[EM] Majority winner set

[MIKE OSSIPOFF]

Dear Markus--


You said:

>you say that the well known and widely used concept that
>criteria and election methods are defined on the reported
>von Neumann-Morgenstern utilities of the voters is
>"inadequate," "vague," "sloppy," "dishonest," "absurd,"
>"faulty," "incorrect," "poor," "silly," "contradictory,"
>"incoherent," "useless," "garbage" and "mumbojumbo." But
>on the other side, your concept has similar ingredients.
>
>First:
>
>Your definitions of SFC, GSFC, WDSC, SDSC, FBC,
>SARC and defensive strategies use "sincere preferences."

Of course they do, because those criteria are about people being able
to vote sincerely without a penalty, to whaterver degree that can
be guaranteed. Since unpenallized sincere voting is the goal, it's
odd that you think I shouldn't talk about sincere voting.


>
>Second:
>
>Your definition of "sincerity" is implausible. You wrote
>(24 Nov 2000):
> > A voter votes sincrely if he doesn't vote a preference
> > that isn't a sincere preference or leave unvoted a sincere
> > preference that the balloting system would have allowed him
> > to vote in addition to the preferences that he actually did
> > vote.
>
>Example:
>
>   Suppose that Approval Voting is used. Suppose that the
>   sincere opinion of a given voter is A > B > C > D > E and
>   that this voter decides to approve A, B, C and D.
>
>   The day before election day, this voter hears that candidate
>   E has no chances to win and that only candidate B and
>   candidate C have realistic chances to win. Therefore, this
>   given voter decides to approve only candidate A and
>   candidate B.
>
>   Due to your definition of "sincerity," this given voter votes
>   "sincerely." But (1) in so far as this voter changes his
>   voting behaviour after he has got additional information
>   about the voting behaviour of the other voters and (2) in so
>   far as this given voter changes his voting behaviour because
>   of strategical considerations, it is clear that this given
>   voter votes strategically. Therefore your definition of
>   "sincerity" isn't suitable to differ between sincere voters
>   and strategical voters.

Take another look at my definition of sincere voting. It doesn't
say that sincere voting must be nonstrategic. With a rank method
the only sincere ballot is a sincere ranking of all the candidates.
In Plurality, the only sincere ballot is one that votes for one's
sincere favorite. But in Approval, I'm not sure what you'd want to call
a sincere ballot. Obviously the 2 kinds of insincerity are voting
a false preference, and not voting a sincere preference when there's no 
reason why you couldn't have voted it. Hence my definition. With rank 
balloting and Plurality, the only sincere vote is one that doesn't 
strategize. Though you'd like it to, that statement would have no meaning 
with Approval. Maybe that doesn't sound like what "sincere" means to you, 
but that's how I define it.

My definition complies with your expectations with rank balloting &
Plurality, and it's general enough that it applies to Approval
too, even though sincerity in Approval isn't as easy to discuss as you'd 
like it to be.

>
>Again: When you really think that the well known and widely
>used concept that criteria and election methods are defined
>on the reported von Neumann-Morgenstern utilities of the voters
>is "inadequate," "vague," "sloppy," "dishonest," "absurd,"
>"faulty," "incorrect," "poor," "silly," "contradictory,"
>"incoherent," "useless," "garbage" and "mumbojumbo" then
>please explain why you think that your "universally accepted"
>concept that criteria should be defined on sincere opinions
>and election methods should be defined on casted ballots

Wrong. I never said that all criteria should be defined in terms of
sincere ballots. I said that some work only if defined that way. And
I never said that even that is universally accepted. And yes I
did and do say that election methods defined on cast ballots is
universally accepted by everyone but you & your head-up-the-ass
academics. Most would agree with me that it's preposterous and silly to add 
your contrafactual assumption about balloting.



>might
>be better. Actually the fact that you define criteria and
>election methods on different inputs

Wrong, voting systems have the same input in my voting system
definitions and my criterion definitions: Actual ballots.

But there's no reason why a criterion can't speak of voters' sincere
preferences as well as their votes. That isn't a voting system
input, but it's part of the overall configuration that makes up an
example. Remember, Markus, that my criteria are about allowing
penalty-free sincere voting to the extent possible. Therefore it's
odd that you don't think I should mention sincere voting in criteria.
The Condorcet Criterion too can be stated in terms of your not having
to do other than vote sincerely as long as there's a SCW and everyone
else votes sincerely.

Have we cleared that up? Sincere preferences aren't part of a voting
system's input, in any of my definitions of methods or criteria. But
sincrere preferences are a relevant part of the overall configuration
when we want to guarantee that sincere voting won't be penalized,
to the extent that that guarantee is possible.




>makes it significantly
>more difficult to check whether a given election method meets
>a given criterion. Example: It hasn't yet been dem
onstrated
>whether PC resp. Smith//PC meets SDSC.

I admit that determining that could involve some work. That
certainly doesn't mean that the criterion isn't valid. If you're
saying I could have instead written a more easily-used criterion,
then I answer that it wouldn't be the criterion that speaks of the
guarantee that I want.

>
>You claim that I "endlessly repeated" the same questions.
>You claim that you are "real tired of that repetition."

No, I said that the other members of the list probably were.


>But
>you apparently neglect that you have never answered any of my
>questions.

You're probably writing this before checking the posting that I
sent Wednesday, around mid-morning your time. In that letter, I answered
the questions you'd asked, questions that I couldn't have answered
until I received and (later) understood the posting that you'd sent
most recently before that time.

>Although I have invited you several times to explain
>why you think that your concept might be better, you have never
>answered.

Again, I answered that in the posting that I sent Wednesday,
mid-morning, your time. I'll say more about it though. There's been
no attempt to evade questions. I answred your questions as soon as
I understood your previous posting. Yes I intend to add more to those
answers.

And now, while we're talking about unanswered questions: How does
your system for criterion compliance determination, with its assumption
of ratings ballots that the voting system somehow converts into
the method's own ballot--how does it deal with Approval and
single-winner Cumulative? Can it be applied to them? Do they meet
Condorcet's Criterion by your approach? Why or why not?


>
>However, I doubt that those who don't promote Approval Voting
>will agree to your definition of "sincerity."

I'm reasonably sure that Brams & Fishburn have said, in their book
_Approval Voting_, that, for Approval, they define sincere voting as
voting without reversing a preferences, without falsifying a preference.

Their definition means the same thing that my definition means when
it's applied to Approval. My definition agrees with how Brams &
Fishburn would define sincere voting for Approval, and it also agrees
with how we'd all define sincere voting with rank balloting and
Plurality.

>
>However, I don't have the impression that your statements have
>anything to do with majority winner sets or beat path GMC.

You've forgotten that this has been about whether Plurality meets
BeatPath GMC. I added Condorcet's Criterion for politeness, and because
it's simpler. You've told me why you say Plurality fails BPGMC & CC,
but your answer leads to other questions about BPGMC, like: Can it
be applied to Approval and single-winner Cumulative? Does your own
method comply with it? I doubt very much that the answer to both of
those questions can be "yes". No, BPGMC is still the topic.

By the way, your abovequoted questsion shows why I said that people
might be getting tired of your repetition.

Mike Ossipoff


>
>Markus Schulze
>

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