[EM] SARC definition improvement

[Markus Schulze]

Dear Mike,

you wrote (9 Sep 2000):
> Markus wrote (9 Sep 2000):
> > You should drop SFC, GSFC, WDSC and SDSC.
> >
> > Consider the following two criteria:
> >
> > Criterion X: If a given candidate has the property Z, then he
> > must be elected.
> >
> > Criterion Y: If a given candidate has the property Z, then there
> > is a way of voting that ensures that this candidate wins.
> >
> > On the one side, if a given reader considers criterion X to be
> > important then criterion Y is superfluous. On the other side, if
> > this reader doesn't consider criterion X to be important, then he
> > will also not consider criterion Y to be important.
>
> Wrong. If you want to claim that if you believe that it should
> be possible for a certain group to make a certain candidate win,
> then that candidate should win automatically, you need to justify
> your claim. I don't agree with it. Sometimes it's possible to
> guarantee the former, but not the latter. That's true of the
> situation we're talking about, as I'll show later.

In the website http://home.pacbell.net/paielli/voting you introduce
7 criteria. 2 of the 7 criteria are violated by Condorcet methods.

4 of the 5 remaining criteria are motivated by the opinion that
if a majority of the voters strictly prefers candidate A to candidate
B then rather candidate A than candidate B should be elected resp.
then there should be a way of voting with certain properties that
will ensure that B cannot win.

The problem is that these 4 criteria (SFC, GSFC, WDSC, SDSC) are so
similar that a reader either considers all 4 to be important or all
4 to be unimportant.

A reader who thinks that the fact that a majority of the voters
strictly prefers A to B has no important meaning will simply reject
all 4 criteria simultaneously.

******

You wrote (9 Sep 2000):
> Markus wrote (9 Sep 2000):
> > You should drop WDSC, SDSC and SARC. These criteria say that under
> > certain conditions there must be a safe way of voting strategically
> > resp. that those who use a certain strategy must not be punished.
> >
> > It makes sense to say that those who act sincerely should not be
> > punished. It makes sense to say that those who act insincerely
> > should not be rewarded. But there is absolutely no theoretical
> > justification for criteria that protect insincere voters.
>
> Markus means that, according to his theory, there's no theoretical
> justification. If Markus could get past his theory, maybe he'd be
> more in touch with what's important to voters.

Can you name ANY scientist who promotes criteria that protect
insincere voters?

You wrote (9 Sep 2000):
> Markus says that sincere voting should be rewarded.

No. I only say that sincere voting should not be punished.

******

You wrote (9 Sep 2000):
> By Markus's theory, whatever it is, there's no
> theoretical justification for minimizing the degree of insincerity
> that voters need when trying to enforce majority wishes. Markus is
> welcome to his theory, but hopefully it's ok with Markus if not
> everyone considers Markus's theory their theory.

What do you mean with "Markus' theory, whatever it is"? If you
believe that everything that contradicts your own opinion is
"Markus' theory, whatever it is" then almost every social scientist
is a "Schulzeist, whatever it is." It would be advantageous if you
could name ANY scientist who agrees with your opinion.

******

You wrote (9 Sep 2000):
> Markus says that I want to protect insincere voters. Markus didn't
> read the criteria. The majority defensive strategy criteria minimize
> the degree of insincerity that is needed. SARC doesn't specifically
> protect insincere voters. It protects all voters who don't vote
> dominated strategies--in other words, for practical purposes, it
> protects all voters from defeating their favorite or electing their
> last choice.  Markus says that there's no theoretical justification
> for that protection. Whatever. But it sounds to me like a good
> thing. You'll like it too when that favorite is your favorite too.

The "Weak Defensive Strategy Criterion" says that if a majority of
all the voters prefers A to B then they should have a way of voting
that will ensure that B cannot win, without any member of that
majority voting a less-liked candidate over a more-liked candidate.
If the used election method doesn't meet the Condorcet criterion
then this way is an insincere way. Therefore WDSC is either
superfluous (when the used election method meets the Condorcet
criterion) or it guarantees that under certain conditions there
is a secure way of voting stategically (when the used election
method doesn't meet the Condorcet criterion).

If the intention of SARC was to protect sincere voters then the
participation criterion would have been sufficient. But SARC does
more. SARC also protects all those voters who don't vote dominated
strategies. And I don't know why a given criterion should protect
voters who use a certain kind of strategy. It would be advantageous
if you could name ANY scientist who thinks that voters who use
a certain kind of strategy should be protected. It would be
advantageous if you could say WHY voters who use a certain kind
of strategy should be protected.

******

You wrote (9 Sep 2000):
> Markus wrote (9 Sep 2000):
> > For example, independence from clones says that it should not be
> > possible to manipulate the result of the elections by spaming the
> > voters with a large number of identical candidates. As soon as a
> > given reader has understood the intention of independence from
> > clones, the exact mathematical definition of this criterion is
> > rather obvious. On the other side, a reader has to agree to too
> > many details before he can consider the exact definitions of WDSC,
> > SDSC or SARC to be intuitive.
>
> You neglected to say exactly what assumptions a reader has to agree
> to before he can consider WDSC, SDSD or SARC to be intuitive. It
> would be difficult to discuss your claim if you don't specify what
> assumptions you mean. Minimizing the degree of insincerity needed
> when it's feasible to do so, and desirable to a majority to do so
> seems intuitive to me.

The reader has to agree
(1) why those and only those voters who use a non-dominated strategy
    should be protected by SARC,
(2) why only the favorite candidate should be kept from losing and
    only the last choice from winning by SARC,
(3) why the fact that a majority of the voters strictly prefers A to
    B has any important meaning,
(4) why an election method should guarantee the existence of a secure
    strategy when a candidate with a given property exists.

Steve once wrote that he doesn't consider the particpation criterion
to be important enough because voters usually don't vote sincerely
but strategically. But a criterion that says that a voter should not
be punished for showing up and voting strategically would have been to
strict. Therefore Steve and you relaxed this criterion and got SARC.

The question is: From all the possible relaxations of that criterion
that says that a voter should not be punished for showing up and
voting strategically, why should we just take SARC?

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