Truncation Resistance #2 criterion (was Re: First Choic

[Mike Ossipoff]

Hugh Tobin writes:



[Mike writes: I'm replying to various statements in this letter from
Hugh, and Hugh's statements begin farther down in the text]


> 
> Steve Eppley wrote:
> 
> [First, here is the relevant portion of Steve=92s original post: =
> 
> > > > I suggest that when people think about a new method they should
> > > > first test them on the following two examples:
> > > >
> > > >      46:ABC                          46:A
> > > >      10:BAC                          10:BAC
> > > >      10:BCA                          10:BCA
> > > >      34:CBA                          34:CBA
> > > >      ------                          ------
> > > >      MUST ELECT B                    MUST NOT ELECT A
> > > >
> > > > In the example on the left, it should elect B (the compromise
> > > > centrist who would beat any other in a head to head matchup).  In
> > > > the example on the right, it should not elect A, else the supporter=
> s
> > > > of A have a clear incentive to strategize.  If truncation would
> > > > elect A, the method has a serious problem.
> > > >
> > > > We may as well call this two-example test a criterion: the
> > > > "Truncation Resistance #2" criterion, perhaps.  Do we have a
> > > > consensus that any method which fails TR-2 should not be posted
> > > > here in EM, unless it's accompanied by a solid explanation why it's=
> 
> > > > better than Condorcet or Smith-Condorcet on some other criterion we=
> 
> > > > should respect?  Such a consensus would save us all a lot of time.
> > > >
> > > >[snip]
> > > >
> > > > ---Steve     (Steve Eppley    seppley at alumni.caltech.edu)]
> > >
> 
> > Hugh T wrote:
> > >Steve's proposed consensus censorship
> > =
> 
> > Censorship seems too negative a description, since I provided the
> > reasonable "escape clause": someone proposing a new method which
> > fails TR-2 needs only include some other criterion--maybe I should
> > have said "standard"-- satisfied by his/her proposed method better
> > than Condorcet or Smith//Condorcet, and explain why that criterion
> > matters.
> > =
> 
> > There may be some value to the list in having people propose methods
> > which are inferior on some standards and not superior on any.  It
> > could stimulate invention of better methods, or help us understand
> > why known methods are better than the proposals.  But I'd like the
> > authors of those proposals to be clearer about what they're writing;
> > if they think the proposal may be better on some standard, we deserve
> > to know which, and if they don't, we deserve to know that too.
> > =
> 
> 
> On re-reading Steve=92s first posting I am inclined to withdraw the term
> =93censorship=94 (which I had thought to soften with =93consensus=94), be=
> cause
> Steve could be read  not as proposing a rule restraining speech, but as
> simply seeking an expression of consensus as to what forms of speech
> would be most useful.  But I find that Steve rejects the term on other
> grounds.  I do think rules that restrain speech, even with "escape
> clauses" that the rulemakers deem reasonable, amount to censorship. =

But considering the heavy continual stream of junk-proposals, it's
reasonable to ask people to say why their proposal is good.

> 
> Whether it is good or bad is another question (for example, postings not
> germane to the list should be censored).
> 
> >If Hugh wants this list to welcome proposed methods which are offered
> > up without explaining why they may be better, and they routinely turn
> > out to be badly flawed, I'd appreciate it if he would better share
> > the burden of analyzing their faults.  Freedom of speech works best
> > when there are a lot of people willing to point out the bugs in
> > "bad" speech.
> > =
> 
> 
> Perhaps I am less concerned about such proposals because I do not think
> one endorses anything by ignoring it.   I do not think anyone has an
> obligation to analyze, respond to, or include in a FAQ any proposal that
> is not accompanied by an explanation of what advantages it has, or at
> least why it is worth investigation.  But some such proposal might have
> a glimmer of merit even if the proposer does not explain it accordance
> with Steve=92s proposal, or does not even grasp it himself.  (A properly
> titled posting that merely defines a method may have value on a list

...and can also become something of a nuisance when it's done sufficiently
frequently.

> called =93Election Methods=94). Someone may have a very cogent narrative
> explanation of the value of a system or certain of its features, and
> might be deterred from posting it by rules that require formal standards

But Steve's proposal wouldn't prevent that person from posting
their method along with the "cogent narrative explanation of 
[its] value". There's no reason for that person to be "deterred".


> or criteria, or that insist  that the poster accept as the premise for
> discussion that TR-2 is important.  Those who support Condorcet with
> other tiebreak methods than [EM] may not agree that there is anything

[EM] refers to a way of judging worst defeat, by votes-against, as
opposed to by margin of defeat or votes-for. Condorcet's method says
to elect the alternative whose worst defeat is the least, though
Condorcet didn't say how to judge the defeats. 

> wrong with an A victory in Steve=92s second example, and may not agree
> that Condorcet, properly implemented, passes Steve=92s test.  Finally, I

If Condorcet were implemented as you propose, it would indeed fail
tests & standards that people here consider important. If you
consider your way "proper" then, as you use the word, a "proper"
implementation would fail various tests & standards that
Condorcet[EM] doesn't fail.


> do not look forward to responses telling a poster that he or she is out
> of order for having the temerity to propose something with an
> explanation that is not =93solid=94 or with a criterion that is not worth=
> y
> of =93respect,=94 rather than simply addressing the posting on its merits=

How about a long string of methods, a veritable book of them, with
no explanation of why they're supposed to be good?

> 
> (IMHO people with something useful to offer may already have been
> deterred from posting on this list by the tone of some of the
> responses.)


Maybe some people have been deterred from receiving the messages of
this list because of some of the garbage.

> 
> In lieu of any statement about what =93should not be posted=94, I would
> suggest an item in the FAQ that explains in neutral terms what format
> and what type of information is helpful to readers when one posts a new
> system or variant, and that goes on to indicate that because that S//C
> [EM] was chosen by vote of the members of this list, posters should be
> prepared to compare the results of their systems to those of S//C[EM] in
> certain examples and to justify any differences.  I believe it should be
> made clear that failing Steve=92s first test poses a much more fundamenta=
> l
> issue -- i.e., what justifies rejecting the Condorcet criterion -- and
> that example 2, if given at all, relates to a claimed advantage of a
> particular Condorcet version.

Nonsense. Where have you been? Majority rule is a standard in
its own right, not just a justification of one method.

> 
> As to sharing the burden, I have been critical of methods like IRO, and
> Condorcet w/ Approval, where I thought that the responses of the
> regulars left anything unsaid.  In general I find that others are so
> quick and prolific in their criticism that one who cannot post daily
> would only be redundant, or appear to be piling on, in criticizing
> systems other than Smith//Condorcet [EM].    =
> 
> 
> > >raises the questions: (1) Why is truncation resistance more
> > >important that resistance to order-reversal?
> > -snip-
> > =
> 
> > Because truncation will probably be a common occurrence when there
> > are many candidates, even with "sincere" nonstrategically-minded
> > voters.
> > =
> 
> I am surprised by this explanation, because I thought truncation meant
> withholding expression of  sincere preferences, and that the

I haven't used it that way, and I don't know that others have.
I've repeatedly said that truncation won't typically be strategically
intended, and will take place because people don't know all the
candidates, or don't have time to rank a long list, or don't
want to bother. Maybe the trunction will be the result of not
having more preferences than listed.

> reason Steve opposed the result in his second example was the incentive
> it gave to A voters to truncate as strategy.  To say that an A victory

Again, are you sure that Steve used the word "incentive"?

> in  that example is intolerable even were we certain the voters were
> entirely
> sincere is another matter, and highly debatable.  If voters who cast

Yes, (sigh), & it's already been debated here at length. No matter
how indifferent the A voters are when they truncate, that
doesn't mean that the truncation should result in a violation
of majority rule, as it does in methods where it causes the
election of A in that example.

> short ballots will most likely be sincere, this argues against Steve=92s
> criterion.  In that case it becomes more important to ensure that these
> sincere voters are not penalized for not being devious enough to cast
> insincere complete rankings.  But if A does not win in Steve=92s second
> example, the sincere A voters are penalized for this.

What nonsense. They're penalized because, since they didn't attempt
the offensive strategy of order-reversal, they don't reap the
possible rewardsd of that offensive strategy? Are you penalized
because you didn't rob a bank today, since you don't have
bank-robbery loot?


> 
> > >(2) Why is it critical to prevent a putatively organized and devious
> > >group of plurality voters from achieving through truncation what
> > >they could also achieve by insincerely dividing their second choices
> > -snip-
> > =
> 
> > Can we agree to make the following assumption?
> > =
> 
> >     The level of "strategic sophistication" will be fairly even
> >     among all the groups.
> > =
> 
> 
> I think that is very unlikely.  More likely there will be systemic bias:
> some groups are highly organized and well-financed compared to others =

The defensive strategy in Condorcet isn't complicated; just don't
rank lower than you probably need to, & especially don't rank
a candidate whose voters are likely to order-reverse. Defensive
strategy is extremely common now, and doesn't require great
sophistication.

> 
> (I suspect that more extreme groups will be more disciplined).  =
> 
> Differences in money and organization will affect the degree to which
> strategic sophistication of leaders will be translated into false votes
> by which their followers will improve their favorites' chances, even if
> the followers do not themselves understand how the system works.  The
> less organized and less doctrinaire voter more likely will vote
> sincerely, perhaps only for one candidate if he knows nothing of the
> others, if he considers them equally detestable, or if he naively
> assumes (like a certain member of this list) that he thereby maximizes
> the chances of this first choice.  This independent voter, by virtue of
> his sincere short ballot, will have less effective voting power in
> Condorcet [EM] than the member of an organized group who knows he should
> cast an insincere long ballot.  (To the extent that latter voter knows
> which way he should cast his insincere votes, he has an advantage even
> in Condorcet methods that fail Steve=92s second test, but it is a smaller=
> 
> advantage).  Even among unorganized voters, there surely will be
> systemic bias in strategic sophistication -- the classes with more
> education and more leisure to concern themselves with the intricacies of
> the system are more likely to vote strategically on their own.

If order-reversal became a problem, the simple counterstrategy
would become common knowledge. And the campaigns needed to organize
the order-reversal couldn't be hidden from the intended victims
of the order-reversal, who then wouldn't feel inclined to help
the reversers by voting for their candidate; they wouldn't
be inclined to participate in their own victimization.

But all this is academic, since order-revefrsal on a sufficient
scale to change an election result is highly unlikely.

> But even if the assumption Steve proposes is made, it does not advance
> his argument that truncation-resistance is so important as to be a
> criterion.

Then how about the fact that Condorcet Criterion methods can
fail to elect a Condorcet winner for only 2 reasons: Truncation
& order-reversal, of which truncation will be common in every
election.

> 
> > Truncation will occur even with low deviousness (and maybe
> > especially with low deviousness), but massive reversal requires a
> > highly devious group.
> 
> This does not make sense to me.  Truncation as offensive strategy
> requires more, not less participation because each ballot is less
> potent.  Order
> reversal can succeed with only a minority of the A voters participating.
> It does not seem more devious to withhold a true preference than to

I don't think anyone is denying that order-reversal is a more
effective (if risky) strategy. In fact truncation wouldn't
accomplish any benefit in Condorcet(EM). But you're forgetting
that not all of us agree with you that trunction will typically
be done with strategic intent.

> reverse it, because in either case one either takes a conscious risk of
> electing one's least favorite in order to enhance the chances of one's
> favorite, or else one changes how one votes in order to follow strategy
> directed by a political leader without understanding why. =
> 
> If a voter would have voted only for A without any strategy or
> direction, then I can only conclude that he or she is indifferent among
> the other candidates.  Indeed, this seems more certain for the A voter
> than for those who did not got to the polls at all, because it is so
> little trouble to express one's true preferences once in the voting
> booth.
> 
> Perhaps one who expects that "truncation" by people who actually have
> preferences will be widespread and will affect important pairwise races,
> not just those involving irrelevant fringe candidates with no hope for
> the Smith set, should support a version of Condorcet that would correct
> for this phenomenon by counting these ballots as evenly split for
> tiebreak purposes.  We have no legitimate basis for concluding that the

****DISORDERLY DISCUSSION ANNOUNCEMENT***

Hugh's arguments for counting truncation as a half-vote
for each alternative in each pair not voted-for have already
been discussed, and Hugh never replied, but is now, instead
just recycling the same proposal & arguments.

***

> A voters actually preferred B more than C, or vice versa, so if we are
> to try to give some effect to their unexpressed preferences (without
> affecting the outcome of the B-C race with phantom votes), the best we
> can do is assume they are equally AB and AC.(I cannot see what

More nonsense. If you don't rank B or C, that doesn't mean you
want to vote half for B & half for C; it means that you don't
want to vote for either. Hugh, it seems would count you as
saying something that you didn't say. We've already discussed
this, Hugh. As I said, check the archives for my reply to 
your arguments.




> =93resistance=94 to nonstrategic truncation can mean, other than trying t=> o
> give effect to unexpressed preferences.)

It means resistance to allowing truncation, strategic or otherwise,
to cause violation of the expressed wishes of a majority.

As I've used the term "truncation-resistance", I've only applied
it to situations where there's a Condorcet winner, an alternative
which would beat everything if everyone sincerely ranked all of
the alternatives. But that isn't the only situation where voting
a short ranking might or might not violate majority rule. My
definition was arbitrarily limited to that situation, but
that isn't the only important situation. GMC says not to
elect something with a majority against it unless everything
has a majority against it. GMC is based on a convincing
democratic principle.

Whether or ot we call it "truncation resistance" when we're
talking about short rankings of indifferent non-strategizing
voters, when there's no Condorcet winner, it's still
possible to prevent the short rankings from causing
violation of majority rule. We don't have to quibble
about the definition of truncation resistance, and whether
it should apply when there's no Condorcet winner. Either
way, truncation can be prevented from resulting in violation
of majority rule.



> 
> >
> >If the assumption above is correct, the
> > reversal will be easily countered by one of the other similarly
> > sophisticated groups.
> >
> 
> But truncation could not be so countered? See below.

In the methods recommended by EM, truncation needn't be countered,
because it can't elect your favorite in violation of majority rule
anyway.



> 
> > >I submit that a system which [I meant =93that=94 -- HT] reaches a diff=
> erent result from
> > >Steve's second example if the "A" voters are divided into 23AB and
> > >23AC creates a clear incentive to insincere voting.
> > -snip-
> > =
> 
> > The "largest loss" scores in Hugh's example are very close:
> >     A=3D54, B=3D57, C=3D56
> > A wins if the B and C voters roll over and play dead.  But the
> > numbers are so close that a small defense is sufficient to counter
> > the massive reversal.  And they're so close that the counter may
> > make the reversal backfire by electing C.
> 
> A good reason why the BA voters might counter the =93counter=94 (if it is=

The  BA voters might counter _what_ counter? The counter that Steve
was referring to was defensive truncation by B voters, where
BA voters vote only for B, making it impossible for A voters
to gain by order-reversal.


> 
> Ossipoff=92s bitter prescription), by voting AB.  But the question here i=

Why would the BA voters vote AB?? You should check out what you're
about to say before you post it. The B voters have no need for
order-reversal.



> s
> only whether truncation strategy is somehow more difficult to counter. =

I've answered that. 



> 
> See below. =
> 
>  My point about incentives for insincere voting did not relate to
> reversal.  It is the sincerely indifferent A voter who has the clear
> incentive to vote insincerely in a system such as I described (including
> S//C [EM]).

Again, Hugh is saying that the A voters has incentive to vote
insincerely because he can't succeed in violating majority
rule & electing A without order-reversal. Hugh would, in
that way, try to represent Condorcet's autmatic resistance
to majority rule violation by truncation into a disadvantage
because it means that a cheater would have to do something
more risky & drastic: order-reversal.

> 
> > =
> 
> > Is it plausible the A voters will be able to successfully reverse
> > without the B and/or C voters easily defending?  TR-2 guards against
> > both innocent and devious truncation.  The other voters (a majority)
> > can guard against, and maybe punish, devious reversal, just by making
> > sure that B and/or C aren't both beaten by a majority.
> > =
> 
> 
> [It is not really the issue here, but the B voters have no real
> "defense" in Condorcet, and those who prefer A to C would be

Excuse me, but they have the defense of not including A in
their ranking. Not voting for the candidate of those who
would steal their win by order-reversal. Refusal to rank
A, on the part of the B voters, makes it quite impossible
for A to be elected by order-reversal. That's a defense, Hugh.



> particularly irrational to use a strategy that would elect C to punish A
> -- rather, all the B voters would want to convince the C voters that the
> B voters would =93cooperate=94 with the A strategy, i.e. vote sincerely, =
> and
> that therefore the C voters had better vote BC, or else A will win the

Oh, here Hugh tells us his solkution: Make the C voters have to
insincerely rank their lesser-evil compromise over their favorite
(Sound familiar? It's what progressives have to hold their nose
& do now, when they vote for the Democrat instead of the progressive).

Avoiding that need was our goal. Earth to Hugh...

It isn't irrational for the B voters to publicize the fact
that they aren't voting a 2nd choice, which would deter
the A voters from order-reversing.

We've been all over this too, Hugh. It amounts to a game of chicken
between A voters & B voters. The B voters have the upper hand
in that game, since the election of C would hurt the A voters
more, and because the B voters are the ones who are defending
rather than offending. Again, Hugh, why don't you check the
archive, instead of wasting everyone's time by continually
repeating refuted arguments?


> circular tie.  C=92s =93defense=94 is to throw in the towel and let B win=
> =2E =
> 
> That prospect would not deter the A voters from offensive strategy.  If
> C himself is unwilling to concede and asks the faithful to vote for him,
> then A=92s strategy looks promising -- if A has enough reliable
> information about the distribution of true preferences among likely
> voters.]

And if B voters have no idea what's going on?  :-)

> 
> The point here is that what Steve says the B and C voters can do must be
> at least
> equally true if the A voters try a truncation strategy in a system, such
> as Condorcet with a margin-of-defeat tiebreak, in which truncation by

There's no reason to want a method in which truncation has
to be countered.

> voters with the true preference AB is equivalent to partial
> order-reversal.  So whatever argument Steve can make about the
> ineffectiveness of order-reversal undercuts his own argument about the
> pernicious incentives allowed by any system that would elect A in his
> second example.  However strong or weak those incentives are, they still

How do you figure that? Condorcet(EM) doesn't elect A in the
2nd example.



> exist in Condorcet [EM].

Let's get this straight: You're saying that "incentives allowed
by any system which would elect A [in example 2]" still exist
in Condorcet(EM), even though Condorcet(EM) wouldn't elect
A in that example?  :-)   Try to pay more attention to
what you're saying, Hugh.

> 
> I am puzzled by the notion of "guarding" against "innocent" truncation.
> (Perhaps the system also should =93guard=94 against complete abstention?)=

Then let me explain it again: What's being guarded-against is
the violation of majority rule due to mere truncation, whether
the truncation is strategically-intended or not.

> 
> If we assume application of Condorcet [EM] to Steve's second example,
> then I think the phenomenon being described is nearly the opposite of
> "guarding" -- it is really the exploitation of the A voters' innocence
> about the features of the system, in order to deny them the victory they
> would have gained, with zero risk, had they been organized or

The victory that they would have gained by order-reversal cheating,
if they tried it, and if they were somehow able to get away with
it? Not at zero risk. Hugh seems to be saying that Condorcet(EM)
denies those people of fruits of order-reversal because
they didn't order-reverse. Well, they could try it, if they
want to risk it,and if the B voters are total suckers.
What Hugh seems to mean here is that Condorcet(EM) is unfair
to the A voters because it doesn't give the election to
A in violation of majority rule.


> well-advised. If they were really indifferent between B and C (which is
> the only rational explanation for innocent truncation), then they should
> have paired their votes or voted randomly for second place.

Why would they do that? That sounds pretty silly. You're indifferent
between B & C, so you think you need to vote one over the other,
instead of just not expressing a preference between them? :-)

> (Steve might argue that the A voters would not truncate in Condorcet
> [EM] even if they were really indifferent, so I needn=92t worry, but I
> don=92t think that is his argument, and if it were he might as well let
> the A voters have the option to cast half-votes and remove the risk that
> the B-C race will be decided by the deviation from 50% among the A
> voters=92 insincere second choices.)

Again, we already talked about your half-votes proposal. I said
at that time that if voters really insist on it, as an _option_
that it would be harmless to grant that silly option, but
that it would be equally silly to start out by offering it
wilthout it having been demanded, since it would be an
invitation that would call attention to & legitimize
order-reversal cheating. Order-reversal tends to be bad
news for all pairwise methods, and various other methods
too. It turns out to be the last remaining problem when
we set out to get rid of as many problems as possible.
If voters don't get the idea to try it, so much the
better. So it would be pretty stupid to start by offering
it as an option on the ballot.


> 
>  Steve, I understood your argument against A winning in your example 2
> to be based on the incentive for truncation strategy by A voters who
> really do have a second preference (i.e., B).  If your basis for
> abhorring that result were instead something like the the so-called
> "Majority Rule" standard (or criterion), then I presume you would not
> implicitly have deemed potentially acceptable a system that would elect
> C (with the largest majority against her) in your second example.  (Do
> we at least agree, then, that given the Condorcet criterion, the goal of
> limiting incentives to insincere voting is more important than the
> =93Majority Rule=94 criterion?)

Both goals are related. Methods that violate majority  rule
tend to favor insincere offensive strategy, and, more 
important, tend to require drastic insincere defensive
strategy. To argue about which is more important, avoiding
the need for insincere defensive strategy or protecting
majority rule, is merely to argue about which description
of the same problem is more important.

> But if incentive is the issue, what plausible set of expectations about
> the votes of others could I have that would give me a rational
> incentive, in Condorcet (margins-of-defeat), to truncate but not to
> reverse order?

In Margins-of-Defeat, if you want to win an undeserved victory,
you have a better chance by order-reversal. With truncation,
you need A to be twice as big as B in order for A to get a 
better Margins-of-Defeat score than B. With order-reversal,
you merely need A to be bigger than B. But this is quite
irrelevant to the topic. We don't propose Margins-of-Defeat.

If you're saying that in Margins-of-Defeat, offensive strategizers
would order-reverse, and that, therefore example 2 isn't important,
you're forgetting that there are methods where truncation by
A voters wouldn't elect A in that example,and where order-reversal
is well-deterred. The fact that order-reversal is a stronger
cheat strategy doesn't mean we don't need methods that violate
majority rule due to mere truncation.


> 
> Finally, let me suggest that making Steve's second example a litmus test
> (even with the reasonable exception), and implying that a =93Condorcet=94=
> 
> system would not elect A (despite his large plurality and the weak

Did anyone imply that a bad version of Condorcet couldn't elect
A there?

And is Pluralty standard for deservingness to win? If so, then
you might just prefer keeping the Plurality system which we
currently use for public partisan sw elections in most states.



> results of B and C), would unnecessarily detract from the much more
> important Condorcet criterion and could put off those who otherwise


That's a bizarre statement. How would that detract from the
Condorcet Criterion? The Condorcet Criterion, by itself,
isn't adequate. So if we add another criterion, you call
that detracting from the Condorcet Criterion?

So no one can apply any other criterion, because that
would "detract from" the inadequate Condorcet Criterion?

> might support some version of Condorcet against the raft of inferior
> alternatives.  =

Other versions of Condorcet _are_ among the raft of inferior
alternatives. Though Margins-of-Defeat is better than MPV,
it isn't much better. And being better than MPV doesn't
mean a whole lot, considering that MPV is the worst.

I've already shown why Margins-of-Defeat is inadequate, in
previous postings here, and I've shown why your 1/2 votes
method is inadequate.


> 
> 
> 
> -- Hugh Tobin
> 
> .-

Mike Ossipoff

> 


--