Re: current A.6 draft
On Wed, Dec 04, 2002 at 06:32:26PM -0500, Andrew Pimlott wrote:
> (I only have time for a quick reply, and I haven't read any of the
> other recent discussion carefully.)
I think a lot of us are a bit busy. I know I keep intending to write
up another draft, but I've not completed it yet.
> > A defeats B by 4:1
> > B defeats D by 4:1
> > D defeats A by 4:3
> >
> > Because D is the default option 4:3 cannot be an instance of the weakest
> > defeat, so the weakest defeat is 4:1.
>
> Your draft says:
>
> c. A weakest defeat is a defeat that has no other defeat weaker
> than it. There may be more than one such defeat.
>
> In this example, none of the defeats has a defeat weaker than it.
> Therefore, they are all weakest defeats, are are eliminated. That
> is the problem I was pointing out.
I see what you mean.
Based on your earlier critique, I planned on changing 4.b. to read:
b. A defeat (A,X) is weaker than a defeat (B,Y) if A is not
the default option and V(A,X) is less than V(B,Y). Also,
(A,X) is weaker than (B,Y) A is not the default option and if
V(A,X) is equal to V(B,Y) and V(X,A) is greater than V(Y,B).
If A is the default option and B is not, (B,Y) is weaker than
(A,X).
Would that satisfy you?
> So is it: A defeat by the default is always stronger than a defeat
> by a real option?
Yes.
> > > It sounds like you're getting at something close to aj's
> > > proposal, in which any option defeated by the default option has no
> > > chance. If that's not what you mean to do, can you clarify the
> > > difference?
> >
> > That's exactly what I mean. The difference between this draft and aj's
> > earlier draft is that this characteristic of the default option doesn't
> > cause us to lose information where an otherwise significant option is
> > defeated by the default option.
>
> I see. However, this system (like aj's) still rewards the strategy
> of ranking the default option second, because a pairwise defeat by
> the default is effectively fatal. So it seems too prone to abuse
> for me.
That is the design intent of this system. The idea is that voters pick
which options are acceptable (these are the options which are ranked
above the default option), and that they rank the acceptable options --
the vote system is supposed to pick the most favored option.
> YAExample: sincere preferences are
>
> 3 ABD
> 2 BAD
>
> but voters vote strategically
>
> 3 ADB
> 2 BDA
>
> We are deadlocked.
D defeats B 3:2
A defeats B 3:2
A defeats D 3:2
A wins.
> To remind, I suggest that the defeat D>A be scored for weakness
> purposes as 2:3.
Why? No defeats need to be eliminated. B isn't even in the Schwartz set.
--
Raul
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