On Thu, May 9, 2013 at 8:14 AM, Kurt Roeckx <k...@roeckx.be> wrote:
> On Wed, May 08, 2013 at 10:28:26AM -0400, Michael Ossipoff wrote:
>>
>> 2 defecting B voters have stolen the election from 99 co-operative A voters.
>>
>> ----------------------------
>>
>> Here's another example in which the 3 factions are nearly equal in size:
>>
>> Sincere preferences:
>>
>> 33: A>B>>C
>> 32: B>A>>C
>> 34: C>>(A=B)
>>
>> Actual votes, when A voters co-operate and B voters defect:
>>
>> 33: A>B
>> 32: B
>> 34: C
>>
>> Again, though A is CW, B wins by defection.
>
> My understanding of this last example and how it works in Debian
> is that A defeats B, so B gets dropped. And A and C would be in
> the Schwartz set, and we would need a casting vote between A and C.
>
> Please correct me if I misunderstand this.
If the procedure were pure CSSD, with defeats measured by "winning
votes" (X's defeat of Y is measured by how many rank X over Y), then
here is what happens:
The set {A,B,C} doesn't contain a smaller unbeaten set (since those 3
beat eachother, so {A,B,C} is the Schwartz set. Drop the weakest
defeat in the Schwartz set. That's the A>B defeat, which measures only
33, by winning votes.
Now B is an unbeaten set. So {A,B,C} is no longer an innermost
unbeaten set, because it contains a smaller unbeaten set, namely {B}.
Now {B} is the only innermost unbeaten set--of course it doesn't
contain a smaller unbeaten set, so {B} is an innermost unbeaten set,
and is the only innermost unbeaten set. So {B} is now the Schwartz
set. The Schwartz set now contains no defeats, and so it's member, B,
wins.
Or, using Schulze's Beatpath implementation of the method, B's
strongest (and only) beatpath to C is a 65-strength defeat. B's
strongest (and only) beatpath to A contains,as its weakest defeat, C's
34-strength defeat of A. So the B to A beatpath has strength 34. No
one can have a beatpath to B stronger than 33, because that's the
strength of B's only defeat, by A. Therefore, B has a stronger
beatpath to A, and to C, than either can have to B. So B wins, by
Schulze's beatpath definition.
(CSSD and Beatpath are,of course, equivalent. Though Beatpath is more
neatly programmed, and more efficiently implemented, time-wise,
nevertheless CSSD has a more compelling definition, and that's why I
advocated it for the official definition of the procedure.)
But that's if pure CSSD is being used. If Debian has modified CSSD so
that it doesn't have the chicken dilemma, that would be of great
interest, because now, while meetng the Mutual Majoriy Critrerion, and
not havng a chicken dilemma, the method might retain some other
desirable properties of CSSD, such as Mono-Raise (also sometimes
called "Monotonicity". I prefer the name "Mono-Raise", because there
are a number of monotonicity criteria, of which Mono-Raise is only
one. Though IRV, Benham, Woodall, and Schwartz Woodall fail
Mono-Raise, all Condorcet methods, including CSSD, fail some
monotonicity criteria, such as Participation, Mono-Add-Top, and
Mono-Add-Unique-Top.).
Anyway, I'd better take another look at the Debian Constitution, at
the added modifications which could make my examples incorrect, if
Debian isn't using pure CSSD.
On to my reply to the other replies:
Ian Jackson <ijack...@chiark.greenend.org.uk>
Michael Ossipoff writes ("Norman Petry and I (Ossipoff) recommended
CSSD, but Schwartz Woodall is a better voting system for Debian"):
> Example 1:
>
> Sincere preferences:
>
> 99: A>B>>C
> 2: B>A>>C
> 100: C>>(A=B)
>
> The A voters rank sincerely, and the B voters defect:
>
> 99: A>B
> 2: B
> 3: C
[quote]
In Debian's system, this will result in A winning.
[/quote]
My apologies for that typo,. Instead of 3: C, I meant to write:
100: C.
so it shsould read:
99: A>B
2: B
100: C
That typo of mine is probably the explanation for why we got different results.
> Again, though A is CW, B wins by defection.
[quote]
However this seems quite a risky strategy by the B voters. The
situation seems contrived and unlikely to arise in practice.
[/quote]
But what if the B voters know for a fact that the A voters are
completely conscientious, responsible, and co-operative, and that the
A voters are sure to rank B over C?
Sure, I agree that there are a number of good reaons why the chicken
dilemma needn't be a problem. But, even if it isn't a full-fledged
problem, it remains a _nuisance_.
Some reasons why chicken dilemma isn't a major problem:
1. The B voters would lose the future support of the A voters,
temporarily at least--but maybe for long enough to make the defection
unprofitable. Maybe the A voters would never again support the B
voters' candidates
2. The A voters could use the Tit-For-Tat strategy: Co-operate or
defect as the B voters did in the most recent election. Eventually,
one side's Tit-For-Tat strategy will result in the system settling
into mutual co-opereation.
3. Strategic fractional rating (SFR). Forest Simmons proposed SFR for
use in Score voting, the points system, or for use, probabilistically,
in Approval voting. But it could probably be done in CSSD as well: The
A voters could rank B with a probability less than unity, maybe by
drawing a number from a bag, to randomize their decision of whether to
rank B. They could, in their best judgment, guess a probability that
would save B from C only if B's faction is bigger than the A faction.
If the B faction is smaller, then the B voters had better have
similarly supported A. Of course it's impossible to accurately
calculate what that probability of ranking B should be. It's just a
guess. But the B voters don't have a better guess, and, for all they
know, their defection could very well elect C, given the A voters'
mere fractional support of B.
4. In public elections (but probably not in organizational elections)
it would be impossible to organize a large-scale defection without the
A voterss hearing about it.
There was a 5th reason, but I don't remember what it was.
------------------------------------
Reason # 1 doesn't count if the current election is particularly
important, and the B voters don't care so much about subsequent ones.
Likewise reasonn #2
#3 requires work, guesswork, and probabilistic, all of which is a
nuisance to have to deal with.
#4 probably doesn't apply to organizational voting.
In summary, the chicken dilemma remains a distinct nuisance. Nuisances
should be avoided if possible. CSSD/Beatpath has the chicken dilemma
nuisance. Benham, Woodall, and Schwartz Woodall don't have that
nuisance. Their Mutual Majority Criterion compliance, and Condorcet
Criterion compliance are therefore, un-marred, and fully operative,
bring unmatched, unequalled freedom from strategy, especially for
members of a mutual majority.
Continuing my replies to the posts:
Kurt Roeckx <k...@roeckx.be>
[quote]
I think we shoud drop both both B and A because they are both
defeated by 1. And C would be the winner.
[/quote]
Yes, but aren't defeat-strengths measured by "winning votes",where the
strength of the X>Y defeat is measured by the number of ballots
ranking X over Y?
You're speaking of "margins" as the measure of defeat-strength.
It's true that if CSSD used margins, it would be _somewhat_ more
resistant to the chicken dilemma, but still not immune to it.
But then voting theorists could criticize it for failing the
Pluralitly Criterion:
Y shouldn't win if (for some X) more ballots vote X at top than vote Y
above bottom.
CSSD (winning votes), IRV, Benham, Woodall, and Schwartz Woodall meet
the Plurality Criterion,
but CSSD(margins) fails it.
Well, I don't know how much _practical strategic_ importance the
Plurality Criterion has. But I can tell you that even
CSSD(margins) retains the chicken dilemma, just not as frequent as
that of CSSD(winning votes)
Michael Ossipoff
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