[EM] New Criterion: The Co-operation/Defection Criterion

[MIKE OSSIPOFF]

Kevin--
 
You wrote:


I see this criterion in effect:

If some candidate A has simple pairwise wins over every candidate in
a set of candidates "B"...
 
[endquote]
 
There is only one candidate B. It would be nice if {A,B} could be replaced
with a larger set of candidates, but the crierion would then probably be
unattainable.
 
You continued:
 
 and has no majority pairwise losses to any
candidate in a set of candidates "C", and every candidate in the set
"C" has a majority pairwise loss to every candidate in set "B," then
candidate A must win.

If it wasn't already clear, this definitely won't be compatible with
the Plurality criterion. I know that won't bother you though.

[endquote]
 
True.

You wrote:
 
As far as methods that will satisfy it, we at least have some clumsy 
ones. Any Condorcet method used to complete majority-defeat-
disqualification or CDTT (i.e. Schwartz set that replaces sub-majority
wins with ties) will do the trick. These methods would also satisfy
SDSC fully.

[endquote]
 
Worth checking out. But, even if you're correct about that, how many of those methods
meet FBC?
 
Can those methods be shown to meet CD?  Of course, the burden of proof, in the 
form of a failure example, is on the person claiming that they don't.  ...because it's
often easier to show noncompliance than compliance. But even so, what method other
than MMPO can be shown to meet CD?
 
 
You wrote:
 
I am not sure that MMPO as you propose it actually does the trick.
It seems to depend on the A-B tied score which I'm not sure is 

[endquote]
 
The A-B tie is sure thing. It's obviously a sure thing if there is only one non {A,B} 
candidate.
 
But, to preserve CD's similarity to the 3-candidate Approval bad-example, and CD's
 ability to disitinguish between methods, when there are more than
one non {A,B} candidates, I said, in the criterion premise:
 
"A majority prefer A and B to all the other candidates, and the rest of the voters prefer all
the other candidates to A and B."
 
So, A and B can't not be tied.
 
As I was saying, I wanted to generalize the Approval bad-example as much as possible, while
keeping it CD similar enough to the example to preserve the method-distinctions made by the
example. i wanted to generalize it, in terms of numbers of candidates, as much as possible, while
still having a criterion that makes a disinction between methods.
 
 
 
 
You wrote:
 
 
...guaranteed. Particularly if "C" is multiple candidates.

It is guaranteed by CD's premise, as described above.
 
However, if {A,B} were replaced with a larger candidate-set, probably no method could 
meet CD.
 
 
 
Jameson Quinn wrote:


My point is that there's no way to distinguish those honest preferences,
from the honest preferences which do meet the criterion (that is, as voted
except for B is really B>A).

[endquote]
 
 
Do you mean that there's no way, in real life, to prove which voted preferences are
sincere? Of course not.
 
But CD, and the Approval bad-example, are about a situation where a majority prefere A and B
to all the other candidates. That's what CD and the Approval bad-example are about. So that's
stipulated in CD's premise.

 
I'd said:

> In your example, C is the Condorcet candidate, and A is the sincere
> Condorcet
> loser. Your example has zero voters preferring A and B to C.
>
> CD's premise stipulates that A is the Condorcet candidate and that there is
> a
> majority who prefer A and B to everyone else.
>
> So CD says nothing about what should happen, who should win, in that
> example.
>


You wrote:
 
Yes it does, because as far as it can tell, those votes could come from
honest preferences which fall under the criterion.
 
[endquote]
 
 
CD has a premise, and in that premise are certain stipultions, including stipulations
about sincere preferences and sincere voting.
 
A criterion only says what should or shouldnd't happen, when its premise is satisfied.
A criterion is about situations that meet its premise. It says something that should or
shouldn't happen when that premise is satisfied.
 
Your sincere preferences that you specified to not satisfy CD's premise, and therefore
CD says nothing about what should happen when those are the sincere preferences.
 
> Moreover, even without this loophole, I just don't like how that first
> election looks.
>
> What first election? Are you referring to your voted ballots?
>

You write:
 
Yes. What I meant was, even if those voted ballots reflect sincere
preferences which meet the criterion, I would not be at all sure that A is
the correct winner, as the criterion says they must be.
 
[endquote]
 
 
You didn't say those were the sincere rankings. You said that _another_ set of rankings
were the sincere rankings. Do you want, in your example, to say that your voted rankings 
are the sincere rankings, that everyone is ranking sincerely? That violates a stipulation
listed in CD's premise, making CD not apply to your example.
 
 
 



> just can't imagine trying to convince people that that's the right answer.
> If there were more than three people in the room, you wouldn't get 5 words
> out before they started laughing and interrupting you with sarcasm.
>
> [endquote]
>
> You're saying that people will reject any voting system that doesn't uphold
> Plurality's standard. If you're right, then we can forget about replacing
> Plurality.
>

You write:

No, I'm saying that if you overrule plurality, you should at least have some
plausible reason to do so; and "plausible" implies, for instance, one that
doesn't rely on inferring preferences which are not visible in the voted
ballots.
 
[endquote]
 
 
Sincere preferences are never visible in the voted ballots.
 
CD doesn't infer them. It stipulates them in its premise.