[EM] Steph, re: CW example

Sat Nov 23 16:14:56 PST 2002

Steph--

you wrote:

Approval definitively favors centrists candidates.

Are you saying that's bad? As i've said, Approval quickly homes in
on the voter median candidate, and stays there. you're right about that.
Also, when voters in Approval err because the all believe an incorrect
poll, Approval errs by picking someone in the middle, unlike
irv and margins methods, which can err by electing an extreme
candidate.

if everyone believes mistakenly that Favorite will outpoll Worst, so
that Favorite voters don't vote for Middle, then the Worst voters,
using those polls, will vote for Middle.

With everyone believing the same poll, Approval can err if Favorite
has a 1st choice majority, but people believe that Worst will outpoll
Favorite. Then the Favorite voters will vote for Middle, and give the
election away to Middle. But that failure is one which elects Middle,
not an extreme.

you continued:

As a voter I should be free to decide if I want to support one or more
candidates without the electing method affecting my winning probabilities.

i'm not sure what you mean by that. if you're saying that Approval
requires more strategy than Condorcet(wv), no one will argue with
you on that.

So let us check another subject:
relative margins (rm) vs winning-votes (wv)

MIKE OSSIPOFF a écrit :

>A margins advocate could say that he doesn't consider the majority
>defensive strategy criteria important, but they measure for the
>standards of majority rule and getting rid of the lesser-of-2-evils
>problem. The wv methods are the ones that do well by the majority
>defensive strategy criteria. The wv versions of Ranked-Pairs and
>BeatpathWinner/CSSD meet all of them.

you wrote:

None of these criteria has shown to me that they can protect a Condorcet
Winner. It seems they show an enhancement of the probability of being able 
to
protect a Condorcet Winner and I like that. By how much are they efficient?

i reply:

Again, i'm not sure what you mean. if you're saying that you want a
method to always elect the CW, no matter what, then i admit that i
can't offer you that. What method can?

But it might be that you're confusing the defensive strategy criteria
with some others, since the defensive strategy criteria say nothing
about probability. if you want to write a probability criteria, then
by all means do so. Then, after you've done that, that would be the
best time to talk about probability in criteria.

>Aside from whether you like those particular criteria, it can't really be
>denied that margins is the big
>violator of majority rule, and is the method that makes greater strategic
>demands on voters who want to protect majority rule, or who want to protect
>the win of a CW.

you said:

Please check  
http://groups.yahoo.com/group/election-methods-list/message/10107
for an example where Winning Votes harms a Condorcet Winner.
So both criteria can harm a Condorcet Winner.

i reply:

That's the old poorly-supported-CW example. i've discussed it many
times. i've answered that objection many times. yes, if there's no
majority who care to vote the CW over candidate B, then the B voters
can steal the election by truncation. i never claimed that a
poorly supported CW can't lose because of truncation. But so what if
he can? in margins, and in your relative margins, a majority-supported
CW can lose to voters who steal the election by truncation. Which is
worse?

As i said, SFC and GSFC don't mention truncation, but they tell what
i claim about wv when no one order-reverses.

you said:

The question is: how big is the
majority rule violation in both cases?

i reply:

in the example that you cite above, there's no majority rule violation
when A loses to B. With 11 voters, A beats B 4 to 3. With 4 voters
voting A over B, out of 13 voters, there's no majority rule violation
if B wins instead of A.

Give me numbers from an A, B, C, AB, BC,
AC, BA, CB, CA distribution. I will do it myself, but for a small number of
voters. I sound like M. Carey, working with 3 candidates and 4 voters...

i've given you examples in which your method defeats a CW in violation
of majority rule under conditions where that needn't happen. you've
shown an example in which a truncation defeats a poorly supported CW
with no majority rule violation. i've shown that wv meets SFC and
GSFC. i'm not sure what you're asking for above.

>It was shown here that, with margins methods, there are plausible
>ordinary situations in which the only Nash equilibria are ones in which
>defensive order-reversal is used.
>
>We probably agree that it's undesirable to have to drop a defeat,
>since each pairwise defeat represents a public vote about the
>relative merit of 2 candidates. Dropping a defeat overrules all the
>voters who won that public vote. So we'd like to at least overrule
>as few as possible.

you said:

Agreed. I even rallied to M. Tidemann's method consequence. It minimizes the
largest overruled pairwise comparison, so it minimizes the largest overruled
opinion created by different people.

i reply:

if you're not going to read my messages, it's difficult for us to
talk. See below:

>Margins advocates would answer that not dropping a defeat overrules
>the voters who voted agains that defeat. Wrong. Those voters were
>overruled by the result of the public vote between those candidates.
>Not dropping a defeat that the public enacted doesn't overrule anyone.

The same is valid for winning votes, no?

No. winning votes doesn't count losing voters as being overruled by
the count rule, because losing voters, opponents of a publicly-voted
defeat, have already been overruled when the voters voted between
those 2 candidates. X beats Y. margins advocates want to say that
the y>x voters are overruled by the count rule if we keep that defeat.
No, they've already been overruled when they lost that pairwise
comparison in the public vote. But if we drop that defeat, then
we're ignoring a collectively-voted public preference, then it is we
who are overruling the voters who voted for that defeat.

Do you see the difference? it's margins, not wv, that tries to claim
that we're overruling voters who actually have already lost and who
have no claim to getting their way.

>For that reason winning-votes (wv) is the more democratic class of
>methods, when it comes to honoring pairwise votes and expressed
>public wishes.

you said:

Because I have not yet been able to quantify (wv) and (rm) Condorcets 
Winners
stilling probability, I cannot use this criteria to select the "most 
democratic
criteria".

i reply:

i admit that i don't quite know what you mean there.

you said:

I prefer to use a quantifiable objective, the minimization of the
probability of overuling the wrong pairwise comparison, which is equivalent 
in
my sense to minimize the largest overuled relative margin.

i reply:

So you're not so much interested in overruled voters, but you want
to judge which proposition is right and which is wrong. First you have
to provide an operational definition of a right or wrong proposition.

That's a definition that contains a test by which we can determine whether 
or not a proposition is right or wrong according to that
definition. Without that, it's meaningless to talk about right or
wrong propositions.

And don't say that your definition of a right proposition is one with
a large margin or relative margin. you see the circularity of saying
that relative margins favors right propositions then, right?

your definition of a right or wrong propositon should be one that
in some way concides with what we expect right or wrong to mean.
how would you test a propostion for rightness or wrongness in a way
that makes sense according to the usual meaning of those words?

mike ossipoff

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