I care if I rank one over the other?

Well, I guess you could complain that you have been forced to waste your
time unnecessarily filling out a ballot randomly.  However, I am more
concerned with the people who do not random-fill than those who do. 

Their votes are not worth as much, for reasons almost everyone would
call unfair.  In a sense, I am not so much concerned that people will be
encouraged to random-fill as that many will choose not to.

> I don't know how meaningful it is to say that Margins
> meets a Sincere Expression Criterion which Votes-Against
> doesn't meet, when Margins requires, as defensive strategy,
> the most extreme forms of insincere expression. And when
> that isn't the case with Votes-Against.

Actually, its the Sincere EXPECTATION Criterion.  In short, it
says that a sincere vote should be justified by its expected result,
assuming no knowledge of how others are voting.  Of course, we know that
if a voter knows how others are voting, strategy does play a role. 
But should there be strategies even if you have no such knowledge?

When there are, it should force us to question whether our definition of
a sincere vote matches our method of vote tabulation.  Why do we define
1. A
2. B C
as a sincere vote for the opinion A > B = C, if either
1. A
2. B
3. C
1. A
2. C
3. B
will both on average get better results for this opinion?  There have to
be some limits on our ability to arbitrarily define what constitutes a
sincere vote.  Votes-Against and Approval are the only methods I know
of with this problem.

> > I notice that when you say X has a majority over Y, you mean a majority
> > of all voters, not just those expressing a preference between X and Y.
> > So, it is in effect, a three way race between X, Y, and the abstainers.
> > Some people might want to use the word majority to mean a majority of
> > eligible voters, or of the population as a whole, etc.  I do not 
> > consider any of these uses of "majority" necessarily right or wrong, but
> > I tend to use it to mean a majority of those expressing a preference
> > between X and Y.

> In a multicandidate election, the universally-used meaning for
> "majority" is more than half of all of the voters who particpated
> in the election. You can use the word differently, and say
> that Jones has a majority over Smith anytime Jones beats Smith
> pairwise. But the word then has less meaning. And we already
> have terminology for that meaning: pairwise defeat.

I wonder what you mean by "universally-used".  I suspect that many
people will actually be confused by this use of "majority".  I know I
was, when I first started reading this list.  Certainly all those MPV
advocates who say that the winning candidate gets a majority in the
final round are implicitly assuming my use of the word majority.  Not
that MPV advocates are always right, but since there are so many of
them, I would consider their opinion before considering something as
universally accepted.  To me, it seems natural to view those people who
do not express a preference between two candidates as not participating
in the simulated vote between them.  So, a candidate can have a majority
in the simulated vote just by beating the other side.

But of course, this is just a semantic argument.  The real argument is
whether a pairwise victory where the winning side constitutes a majority
of all voters should always take precedence over a pairwise victory
where it does not.  I think it is a big stretch to believe that this is
a direct result of the principle of Majority Rule, as you imply.

> A genuine majority has the power to get whatever its members
> all want. They should be able to do so without insincere
> voting. When they need insincere voting to get a result that
> they all want, I call that "defensive strategy". The need for
> extreme degrees of defensive strategy is very undesirable.
> When it's necessary to insincerely rank a less-liked alternative
> equal to or over a more-liked one I call that "drastic defensive
> strategy". As I said, that's what we don't like about FPTP
> (1-Vote-Plurality).
> Obviously, when the more-liked of those 2 is your favorite,
> that's even worse. And when it's necessary to rank a less-liked
> alternative _over_ your favorite--can a method get any
> worse than that?

According to Arrow's theorem, every ranked method has that property. 
Perhaps I have not understood you correctly.  Are you assuming there is
a Condorcet Winner?  Are you assuming middle voters do not use
order-reversal?  You will have to state your implicit assumptions before
I can respond to this.

> > However, I think we should consider that the same votes could result
> > 44 A C B
> > 28 B
> > 28 C B A
> > And that they are actually all sincere.  This results in
> If they're all sincere, there's no Condorcet winner to protect.
> And it isn't possible to avoid violating the expressed wishes
> of a majority. That isn't the kind of situation where there's
> a LO2E problem, where it's necessary & possible to avoid 
> serious violations.

I think this may be our main difference of opinion.  You are only
interested in situations where there is a Condorcet winner.  I think it
is important to use a method that is fair and reasonable even when there
is no Condorcet winner.  A fair method would not punish voters for
ignorance of the random-filling strategy.  A reasonable method would not
consider a vote of 
	52 to 48
as more decisive than a vote of
	51 to 1

We should remember why we abandoned GMC in its original form.  To do so
meant we had to abandon some of the stronger statements about the power
of a "genuine" majority.  And the difference between original and beat
path GMC only affected those cases without a Condorcet winner.  But we
abandoned it anyway because of the strange way it forced a method to
behave in these cases.  I think the next step is to abandon GMC and the
genuine majority distinction altogether for the strange results it

I imagine someone could at this point say, "All right, it does not make
any sense to sincerely leave candidates unranked in Votes-Against, but
that is a small price to pay for the defensive strategy it creates for a
Condorcet winner against order reversal.  That is, the purpose of
leaving candidates unranked should not be because you consider these
candidates equal, it is because your favorite is a Condorcet winner and
you want to try to protect against order-reversal."

Presumably, the introduction of the Votes-Against method would go
along with a public education campaign.  The campaign would explain how
leaving candidates unranked is not intended for cases where you think
they are equal and lower.  It would be explained that this is instead
intended to be used by voters if they are sure there candidate is a
Condorcet winner, and want to defend against possible order-reversal.

> Blake said that in Votes-Against, everyone would start
> ranking everyone, even if indifferent between them, and then
> the method would become equivalent to Margins, except for
> offensive strategies. Big difference.
> Say everyone starts ranking everyone, even without having
> a preference between them, and that, as Blake suggests, that
> will lead to order-reversal the way marijuana leads to heroin.
> But what's the Votes-Against defense against order-reversal?
> Strategic truncation. Avoid ranking more candidates than you
> estimate necessary. Oh what a cruel dilemma that puts the
> strategists in! They can't resist ranking everyone,even though
> they know that it sets them up for the order-reversal that
> everyone has been led to because of discovering the benefits
> of ranking everyone.

I would like to deal with the contradiction between the statements

1.  You should always random-fill instead of truncation
2.  Truncation defends against order reversal

The problem is that although the random-fill strategy is best if what
you care most about is getting your candidate elected, truncation can be
used as a way to punish people who insincerely vote against you.  That
is, given voters who vote X first, and then are evenly split between
voting Y and Z second, truncation will never help X win.  It will make X
more likely to lose.  It does not defend in the sense of protecting X,
and for this reason I am doubtful of whether people could be convinced
to use it.  However, it does mean that the election will tend to be won
by whichever of Y and Z, has voters who sincerely or insincerely rate X
the highest.

> But wait, it gets better than that: In VA, the defensive strategy
> punishes, & deters the order-reversal, while, in Margins, the
> more effective your defensive strategy, as a C voter in my
> example, the _safer_ you make the order-reversal. You make
> it safer if you vote B equal to C. You make it completely safe
> if you vote B over C. When order-reversal is less risky, it
> will be more tempting.

I doubt whether order-reversal will really be less risky.

> In a public election, if you organized the B voters to
> vote C in 2nd place, whether sincerely or not, do you think
> that the C voters wouldn't hear about that? You'd be setting
> B up for offensive strategy by C voters. And with Margins,
> it wouldn't even take order-reversal. Mere truncation would
> often do the job.

I do not think you can criticize a method for both being more safe for
the initial reversers and more likely to give the election away to the
other side.

> Look what you're saying the B voters would have to do to defend
> against order-reversal. The defense that they have in Margins
> is just the general pairwise defensive strategy. Whereas in
> Votes-Against, they can defeat the truncation by merely not
> voting for A or B, in Margins they have to vote the other
> extreme over the extreme whose voters they expect to use
> order-reversal. For 1 thing, maybe they don't know which
> extreme will try order-reversal. Also, anytime defensive 
> strategy requires you to insincerely raise someone in your ranking,
> that can give away the election when you misjudge and do so
> when you didn't need to. That's the trouble with drastic
> defensive strategy.

Remember that the whole purpose of the truncation strategy is to give
the election away.  It cannot make your candidate win, it can only make
the order-reversers lose.

Furthermore, I suggest that the normal pairwise defense strategy is more
natural than the Votes-Against truncation strategy.

For example, lets say my preference is 
B > C > A  with B being the suspected Condorcet winner

Now, I here that A is mounting an order-reversal or truncation
campaign.  This probably confirms my worst suspicions about them.  So,
what does the truncation defense strategy suggest I do about this?  Rank
B > C = A.  That is, increase A in my ballot.  Is it because this will
help B win?  Well, not exactly.  On average my change of vote will hurt
both B and C.  I am doing it so that if C order-reverses too, then A
might win.  A is my last choice remember.

This just seems totally unnatural to me.  What seems more natural is
that people who would have voted B > A > C will now consider B > C = A 
to punish A voters for their conduct. And that people who would vote B >
C = A will now consider B> C > A.

This is a clear punishment and deterrent to A in both methods.  I think
it is important to remember that the real purpose of order-reversal
punishment strategies is as a deterrent.  If the deterrent is strong
enough, no one will attempt to organize order-reversal campaigns.

You also mention the possibility that you do not know who will be doing
the order-reversal.  Well, if both sides have order-reversal campaigns,
both deserve to be punished.  You cannot punish them both under any

I am not sure whether I would ever accept a method that violates SEC. 
Such a method seems somehow fundamentally dishonest, or at least
confused.  However, I do know its violation would have to be offset by
tremendous advantages, and I do not see this with Votes-Against.

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