[EM] Definitions of FBC, Strong FBC, and Intermediate FBC.

[Michael Ossipoff]

I realize now that I thoroughly mucked up the attempted definition of
Intermediate FBC. As I said,
this subject of stronger FBCs (stronger than the FBC that I've been
defining and using for years, which
we can call Weak FBC, or just FBC) is completely new to me.

I should start by re-posting my definition of FBC (Weak FBC):

A method meets FBC if, with that method, it isn't possible to contrive a
configuration of candidates,
voters, and ballots of all but one voter, such that that one voter can, by
voting someone over hir favorite,
get an ourcome that s/he prefers to every outcome that s/he could get
without voting someone
over hir favorite.

[end of FBC definition]


Now, if I try to write definitions for Strong FBC, and especially for
Intermediate FBC, those may well be
almost as wrong as the Intermediate definition that I attempted earlier
tonight. But I'll try anyway, with
the understanding that I or someone else may well have to fix it later.

Strong FBC:

A method meets Strong FBC if, with that method, it isn't possible to
contrive a configuration of candidates,
voters and ballots of those voters such that one of those voters, having
his favorite initially at1st rank position, can,
by lowering his favorite to a lower rank position, gain an outcome that
s/he prefers to the one that would result
from the ballot as it existed before that modification.

[end of Strong FBC definiition]

In other words, no one can ever gain a better result by lowering his
favorite from 1st rank position.

[end of briefer definition of Strong FBC]

Maybe the brief wording is just as good.

Approval meets Strong FBC.

Maybe all of the methods that I refer to as methods that meet FBC also meet
Strong
FBC. I don't know. As I said, the subject of FBCs stronger than the one
I've been using, is new to me.

Does anyone know which FBC-complying methods also meet Strong FBC?

An Intermediate FBC (various ones could be defined) would be about some
other kind of
 mild "protective measure" that a voter could take, such that, even if s/he
could
improve hir outcome by favorite-burial, s/he could also
improve it by that specific mild measure.

An Intermediate FBC that seems to describe the usual protective measure in
FBC methods is:

Suppose that there is a candidate, Worse, whom some
particular voter, V, would like to prevent from winning.
A method meets Intermediate FBC if it isn't possible to contrive a
configuration of additional candidates, other voters and
 their ballots, such that that V can prevent Worse from winning by voing
someone over hir favorite, and such that
it is not also possible for hir to keep Worse from winning by voting some
other candidate at 1st rank position (in addition
to hir favorite) and voting Worse alone at bottom.

[end of one tentative possible Intermediate FBC definiition]

The above definition is only tentative.

If I refer to "Intermediate FBC", in the singular, without "an" in front of
it, I'm referring to the above-defined version.

Of course it could be that these definitions of Strong and Intermediate FBC
don't act as intended, but right now it
appears that they probablly do (especially Strong, but maybe Intermediate
too).

If Intermediate FBC, as defined above, does act as it appears to, then I'd
say that all of the methods that I've been referring to
as meeting FBC, also meet Intermediate FBC.

Mike Ossipoff
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