Reply on EM to Mike's Reply on ER

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Reply on EM to Mike's Reply on ER

Craig Carey-2
Bruce Anderson writes:

[I'm replying to enough statements in this letter to justify copying
the letter, but I have no way to delete lines or blocs of text, and
so it's necessary to copy the whole thing. The parts that I reply
to are a little farther down. Please any displaced or duplicated
lines due to wraparound caused by line-length mismatch]


>
> First, this message directly only replies to Steve's reply.  I'll try to get to
> (at least some of) Mike's reply this weekend.
>
> Second, I think that if these interchanges of messages are to have any merit, we
> need to be as specific and precise as reasonably possible.  One way to do this
> is to point out places in messages where increased precision would be more
> helpful than harmful.  I think that Steve's reply to me does exactly this.
>
> Third, "specific and precise" does not rule out judgments.  What, in my opinion,
> it does rule out is treating judgments as facts.  Making judgments as clearly
> labeled judgments is fine.  Let me try to do that here.
>
> On Apr 3,  8:25pm, Steve Eppley wrote:
> > Subject: Re: Reply on EM to Mike's Reply on ER
> > Bruce Anderson:
> > >I don't think I ever said that (in my notation) Smith//Condorcet is
> > >too complicated to propose to the public.  I said that it is
> > >significantly more complicated than just Condorcet.
>
> >>  I also said that it is significantly better
> than just Condorcet.  I also said that I thought that there are still other
> voting methods that are both better and simpler than Smith//Condorcet.  None of
> these statements mean that Smith//Condorcet is too complicated for public use.  
> In fact, I think that it is too simple, and that the public could accept the
> slightly more complex method I denote by Smith//Condorcet//Plurality.  I presume
> that Mike thinks that Smith//Condorcet is slightly more complicated and slightly
> better than just Condorcet.  Maybe we'll never reach agreement on "slightly"
> >>versus "significantly," but maybe we can agree on the unmodified "more."
>
> > How do you define significantly more complicated, then?  Does your
> > definition relate to whether the public can be persuaded to approve
> > it when it's offered in state initiatives?  (To me, that seems the
> > practical benchmark.)
>
> I certainly agree that I could have more clearly labeled these remarks as being
> personal judgments, not scientifically or mathematically proven facts.  In
> particular, it is my judgment that Smith//Condorcet is significantly more
> complicated than just Condorcet.  The following are my main reasons for making
> this judgment.
>
> First, Smith//Condorcet involves two fundamentally different methods, so it
> involves explaining and asking people to understand and accept two different
> methods.  Condorcet alone, of course, does not.

Admittedly, given people's liking for brevity, it would be nice to not
have to add the Smith Criterion to a definition of Condorcet's method.
But Bruce's attack shows that the academics will be making full use
of their candidate-counting critera in their anti-reform efforts, if
plain Condorcet is proposed. So we may be forced to include the Smith
Criterion. But it might not be necessary to do so at first. Let the
academics first convince people that Condorcet isn't adequate (if they
can) due to the candidate-counting criteria, and then anyone who
understands those criticisms would also understand, and understand
the reason for, the addition of the Smith Criterion to the definition
of Condorcet's method.

So it's not a problem, because if people believe the candidate-counting
criticisms of plain Condorcet then they'll have no trouble understanding
the Smith Criterion or its justification.

>
> Second, in attempting to advocate Smith//Condorcet, one has to explain, if
> asked, why Condorcet alone is not good enough.  In my opinion, such an

Not good enough in _your_ opinion, Bruce. Remember, we're going to
distinguish between facts & judgements.

> explanation is quite simple, for example, for either Condorcet//Plurality or
> Copeland//Plurality; namely, Plurality is quite poor as an initial voting
> method, but it serves well as a tie-breaker.  In my opinion, the corresponding
> statement for Smith//Condorcet (i.e., Condorcet is quite poor as an initial
> voting method, but it serves well as a tie-breaker) is much more difficult to
> accept.

And is a judgement of Bruce's rather than a fact.

Besides, as I said earlier, if Bruce & other academic authors succeed
in convincing people that the candidate-counting criteria are a
genuine problem for plain Condorcet, then we certainly won't have
any trouble explaining why we're adding the Smith Criterion.

>
> Third, while neither Smith nor Condorcet, alone, is extremely complex, neither
> one is all that simple either.  As evidence of this, note that erroneous or
> vague statements of these methods frequently appear on these lists.  In fact,
> I'm not sure I ever seen a technically correct definition of the Smith set
> (i.e., of the set of winners according to the Smith voting method).  With two
> exceptions, one such definition is as follows.

First, the Smith set needn't be defined as a set of winners according
to a method. And I remind you, Bruce, that we're talking about
_single-winner_ methods. One winner. More than 1 winner is something
in PR, not SW. A tie, requiring a tie-breaker to determine who that
1 winner is, sure, but never more than 1 winner.

If part of your criticism of my definition of the Smith set is that
I don't define it as a set of winners according to a method, then
we can start by discounting that criticism.

>
> DEFINITION:  An alternative is a winner according to the Smith voting method if
> that alternative is a member of the smallest non-empty subset of the
> alternatives such that each alternative in that subset pairwise beats each
> alternative not in that subset.

So then, where I said the Smith set is a set of alternatives, you call
it a subset of the alternatives. Does that mean it isn't valid to
say it's a set of alternatives? Also, I left out the words "non-empty".
Is that where my definition isn't valid. Excuse me, but a set that's
empty isn't a set of alternatives--it isn't a set of anything. If
you have an empty bucket, then you can't call it a bucket of sand.

You know, I don't care how much stilted language or formulese the
mathematicians use in their journals, but they go too far if they
say that anything that isn't said in their language isn't valid.

>
> The two exceptions are:  1) "pairwise beats" needs to have been defined, and 2)
> to be a valid definition, it must be shown that such a subset always exists and
> is always unique (it does and it is, but this still needs to be shown).

When I define Condorcet's method, I start by saying:

A beats B if more voters rank A over B than vice-versa.

So I define "beats" in my definition of Condorcet's method.

Since you say the Smith set exists & is unique, it isn't quite
clear just who it is that you're saying we have to prove that to.
The man in the street? Maybe you'd have us include proofs of
existence & uniqueness theorems in our street flyers?


>
> As are as Condorcet goes, it seems to me that most people on this list, except
> for Mike, say (as you imply below) that the Condorcet winner is the candidate
> whose worst pairwise defeat is the smallest, whenever there is no candidate that
> pairwise beats every other candidate.  There are two problems with this
> statement.  First, there can be two or more such candidates, which this
> statement does not allow.  Admittedly, it is not hard to construct a more
> complex correct statement, but complexity is the issue here.  Second, consider
The reason why the definition doesn't allow for there being more than
1 such candidate is that it's a statement of what alternative wins. In
any such statemenet, the implication is that there's only 1 such
alternative. It's a statement about how to find the 1 winner. Sure,
there could turn out to be a tie, where more than 1 alternative are]
equally qualified according to that statement, and ties are a different
subject. Ties can safely be ignored in public elections. Or we could
say to solve ties by Plurality. Complex?

No, we don't want a more complex statement. This isn't a mathematics
journal.

> the following example.
>
> 46:  A, (B & C tied)
>  6:  B, A, C
>  4:  B, C, A
> 44:  C, B, A
>
> Then #(A>B) = 46 and
>      #(B>A) = 54, so B beats A by 54-46 =  8.
> Also #(A>C) = 52 and
>      #(C>A) = 48, so A beats C by 52-44 =  6.
> Also #(B>C) = 10 and
>      #(C>B) = 48, so C beats B by 48-10 = 38.
>
> A says:  "I scored 46 in my only defeat, while C only got 44, and B only got 10.
>   So my worst pairwise defeat was the smallest."

I daresay anyone could say anything, Bruce. A could also say he should
win because he has a plurality. So what?

You're having A cite his "votes-for", in his worst defeat. For 1 thing,
votes-for doesn't mean much. If you rank A over B, that means that
you're voting against B winning, but it _doesn't_ mean that you're
voting for A winning.

That's why Condorcet counts votes against. If the point of this
example is to claim that people won't understand why Condorcet
counts what it counts, the explanation is simple, and I've given
it so often that I'm sure this list is tired of it:

Condorcet counts votes-against for the reason given in the paragraph
before last. So that you'll be counted as voting against your last
choice, by ranking a compromise over him, even if you don't rank
the compromise in 1st place.

So Condorcet's count of votes-against transparently carries out the
goal to get rid of the lesser-of-2-evils problem & the need for
defensive strategy (to the best degree possible), and to carry out
majority rule.

These things, Bruce, are what electoral reformers want. And, based
on what progressives say about their voting behavior, these considerations
are important to voters too. That isn't a judgement, it's a fact.
But you won't find it in academic journals; you'd have to talk to
voters.


>
> B says:  "My opponent only scored 48 in my one defeat, while C's opponent got
> 52, and A's opponent got 54.  So my worst pairwise defeat was the smallest."

Actually, B was beaten by only 44-10. B has the fewest voters saying
that a particular other alternative is better.


>
> C says:  "I lost by only 6 in my one defeat, while A lost by 8, and B lost by
> 38.  So my worst pairwise defeat was the smallest."

Now, through some sleight-of-hand, we're talking about margins of
defeat, rather than absolute number of voters. And wasn't C's margin
of defeat only 4, rather than 6?  (unless I miscopied it).

***

Bruce has surely seen my definition of Condorcet's method, and
he knows that A's & C's claims, as he writes them, have nothing
to do with Condorcet's method's scoring. If his point is that
people won't understand why Condorcet scores as it does
(instead of counting votes-for, or margins of defeat), I hope
I've demonstrated how briefly & simply that can be explained.

>
> This is simple?  At best, it's understandable only if it's very carefully

No that isn't simple. It's called "obfuscation". But I've answered it.

> explained.  And the need for such a vary careful explination is part of my
> argument for complexity here.

My explanation, given above, for why Condorcet counts as it does, isn't
complicated. It's brief & simple.

>
> It's late in EST, I'm tired, and it took me several hours to get this far.  I'll
> try to continue tomorrow (unless I get an offer I can't refuse, which does't
> take much these days).  I still have two more reasons to present; and then
> there's the rest of Steve's letter.  And then Mike says he wants to know why I
> like Copeland//Plurality better than Smith//Condorcet.  Does anyone really care?

Yes, people really care how claims are justified. By all means, I
believe it would be good to say why you like Copeland//Plurality
better than Smith//Condorcet, but that wasn't my question. I specifically
asked several questions in my previous letter--I asked what your
answer is to several statements.

***

Mike Ossipoff

>
> Bruce
>
> > >Determining which standards are most desirable would be a good
> > >topic to debate--too good to try to rush out in a "quick-and-dirty"
> > >e-mail posting.
> >
> > Did you receive the Glossary of standards I posted about a week ago?  
> > It's overly inclusive of standards.  If you have more standards you
> > want added, though, I'd like to hear them so I can add them.
> >
> > Several weeks ago we had two proposals for how to proceed here.
> > Both involve our voting on the order in which we will discuss
> > standards (and how well the methods score on each standard).  
> > Maybe we'd vote all at once on the complete order, or maybe just
> > periodically pick the next few.  To be considered in the voting,
> > they should be in the Glossary.
> >
> > >As an aside, in my notation X-Y either means a particular voting
> > >method jointly proposed by X and Y, or it means a particular voting
> > >method where X and Y alone have no intrinsic meaning.  X//Y means
> > >that X and Y are both ranked-ballot single-winner voting methods
> > >where, if X produces a single winner, then that winner is the X//Y
> > >winner; while if X results in tied winners, then the result of
> > >applying method Y to this set of tied winners yields the overall
> > >X//Y winner(s).
> >
> > So with this syntax the order of the two (or more) methods is
> > important.  Smith//Condorcet and Condorcet//Smith would be two
> > different systems.  In Smith//Condorcet, if the Smith set doesn't
> > have exactly one candidate, then smallest worst defeat breaks the
> > tie.  
> >
> > Smith//Condorcet has three cases:
> >
> > 1. Smith set is empty:  Condorcet picks from the candidates not in
> > the set (i.e., picks from all the candidates).
> >
> > 2. Smith set contains exactly one candidate:  This is the winner.
> >
> > 3. Smith set contains more than one candidate:  Condorcet picks from
> > the candidates in the set.
> >
> > >In fact, I have never used and I strongly oppose the use of the
> > >term "Instant Runoff" to mean MPV/STV/Hare voting.  Runoff has an
> > >established meaning, at least it does in the United States--it's
> > >the pairwise match between the top two plurality leaders, if
> > >neither has a strict majority.  So an "instant runoff" should be
> > >that pairwise match based on the voters ranked ballots.
> >
> > How about "Instant Runoffs"?
> >
> > But I'd rather reserve this moniker for pairwise methods, since the
> > pairings are just as much (maybe more so) "runoffs" as MPV's
> > attrition runoffs.  And maybe reserve it for one particular pairwise
> > method, so it can be used before the public when it's campaign time.
> >
> > --Steve
> >
> >-- End of excerpt from Steve Eppley
>
>
> .-
>


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