[EM] Why RP(wv) & CSSD meet GSFC

[MIKE OSSIPOFF]

Steph--

You wrote:


To Mike Ossipoff...

I find some of your criterias partially subjective.

Please let me explain.

If a voter decides to truncate its preferences,
he changes some of his pairwise opinions from
A>B to A?B (meaning he does not care anymore).
It seems to me reasonable to accept that a change in
ballots can then imply a change in A or B's support.

I reply:

Sure, and that's true with any method, including the ones that
meet GSFC. GSFC doesn't prevent loss of support from being counted.

You continued:

Hence if C was the winner, but A or B's support
growths enough without changing C's support
It seems acceptable that C could loose his winner status.

I reply:

Certainly, and that happens with GSFC complying methods too.

GSFC & SFC don't actually mention truncation, but invulnerability
trunation has usually been defined to mean that truncation can't
steal the election from a well-supported CW.

But SFC & GSFC, as I was saying, don't mention truncation, and are
instead more general. They merely say that, without falsification
of preferences, no one should win who has a sincere Smith
set member preferred to him by a majority who vote sincerely.
(no one, that is, who isn't a member of the sincere Smith set).

That's a reasonable thing to ask for. It's reasonable for the winner
to come from the sincere Smith set, and if that candidate is well
supported against someone else, it's reasonable that that other
candidate shouldn't win. The important thing about GSFC is that
it doesn't specify that anyone uses defensive strategy, and so
complying methods have GSFC's guarantee even if that majority doesn't
use any strategy, or do other than vote sincerely. That's why it's
called the Strategy-Free Criterion. It talks about a plausible conditions 
under which complying methods are strategy-free. That's
what I most like about the Condorcet(wv) versions.

You continued:

SPC (secret preferences criteria) should ask for C's support
invariance by any change in the pairwise comparison between
A and B, not for C's status immuability.

I reply:

That would be a different criterion, but GSFC doesn't ask for
anything unreasonable.

The SPC that you describe sounds similar
to IIAC, Heritage, & Regularity, criteria met by Approval, but not
by any rank method that I know of. With rank methods, deleting a
candidate from the ballots, and recounting the ballots, can reduce the
win-probability of an undeleted candidate. Though A initially wins,
deleting C can cause A to lose to B. That won't happen in Approval.

Steph.



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