[EM] u/a for criteria. u/a FBC. Voter's Choice. SSCS. Strong FBC.

[Michael Ossipoff]

Kristofer:


On 05/11/2012 11:31 PM, Michael Ossipoff wrote:


> Of course the way to define u/a for criteria would be in terms of votes.
> A definition of u/a for criteria:

> In a critrerion failure-example, an election is u/a for some 
> particular voter V iff:

> The candidates can be divided into two sets, A and B, such that V 
> votes all of the candidates in A over all of the candidates in B, and 
> doesn't vote a preference within A or B unless the failure-example 
> critrerion-writer can prove conclusively that it isn't possible to 
> contive a configuration of ballots other than that of V, such that:

> .....V, by voting that particular preference within A or B, causes the 
> winner to come from set B, where the winner would have come from set A 
> if V hadn't voted

> .....that paraticular preference within A or B.

> [end of definition of u/a for criteria]

> An election is All-u/a if it is u/a for every voter in that election.

> [end of All-u/a definition]

> A tentative definition of u/a FBC:
> In an All-u/a election, FBC should never be violated.
> [end of tentative definition of u/a FBC]

You wrote:

This seems reasonable enough. It's also less strict than my attempt at
formulating an u/a FBC criterion, because my attempt only considered one
voter (the last voter) as being u/a.

[endquote]

Maybe your approach is more workable: There shouldn't be an FBC failure for
someone for whom the election is u/a.  That might be better and more usable.


You wrote (as a tentative possibility):

- An incentive criterion X is passed if for every situation where a voter
might want to do an action defined by X to make A win/make all but Z win,
there instead exists some other action that is at least as effective and
doesn't fall within the set of actions guarded by X.

[endquote]

That's like what FBC says. It shouldn't be, for any voter, that by burying
hir favorite, s/he can get a better outcome than she could get without
burying hir favorite.

You're describing it more generally, but FBC is a special case of what
you're saying. One difference is that FBC doesn't say anything about the
details of that better outcome, what it consists of.

SSCS, which I initially called "Intermediate FBC" is more specific about the
goal, and also about the method that should achieve it. SSCS stands for
Specific Simple Compromise Strategy. 

FBC and Strong FBC aren't as specific about the required result or the
strategy needed to get it.

You wrote:

- With respect to some incentive criterion X, a voter V's ballot is u/a if
that voter has an internal division of the candidates into sets A and B, and
votes all A-set members ahead of all B-set members but doesn't rank within
each set unless that's the only way to get the strategic benefit without
violating the criterion.

[endquote]

It's difficult to generalize with these criteria, because different ones
take different approaches. But I'd say, about V ranking within one of the
sets, that s/he must not do so unless it is proved that there no possible
configuration of other voters' votes such that doing so would make the
winner come from set B. That should be the requirement for V's ballot being
u/a (consistent with the election being u/a for V).

You wrote:

- With respect to some incentive criterion X, an election is u/a if all
voters' ballots are u/a.

[endquote]

Yes, but maybe (probably) your approach, of just requiring FBC to not be
violated for a voter to whom It's a u/a election, is better for making a
usable critrerion.

You wrote:

But if the voters truly vote all A-set members equal, who's the favorite
they have to not betray in u/a FBC?

[endquote]

When I was speaking of the election being u/a for everyone, I meant for the
voters' divisions of the candidates into sets A and B to not necessarily be
the same. Could be, or could be different for all. (anyway, saying it the
way you did is probably better than stipulating that the election is u/a for
everyone)

For all or most rank methods, the best strategy in a u/a election is to
top-rank all of the acceptables, but the criterion doesn't go into specifics
like that.

But for the FBC compliance part of the criterion, FBC failure is found if
there is even _one_ voter who needs favorite burial for hir best outcome. So
the criterion would only be talking about one voter in regards to FBC.

You wrote:

 Is it "never vote a B-member above an A-member"

[endquote]

You certainly would never do that of course, but the requirement for it
being u/a for voter V should just be that V doesn't vote a preference within
one of the sets unless it can be proven that doing so can't make the winner
come from B, where the winner wouldn't have otherwise come from B.

You asked:

, or does each voter have a hidden "favorite" above whom they have to rank
nobody, not even a Compromise from the A-set?

Yes.

The assumption is that every voter has a single favorite, and the
requirement is that no voter should never need to rank anyone over hir
favorite in order to gain hir best outcome.

> To questions suggest themselves:
> 1. Does compiance with u/a FBC guarantee that there won't be a 
> societally-damaging favorite-burial incentive?

As I've said, it would probably be like clone independence. The benefit
tapers off the less u/a-like the election is but you would get some general
resistance.

[endquote]

I've just begun to look at the possibility of a u/a FBC, and I haven't
gotten far with it at all. I still don't know how it will turn out, or
exactly what its compliance would promise.
And, as I said, it might be better to say, as you did, that FBC must not be
violated for a voter for whom the election is u/a.   ...instead of saying,
as I did, that FBC shouldn't be violated if the election is u/a for
everyone. 

Both approaches would have to be tried, to see which one yields a useful
criterion.

> 2. Do Smith-Approval and Smith-Top meet u/a FBC?

I doubt Smith-Top (or in my terms, Smith,Plurality) meets it. The sketch
would be like this: set up an election where every candidate is in the Smith
set. Then you might need to rank Compromise first for the same
vote-splitting reasons as in ordinary Plurality-

[endquote]

Now that you mention that, it does look that way. 

Mike Ossipoff