[EM] 3 questions for Markus

Markus Schulze schulze at sol.physik.tu-berlin.de
Sat Sep 23 04:11:18 PDT 2000


Dear Mike,

you wrote (20 Sep 2000):
> Markus wrote (20 Sep 2000):
> > It seems to me that you believe that criteria that are defined on
> > the actually casted ballots and not on the sincere opinions of the
> > voters don't say anything about the need for insincere voting.
> > I don't agree with you because in praxi a criterion that is defined
> > on more than the actually casted ballots cannot say anything that
> > cannot be said by a criterion that is defined only on the actually
> > casted ballots because --in so far as election methods are always
> > defined on the actually casted ballots and not on the sincere
> > opinions of the voters-- the fact that a given election method
> > meets a given criterion must be reflected in the way in which this
> > election method evaluates the actually casted ballots. Therefore
> > whether a given election method meets SFC (resp. GSFC resp. WDSC
> > resp. SDSC) must depend only on how this election method evaluates
> > the actually casted ballots. Therefore it must be possible to
> > define SFC (resp. GSFC resp. WDSC resp. SDSC) on the actually
> > casted ballots.
>
> I think you're saying that, for any criterion that mentions
> sincere preferences, another criterion can be written that
> doesn't mention sincere preferences, and which is met by everything
> that meets the 1st criterion and is failed by everything that
> fails the 1st criterion.

Correct.

You wrote (20 Sep 2000):
> Even if that's true, that other criterion isn't saying the same
> thing. It could be used to test for my criteria, but its value
> would only be indirect, as a way of testing for the criteria that
> say what I want to say. It would obscure the purpose of
> the criterion.

You can use your lesser-of-two-evils concept as a heuristic to explain
your criteria, like Blake uses his best-guess-for-best-candidate
concept or many PR supporters use their wasted-votes concept. But I
am very sceptical when you use your lesser-of-two-evils concept
itself as an "academic criterion."

******

You wrote (20 Sep 2000):
> According to you, a criterion shouldn't mention the sincere
> CW, or stipulate sincere voting. When the Condorcet Criterion
> is defined in accordance with your rule, it's met by Plurality.
> So is Beatpath GMC.
>
> You could just arbitrarily say, in the definition of Condorcet's
> Criterion or Beatpath GMC, that nonranked methods fail the criterion,
> by fiat. That would be awkwardly arbitrary.
>
> Or, you could define Condorcet's method by saying:
>
> If everyone votes sincerely [as I defined it a week or so ago]
> and if there's a sincere CW, then that SCW should win.
>
> You could define Beatpath GMC in an analogous way.
>
> But then you've mentioned something other than actual votes.
> Shame on you :-)
>
> I don't know whether you have an additional way to make
> the Condorcet Criterion or your Beatpath GMC apply to all
> methods. I don't know if you have a way of doing that without
> mentioning sincere preferences. If you do, I just haven't heard it
> yet.

To circumvent this problem it is sufficient to presume that the
voters always cast their full (not necessarily sincere) vNM
utilities on the ballots.

******

You wrote (20 Sep 2000):
> The same is true of BC. Arbitrarily saying that nonrank methods
> fail wouldn't be so bad with BC, because, unlike Condorcet's
> Criterion & Beatpath GMC, BC isn't claimed to be its own reason
> for being: It's intended as a way of determining compliance with
> the majority defensive strategy criteria. Plurality doesn't pass
> any of those, and it's not unreasonable to arbitrary say that
> nonrank methods fail BC. Or, if one wanted to, one could
> seamlessly make BC apply to all methods in the way that I suggested
> for Condorcet's Criterion & Beatpath GMC.

In so far as BC doesn't take into consideration whether the
considered pairwise majorities are absolute or relative majorities,
I don't see any connection between BC and your majority defensive
strategy criteria.

******

You wrote (20 Sep 2000):
> I should add that, though the definiton that I posted for
> Participation says nothing about sincere preferences, the
> Participation definition that you stated stipulates sincere voting
> and the worsening of the outcomes with respect to the voter's
> sincere preferences. So you don't do a good job of abiding by
> your own rule.

I wrote (9 Dec 1998):
> Participation Criterion: Suppose, that candidate X is elected.
> Then an additional voter, who strictly prefers candidate X to
> candidate Y, must not make Y win the election.

I wrote (10 Dec 1999):
> The participation criterion says that an additional
> voter who strictly prefers candidate A to candidate B
> must not change the winner from candidate A to candidate B.

The itention of the participation criterion is to say that
a voter must not be punished for showing up and voting
sincerely. But the participation criterion itself is
defined only on the actually casted ballots.

Similarly you can use sincere preferences to explain the
intention of your lesser-of-two-evils criteria. But the
exact definitions of your lesser-of-two-evils criteria
should work only on the actually casted ballots.

******

You wrote (20 Sep 2000):
> I'd considered an approach to SFC that only spoke of actual votes,
> rather than mentioning the sincere CW. But that doesn't say the
> same thing. Mentioning the SCW more clearly tells what makes the
> scenario possible. A criterion mentioning only votes, though
> met & failed by the same methods, wouldn't tell what I wanted
> to tell.
>
> But even if those other criteria could be written,
> it isn't clear what you think that would mean about criteria that
> mention sincere preferences. You didn't say they aren't valid,
> because you know that wouldn't be so. You didn't say they're
> not clearly-defined, though you unsuccessfully tried to show that
> 2 of them were. So far, all we have is that you don't want to
> discuss them. Suit yourself. We can assume, then, that you've
> said the worst that you can about the defensive strategy criteria.

In your website at http://home.pacbell.net/paielli/voting, four of
the five criteria that you use to promote Condorcet methods are
based on your lesser-of-two-evils concept. You promote the Condorcet
methods in such a way that the reader gets the impression that if
he doesn't consider your lesser-of-two-evils concept to be important
then Condorcet methods are worthless. You don't consider this to
be a problem because you consider it to be obvious that everybody
who values majority rule also values your lesser-of-two-evils
concept. But I don't see any reason for your optimism.

Actually, to my opinion, the currently discussed Condorcet methods
are very good methods compared to the non-Condorcet methods even if
the reader doesn't consider your lesser-of-two-evils concept to be
important. But he will never know that because you spend four fifths
of your time with your lesser-of-two-evils concept.

******

You wrote (20 Sep 2000):
> Markus wrote (20 Sep 2000):
> > When you have defined SFC, GSFC, WDSC and SDSC on
> > the actually casted ballots, then we can discuss whether these
> > criteria or BC or beat-path GMC should be used.
>
> They wouldn't be the same criteria. They'd be different ones that
> are met or failed by the same methods, but which don't say what
> I want to say.
>
> Discussion concluded.
>
> You have the amusing conceit to tell me that we can discuss
> the defensive strategy criteria when I've defined them so
> that they make no mention of anything other than actual votes.
> Look, I don't care if you discuss them or not. You're invited
> to, so that we can show that you've done your best to try to
> argue against them. Maybe the time has come when you have already
> done that.
>
> That's what we have to assume now.
>
> That's as good a way as any to end the discussion.
>
> By the way, you've been hopping from one criticism attempt
> to another. When one fails, you try another.  You seem to be
> desparately trying everything. You want to find fault with
> those criteris so badly that it really shows.

A few years ago I proposed beat-path GMC as an alternative
wording for your lesser-of-two-evils criteria. Beat-path GMC
has the advantage that it is defined only on the actually
casted ballots so that it is significantly more simple to
check whether a given election method meets beat-path GMC
than to check whether it meets your lesser-of-two-evils
criteria.

But very recently (e.g. in your 4 June 2000 mail, in
Steve's 2 June 2000 mail or in Steve's 26 Feb 2000 mail)
you rejected beat-path GMC as "overly strong." Therefore
--even if you don't want to define in your website at
http://home.pacbell.net/paielli/voting your lesser-of-two-evils
criteria in such a way that they depend only on the actually
casted ballots-- it would be very advantageous for the
discussion in this mailing list if you could define your
lesser-of-two-evils criteria in such a way that they depend
only on the actually casted ballots. Then the participants of
this mailing list can see in how far beat-path GMC is "overly
strong" compared to your lesser-of-two-evils criteria. And
they can also see more clearly e.g. why compliance with BC
means compliance with SFC, GSFC, WDSC and SDSC as you suggest
in your recent mails.

******

You wrote (21 Sep 2000):
> I'd like to comment again on some things that Markus said:
>
> Markus wrote (20 Sep 2000):
> > It seems to me that you believe that criteria that are defined
> > on the actual casted ballots and not on the sincere opinions
> > of the voters don't say anything about the need for insincere
> > voting.
>
> Well, I must admit that it isn't quite obvious how a criterion
> that doesn't mention sincere preferences (and therefore can't talk
> about sincere & insincere voting) could say anything about the need
> for insincere voting.
>
> Maybe he means that if we wrote an equivalent criterion, that
> doesn't mention sincere preferences, compliance with that criterion
> would imply compliance with my criterion that mentions sincere
> preferences. (Let's say that 2 criteria are equivalent of they're
> met by the same methods and failed by the same methods).
>
> But in no way could that other criterion be said to say anything
> about the need for insincere voting.
>
> Markus seems to be saying that if I want criteria about avoiding need
> for insincere voting, then he wants me to write them without any
> mention of sincere preferences, sincere voting, or insincere voting :-)
>
> Markus, the only thing that you've succeeded in proving is that you're
> driven by some desperate need to try one silly & nonvalid objection
> after another. I have to say that it was true when I said that if
> that's the best you can do then you're only wasting our time.
>
> By the way, Markus claimed to show that it's always possible
> to write an equivalent criterion that doesn't mention sincere
> preferences. Well do you have a way of stating Beatpath GMC in a
> way that applies to all methods without arbitrary failure-fiat for
> some methods, and which makes no mention of sincere preferences?
>
> Anyway, even if it's possible to write such equivalent
> no-sincere-preference criteria, Markus hasn't shown that it's
> feasible & practical, much less that it's necessary or desirable
> or even useful.
>
> For instance, for FBC, one could say "The voting system must be
> Approval". That would satisfy Markus's request for an equivalent
> no-sincere-preferences requirement, but it couldn't be said to be
> useful. People would tell me that I can't argue for Approval by giving
> them a criterion that says that the method must be Approval. FBC is
> worded to say something that's desirable. I want to say that no one
> should ever have incentive to dump their favorite, and Markus wants
> me to somehow word that without any mention of sincere preferences
> (including favorite). Excuse me, but that request is asinine.
>
> If Markus wants equivalent no-sincere-preferences criteria for
> the defensive strategy criteria, then let him write them. After
> he does, then we can judge their usefulness.

I have proposed beat-path GMC as an alternative wording for your
lesser-of-two-evils criteria that has the same intention and that
is defined only on the actually casted ballots. So if you really
want to discuss the lesser-of-two-evils criteria defined only on the
actually casted ballots, then you have every possibility to do so.

You claim that beat-path GMC was too strong compared to your
lesser-of-two-evils criteria. But actually beat-path GMC is
significantly weaker that GMC that you have proposed until
very recently (until Feb 2000?).

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de



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