Re: current A.6 draft

[Andrew Pimlott <andrew@pimlott.net>]

(I only have time for a quick reply, and I haven't read any of the
other recent discussion carefully.)

On Fri, Nov 29, 2002 at 11:48:53AM -0500, Raul Miller wrote:
> A has a 2:1 supermajority requirement, B has no special majority
> requirement, D is the default option, votes are
> 3 ABD
> 1 BDA
> 1 DBA
> 
> 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.

So is it:  A defeat by the default is always stronger than a defeat
by a real option?

> > 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.

YAExample: sincere preferences are

    3   ABD
    2   BAD

but voters vote strategically

    3   ADB
    2   BDA

We are deadlocked.

To remind, I suggest that the defeat D>A be scored for weakness
purposes as 2:3.  In this case, if the A voters truncate[1]

    3   A
    2   BDA

then

    D>A 2:3
    A>B 3:2
    B>D 2:0

and A wins.  Although A has escaped its supermajority requirement, I
find this a lesser evil.

Andrew

[1] From http://www.electionmethods.org/evaluation.htm, in
Condorcet/CSSD,

    "a majority never needs any more than truncation strategy to
    defeat a particular candidate, even when countering offensive
    order reversal by that candidate's voters."

I haven't verified that this is true of my proposed system, but I
believe it is.