Margins, majority, strategy
ntk at netcom.com
Tue Sep 22 19:26:28 PDT 1998
I'm replying farther down in this letter, a different part
in each installment:
> 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.
Exactly what problem do you refer to? The need for insincere
voting? I've showed that Margins requires degrees of insincere
voting not even required by Approval. Approval offers half as
much as Votes-Against, in terms of strategic guarantees. Margins
offers nothing, and, unlike Approval, can require voting a
less-liked alternative over your favorite. But there'll never
be agreement among all the types of rank-count theorists
that Approval is a good compromise--no reason to expect their
various theories to agree on anything. But Approval is veryk
easy to ask for, an un-arbitray, being merely a big but obvious
improvement on Plurality.
> > > 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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