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-
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