[EM] Steph: Truncation example

Mon Nov 25 09:21:15 PST 2002

Thanks to you Mike, for taking the time to
answer a stubburn opponent like me...
I agree with several of your statements now that I understand how you define
a strong CW and SFC...

> Your method fails the CW more flagrantly than wv does.
>
I think this is the main question! And I do not conceide it.
It is more complex, please check what I just sent to Adam...

As I just said to Adam, I do not think the CW in my example
is poorly supported. Taking the winning votes advance as a support measure,
my CW leads by 10 points over both its contestors.
Compared to your "Strong" CW in Adam's example (51 to 49) who only
has 2 points of advance, I find your definition not that relevant...

One point good for you, my counter example does not invalid SFC and GSFC.
It just questions their relevance.
At least, thanks, I understand better what SFC represents now.

MIKE OSSIPOFF a écrit :

> Steph--
>
> You said:
>
> With X=1:
>
> 3: A
> 2: A > B > C
> 2: B > A > C
> 2: B > C > A
> 4: C
> Ranked pairs with winning votes produces:
> A (7) > C (6) , B (6) > C (4) and A (5) > B (4).
> A is the Condorcet winner and wins.
> Margins and relative margins produce of course the same result.
> If I am one of the two B > A > C voter, my 2nd (A)
> choice harms my favorite 1st choice (B).
> The proof is, if I and my co-thinker vote B only:
> 3: A
> 2: A > B > C
> 2: B   (truncated !)
> 2: B > C > A
> 4: C
> Ranked pairs with winning votes produces:
> B (6) > C (4), C (6) > A (5) and A (5) > B (4) can't lock.
> B wins now.
>
> I reply:
>
> Another example of the old "poorly-supported CW" objection.
>
> Out of 13 voters, only 5 rank A over B. But you still want wv
> to guarantee A's win.
>
> You have here an example in which relative
> margins doesn't let the truncation take victory from the CW. But
> one non-failure example means nothing. Even a majority ranking the
> CW over B doesn't keep truncation by B voters from stealing the election
> sometimes with relative margins, without any order-reversal. Relative
> margins fails to a degree that wv doesn't. Relative margins has a number of
> kinds of majority rule failure that wv doesn't have.
>
> It's an example in which the CW doesn't have a majority over the
> candidate who is able to steal the election from him by offensive
> truncation. I say he's poorly supported because, though he's CW,
> he has a pairwise victory that isn't a majority, either due to sincere
> indiferrence, or perhaps someone's truncation strategy. That's what
> I meant by "poorly supported CW".
>
> The trouble with your "poorly-supported CW" objection is that you're
> asking a lot when you ask me to protect the CW from someone over whom
> no majority bother to rank him. However, you could write a
> "Strong SFC" that doesn't mention majority. I encourage you to post
> a definition of a method that meets such a criterion. No one would
> be more pleased than I. In fact, after doing that would be the best
> time for criticising wv for not meeting such a criterion.
>
> >if you say that truncation can take victory from a CW in wv, you're
> >probably intending the old example in which a poorly-supported CW loses
> >to truncation. i've many times said that truncation can work against
> >a cw when there's lots of indifference toward that cw. When there's
> >no majority voting the cw over the candidate who steals the election.
> >A candidate can be CW even if he beats the other candidates with
> >sub-majority defeats. And if he beats y with a submajority defeat,
> >i make no claim that y can't steal the election by truncation.
>
> You continued:
>
> Please define a poorly-supported CW. If the definition is criteria (wv or
> rm)
> independent it should be really helpful.
>
> I reply:
>
> My definition of a poorly-supported CW is: A CW who has a pairwise
> victory that doesn't have a majority voting him over the other
> candidate. The only place that I've used "poorly supported CW" is
> in my term "the old 'poorly-supported CW' objection". I don't use
> that definition or that term in criteria.
>
> That definition is independent of how defeats are measured.

I was thinking like you at first. Now, I do not think so.
This definition is implicitely linked to the 50% limit,
which is a root for building the winning-votes criteria.
It is more obvious to me, because when I try to replace this
with a strong CW that meets my understanding, I end up
with something equivalent to a relative margin limit.

> You continued:
>
> All votes I gave previously were sincere preferences. Only the truncation
> that leads
> to a better result for the truncaters is unsincere as you were doing.
>
> The CW I used (namely A) was a "CW who is preferred to
> candidate y (namely B or C) by a majority who vote sincerely".
>
> I reply:
>
> What I say in that paragraph that you quote should make it obvious
> that the "Y" in that quote is the Y in SFC. In SFC, I say that
> if no one falsifies a preference, and if a majority prefer the CW to
> Y, and vote sincerely, then Y shouldn't win.
>
> Your CW has victory taken from him by a candidate over whom he
> doesn't have a majority. If a majority preferred him to B, and voted
> sincerely, then he'd have a majority over B.
>
> The fact that you may be able to find some other candidate over whom
> your CW has a majority is irrelevant with regard to your method's
> SFC failure.
>
> You continued:
>
> Thus if this
> is the definition of a non "poorly-supported CW", my counter-example fits...
>
> I reply:
>
> But, by "poorly-supported CW", I didn't mean a CW who doesn't have
> a majority over anyone. In the spirit of SFC. Not having a majority
> over one candidiate, B, makes A poorly supported enough that you shouldn't
> expect wv to protect his win.

I conceide that. Using your definition you are totally right.

> You continued:
>
> If SFC & GSFC apply to non-poorly supported CW, please explain why the
> sincere CW (namely A) can get stolen with an unsincere truncation in my
> examples.
>
> I reply:
>
> SFC & GSFC make no use of the term "non-poorl-supported CW", or
> "poorly-supported CW".
>
> You ask why the sincere CW can have victory stolen from him by
> offensive truncation in your example, with wv: It's because he doesn't
> have a majority over B. That's why B can steal the election from him
> by truncation.
>
> You continue:
>
> I will consider "non poorly-supported CW" as a sincere CW. I hope it is what
> you mean.
>
> I reply:
>
> It isn't. In referring to a "poorly-supported CW" objection (my
> only use of the term "poorly supported CW"), the term "poorly supported
> CW" means: A CW who has a pairwise victory that isn't supported by
> a majority. But I re-emphasize that that definition isn't important,
> since I only used it in the name that I gave to your objection-example,
> an example that I've replied to so many times that it deserves a name.
>
> "Sincere CW" means a candidate who would beat everyone if all the
> voters voted sincere rankings. But we just use "CW" to mean the same
> thing, for brevity. If someone beats everyone, but not necessarily with
> sincere rankings, I call him the BeatsAll winner.
>
> You continued:
>
> The only conclusion I was able to obtain by myself, was that your SFC & GSFC
> analysis was good when there was no truncation (nor sincere, neither
> unsincere) present.
>
> I reply:
>
> SFC & GSFC make no mention of truncation. But if you mean that
> SFC & GSFC distinguishe between wv, margins, and relative margins only when
> there's truncation, sure, that's true of SFC, and probably GSFC.
>
> But it isn't at all clear why you think that SFC & GSFC aren't "good"
> unless there's truncation, because margins only fails when there's
> truncation. When there's no truncation, and margins doesn't show a
> failure of SFC, SFC is still good. Criteria usually say that a method
> fails if there's any instance of it failing the criterion's requirement.
> No one says that criteria are "not good" in other instances.
>
> You continued:
>
> In this particular case, margins, relative margins and
> winning votes all
> produce the same results.
>
> I reply:
>
> The fact that you can find an instance in which your method doesn't
> fail a criterion's requirement doesn't mean anything when, as is
> always the case, the criterion requires that, when the criterion's
> premise is true, the method must never fail the criterion's requirement.
>
> Conceivably someone could write a criterion that isn't written that
> way, but I can't name one right now. In any case, SFC & GSFC explicity
> require that, under their premise conditions, a method never fail
> their requirements. Most or all criteria also do.
>
> You continued:
>
> Still I think you are right in assuming the
> probability of gain from an unsincere truncation is lower with winning votes
> (maybe null as you say, I am not sure).
>
> I reply:
>
> I don't make claims about probability. But margins and relative
> margins let truncation steal elections from CWs under a wider set
> of conditions, failing more flagrantly, compared to wv.

I am not yet convince about that. See the proportion of truncaters you need
to convince...

> You continue:
>
> But your analysis seems to be built on the assumption only one truncation
> (unsincere) occurs.
>
> I reply:
>
> SFC & GSFC make no reference to truncation at all, much less any
> specification about how many truncations there are, or whether they're
> sincere or insincere. Nor have I said anything about that.
>
> You continue:
>
> I think many can happen, sincere ones as much as
> multiple unsincere (many voters could expect an improvement) or both types.
>
> I reply:
>
> Truncation will be common in public elections, as it is in committee
> rank-ballotings.
>
> You continued:
>
> I have just proved to you that
> this probability is not null using (wv) with multiple truncations.
>
> I reply:
>
> That was already proven, and often said by me, that even wv can't
> protect an indifferently-supported CW against truncation.
>
> You continued:
>
> Even,
> relative margins would protect the CW in these examples (except for X=0
> where a tie occurs).
>
> I reply:
>
> One nonfailure example says nothing. There are examples in which
> your method lets victory be stolen from a CW, by truncation, when
> a majority vote the CW over that candidate, when no one falsifies
> a preference. Your method fails the CW more flagrantly than wv does.
>
> You continued:
>
> Finally, once we know that because of sincere truncations, unsincere
> truncations can
> lead to (rare I hope) special cases where a CW can get stolen, it increases
> the probability of unsincere truncations occuring.
>
> I reply:
>
> Especially with margins and relative-margins, since with those methods
> truncation can even steal victory from a CW in violation of majority
> rule, something that won't happen with wv.
>
> Mike Ossipoff
>
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