[EM] attempt of a grand compromise
Steve Eppley
seppley at alumni.caltech.edu
Fri Oct 15 09:13:32 PDT 2004
Hi,
Jobst wrote:
> Below is an attempt to formulate a compromise proposal
> which combines what I think are the most useful
> ingredients to a good Condorcet method.
-snip-
> The GOALS are:
-snip-
> 2. DEFEATS
> • Determine all defeats as usual.
> • Strength of defeat X>Y
> = number of voters which approve of X but not of Y
> (= number of voters which "strongly prefer X to Y")
-snip-
> PROPERTIES:
> Since step 3 uses the River method's technique to break
> cycles, we have immunity (implies Pareto efficiency,
> Majority criterion, Condorcet efficiency, Smith
> criterion, and Steve Eppley's strategy criteria),
-snip-
I'm not sure which "strategy criteria" Jobst credited me
with, but I suspect they're the ones for which I credit
Mike Ossipoff:
minimal defense, which is nearly the same as Mike's
"strong defensive strategy criterion" (SDSC).
non-drastic defense, which is nearly the same as
Mike's "weak defensive strategy criterion" (WDSC).
truncation resistance, which is nearly the same as
Mike's same-named "truncation resistance criterion".
Jobst's "immunity" is weaker than the "immunity from
majority complaints" defined in my web pages (linked
from <www.alumni.caltech.edu/~seppley>), which MAM
satisfies but River does not. Unfortunately I haven't
yet found time to discuss with him what might be the
best set of terms to name and describe these properties.
But being a weaker property, perhaps it would be better
to call his criterion "resistance to majority complaints"
rather than "immunity from majority complaints."
That would be in the same spirit as the use of
that word in the "truncation resistance" criterion.
Since the strength of pairwise "defeats" in Jobst's
proposed compromise method is determined by "approval"
rather than by preference, it's not obvious to me
that that method satisfies all the criteria Jobst
listed. Does it really satisfy either of the two
immunity criteria, for instance?
There's another "compromise" method that may be worth
comparing to Jobst's, which I wrote about long ago
when I defined the "sincere defense" criterion
(which is stronger than minimal defense and
Mike's SDSC.) My first impression of Jobst's
proposed compromise method is that it satisfies
sincere defense but that it would not be as robust
as the methods I wrote about (that also satisfy
minimal defense) in the case where a significant
number of voters know their sincere order of preference
but do not know where to strategically place the
dividing line. However, I think it would be simple
for Jobst to modify his new method to make it as
robust as the methods I wrote about that satisfy
sincere defense. That is, the size of the majority
that ranks x over y does not need to be ignored.
--Steve
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