[EM] Majority winner set

[MIKE OSSIPOFF]

Markus's definition of sincere Approval voting says that reversing or
falsifying preferences among candidates other than the incumbant is
sincere. Nonsense.

Besides, it seems real funky to have different sincerity definitions
for different methods.
>To my opinion, "sincerity" must be defined in such a manner that there is
>a unique (but not necessarily deterministic) way of voting "sincerely" for
>a voter with a given opinion.

Though everyone has a right to their opinion, you'd have a difficult
time convincing others to share that one.

Likewise, sincere means that you're not misrepresenting your
preferences, but it certainly doesn't say anything about whether
or not your voting is influences by strategic considerations. As
was pointed out, a sincere ranking can be a strategic vote, if it's
done after a strategic calculation when other ways of voting were
considered.


>Mike wrote (24 Nov 2000):
> > A voter votes sincerely 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.
>
>To my opinion, this is only a necessary but not a sufficient condition
>for "sincerity." To my opinion, it is also necessary that the voting
>behaviour of a "sincere" voter does not depend on his information
>about the voting behaviour of the other voters.

I answered this mistaken claim earlier in this message. Say I
sincerely believe that candidate X is corrupt. So I spread the word
everywhere that he's corrupt, so that he won't win. I'm doing it
for a strategic purpose, with an intent to change the outcome of the
election. But I also sincerely believe that it's true. Am I acting
insincerely?

>
>Mike wrote (1 Dec 2000):
> > Markus wrote (30 Nov 2000):
> > > 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.
>
>Brams and Fishburn are well known supporters of Approval Voting.

I'd misunderstood that sentence, and thought that you'd said
"promote" instead of "don't promote".

But what are you saying?
That the person who doesn't vote Gore over Bush because he wants to
vote Nader over Gore is voting insincerely?. He can't express both
preferences. As I said, not doing the impossible can't be counted as
an act, and so it also isn't an insincere act.

>
>Mike wrote (1 Dec 2000):
> > 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.
>
>When Approval Voting is used then the optimal strategy looks as
>follows:
>
>1. Approve all those candidate you prefer to the expected winner.
>2. Disapprove all those candidate to which you prefer the expected
>    winner.
>3. Approve the expected winner when rather a less preferred than
>    a more preferred candidate is elected. Otherwise disapprove him.

#3 isn't clear. It should say "Vote for the expected winner when
the other of the 2 frontrunners is someone whom you like less."

This is a better way of saying what you said:

Vote for whichever of the likely 2 frontrunners you prefer to the other,
and vote for everyone whom you like better than him.


That's one way of saying that you should vote for the candidate you'd
vote for in Plurality, and for everyone whom you like more.

But the person who likes mathematics might want to be more
elaborate, and take into account estimates of frontrunner probabilities
for the various pairs of candidates, to calculate strategy for
Plurality or Approval. I emphasize that that isn't necessary, and
that one can do fine in Approval by voting for the candidate he'd
vote for in Plurality and for everyone whom he likes better--for
his favorite of the 2 expected frontrunners and for everyone whom
he likes better.

>Due to Mike's definition of "sincerity," a voter who uses this
>strategy votes "sincerely." To my opinion, this voter votes
>"insincerely" at least in those cases where he would have voted
>in a different manner when he had no information about the voting
>behaviour of the oher voters.

Did you say that with the purpose of convincing anyone or influencing
anyone? Then you didn't say it sincerely. It was an insincere
statement :-)

Mike


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