[EM] "FBC vs Condorcet's Criterion"

[Michael Ossipoff]

On 05/08/2012 08:46 PM, Michael Ossipoff wrote:
> Since Richard wants to make a "which one wins" comparison between FBC 
> and Condorcet's Criterion (CC), then I'll remind him that, when FBC 
> failure sufficiently makes its problem, CC compiance becomes quite 
> meaningless and valueless. And there is good reason to believe, as 
> described in my previous post, that Condorcet's FBC failure _will_ 
> fully make its problem in our public elections.

Kristofer:

You wrote:

I'll get to your larger post later, but it seems what need isn't FBC as
such, but rather u/a FBC.

[endquote]

You're referring to a requirement that FBC not be violated in a u/a
election.

But does the requirement only apply if _everyone_ regards it as u/a?

And of course they can't all agree on what's acceptable and unacceptable, or
nothing unacceptable could win, and that would
Prevent it from being a u/a election--an election in which there are
unacceptable candidates who might win.

One could consider writing it so that it applies only if the criterion
failure-example writer considers it a u/a election.

I'm interested in alternative versions, strengthenings and weakenings, of
FBC.  That's why I posted a definition for Strong FBC.
I posted one for Intermediate FBC too, but, later, it seemed to me, and
still does, that "Intermediate FBC" would be better
named "Specific Simple Compromise Strategy" (SSCS). I don't suppose that it
would be of interest to any of us. It was an effort to
say something about exactly what it would take to make Compromise beat
Worse.   ...after you'd commented on that matter.

Approval, and almost surely ABucklin, in all of its versions, meets SSCS. I
don't know if pairwise-count methods can meet it.

Anyway, because I consider all of our public elections to be u/a, then an
FBC that only applies in u/a elections is of interest. Maybe
such a weakening of FBC could be acceptable, while still compatible with
criteria important to some voting system reform advocates.. I don't know,
because of course the
idea of a u/a FBC is completely new to me. But it's definitely of interest
if there could be a good enough FBC version that wouldn't
be incompatible with criteria important to some voting system reform
advocates.

If enough people, all of the ones who agree with me about something
important, don't agree on what's acceptable and what isn't, that can be a
problem.

There was once a book entitled _I've Been Down So Long, It Looks Like Up To
Me_. 

Many voters, probably a very large proportion of them, are like that, in
their judgment of what is acceptable.

I don't know how such disagreements would affect the possibility of a u/a
FBC.

Mike Ossipoff




Here's a Condorcet method I think meets u/a FBC: Each voter submits a ranked
ballot with an Approval cutoff. The most Approved candidate in the Smith set
wins.

If everybody ranks Approval style, then this becomes Approval. So let's see
if there's any reason to favorite betray instead of ranking Approval style.

If there is no cycle, then you can't make an acceptable have a greater
chance of winning over an unacceptable by ranking Compromise over Favorite
versus ranking Favorite over Compromise.

If there's a cycle and Favorite is in the Smith set, but Compromise is not,
then the only reason for getting Compromise into the Smith set would be to
defend against an unacceptable candidate winning. However, you can do that
by just voting Approval style. Since Smith set members are "only beaten by
other Smith set members", Favorite vs Compromise doesn't enter into it as
long as you put both above the cutoff and all the unacceptables below it.

If there's a cycle and Compromise is in the Smith set, but Favorite is not,
then because this is an u/a election, it doesn't matter. You'll still get an
acceptable.

If there's a cycle and neither Compromise nor Favorite is in the Smith set,
then voting Approval style will make Compromise and Favorite both maximally
work to push the unacceptables out of the Smith set.

Hence it seems that the method above meets u/a FBC. By the time people get
past u/a, they'll no longer be overcompromising and so "proper" FBC failure
doesn't matter. So Condorcet can meet u/a FBC.

I'm not saying Smith,Approval is necessarily a good method, but I only have
to show a single method to disprove that u/a FBC and Condorcet is
incompatible.