Margins, majority, strategy
ntk at netcom.com
Tue Sep 22 21:17:47 PDT 1998
Sorry, but I've found out that deleting lines is much slower
than spacing down in the letter, and I usually don't get to
the part I'm replying to before netcom has its problem. And
so I've got to return to spacing down. Each installment replies
to a different part of this letter, farther down:
> 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
Please understand that majority rule within a subcycle isn't
as important. Nothing within a subcycle is as important than
what happens in the main cycle, the cycle that contains the
CW, and the truncators' or order-reversers' candidate. ldeally
it would be nice to honor all majorities, but people here feel
that clone criteria are more important. I have no problem with
that, because, as regards LO2E, it's what happens in the main
cycle that counts.
> 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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