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

[Kristofer Munsterhjelm]

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]

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.

So let's see if I got this right:

- 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.

- 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.

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

- A method passes u/a X if every election that is u/a also passes X.

But if the voters truly vote all A-set members equal, who's the favorite 
they have to not betray in u/a FBC? Is it "never vote a B-member above 
an A-member", or does each voter have a hidden "favorite" above whom 
they have to rank nobody, not even a Compromise from the A-set?

> 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.

> 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-