Margins, majority, strategy

Mike Ositoff ntk at
Fri Sep 18 20:20:20 PDT 1998


Blake writes:

> I have made some comments on your example.
> On Mon, 14 Sep 1998 23:05:24   Mike Ositoff wrote:
> >
> >Hi--
> >
> >When I posted 2 Margins truncation bad-examples the other day,
> >I didn't accompany them with any comment, and so I'd like
> >to point out a few things about them.
> >
> >In both examples, the A voters, by truncating, succeeded in
> >gaining the election of A, by defeating a Condorcet winner,
> >in violation of the expressed wishes of a majority.
> >
> >In example 1, Margins, by electing A, elected the only
> >candidate with a majority against him.
> 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.

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

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?

(I've deleted the parts of my earlier message that weren't

> >Example 3:
> >
> >100 voters.
> >
> > 44  28  28
> >  A   B   C
> >  C       B
> >
> >The A voters are using order-reversal against B. It succeeds,
> >using Margins, but is thwarted, in the votes-against versions,
> >by the B voters declining to list a 2nd choice.
> I do not think your example is very realistic.  It assumes that
> B voters have no preference between A and C.  For example, if the

I made no such assumption. Maybe the B voters are using the
non-drastic defensive strategy of truncation, to thwart possible
order-reversal by A voters or C voters.

>[If the] true preferences were
> 44 A B C
> 14 B C A
> 14 B A C
> 28 C B A
> The insincere would be
> 44 A C B -- order reversal
> 14 B C A
> 14 B     -- defensive truncation
> 28 C B A
> That is, I think it more likely that B voters will have preferences
> between A and C.  If this is the case, and the B voters who prefer
> A to C truncate, this can have the effect of order reversal.  So, the
> B voters are not likely quite as helpless as you suggest, even under
> Margins.

In Votes-Against, the defensive truncation thwarts order-reversal,
but not in Margins. In Votes-Against, if offensive order-reversal
isn't tried, and if there's a Condorcet winner, then no one
has any need for _any_ defensive strategy, not even defensive
truncation. But in Margins, even if some voters truncate,
maybe with strategic intentions, maybe just out of laziness or
feelings of principle--in Margins that truncation can force the
use of the drastic defensive strategy of ranking a less-liked
alternative over a more-liked one.
> Furthermore, if they truly have no preference between A and C, then
> they will not mind ranking C over A, if A is trying order

> reversal.  This is unlikely to even be insincere.  B voters will
> be genuinely outraged by A's tactics.

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.

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.

> To put it another way, if I vote B > A=C because I hope this will
> elect C instead of A, I am voting insincerely.  If I would prefer
> to see C elected, even if only to punish A, then the sincere vote
> is B > C > A.  This sincere vote is often refered to by Votes-Against
> advocates as a drastic strategy.

And it can be greatly regretted if, through misjudgement, it's
done unnecessarily. That's the problem of FPTP. It's the LO2E
problem, and the reason why we want to replace FPTP.

> 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.

>               Majority of
> B > A 56:44   12
> A > C 44:28   16
> C > B 72:28   44
> What we have here is 3 contradictory majority votes.  We have to over-rule
> one of them.  It makes sense to over-rule the majority that is least
> decisive.  If we use Margins this is B > A, if we use Votes-Against
> this is A > C.  So, the question is, if we consider votes to be sincere,
> which is more decisive, a higher margin or a higher Votes-Against
> Well, Votes-Against says that a majority of 51 to 49 is more decisive
> than one of 49 to 1, if there are 100 voters.  Why?  Because "Votes
> Against" assumes that the non-participants in the 49 to 1 victory are
> abstaining for strategic reasons, and that this throws this victory into
> deep suspicion.  However, this has the effect of creating a rather

Not at all. I've never assumed that all truncation is strategic.
In every rank-balloting election that I've particpated in, there's
been trunction, most of it not strategically intended. I've
voted short rankings because of principle.

It's just that violating the wishes that have been expressed
by more than half of the voters seems not a good thing.

And doing so has the bad strategic consequences that I've

> strange result if the voters are sincere.
> So, in conclusion, marginal methods give better results when the voters
> are sincere and do not have the problems inherent in violating SEC.

deBorda said, when confronted with his method's strategy problems,
that his method was intended for honest men. Good luck. 
Margins would work fine if all the voters were honest, and
believed in Margin's principle, and considered that a social good
that outweigh's their individual advantage. Good luck.

Mike Ossipoff (netcom calls me Ositoff)

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