Re: Norman Petry and I (Ossipoff) recommended CSSD, but Schwartz Woodall is a better voting system for Debian
On Thu, May 9, 2013 at 4:30 PM, Kurt Roeckx <kurt@roeckx.be> wrote:
> On Wed, May 08, 2013 at 10:28:26AM -0400, Michael Ossipoff wrote:
>>
>> Below, I'll show examples of what can happen, but first I'll just
>> verbally summarize what can happen: First of all, of course A is the
>> CW. A is the "sincere CW". In comparison to each of the other
>> candidates, more people prefer A to the other candidate than
>> vice-versa. A should win, and would win in CSSD, or any Condorcet
>> method, under sincere voting.
>
> So my understanding of things is that for your first 2 examples,
> voters for B being dishonest resulted in C winning
In CSSD, as defined in the Debian Constitution (and as I define it
too), but disregarding the default alternative, D, and disregarding
the local or per-option quota, R, B would win, by defection in all 3
of my examples (when my first example is corrected to "100: C",
instead of "3: C".
When I posted my examples, I didn't know about D or R.
II understand that, before the CSSD count is done, any option X that
loses to D (more people rank D over X than X over D) is dropped. And,
likewise, any option that isn't ranked over D by some specified
number, R, of people is dropped.
I want to add that I can't find any rule for choosing the numerical value of R.
If my conclusion that B wins in my examples is wrong, due to my
disregard of D and R, and if really the Debian procedure is more
defection-resistant than I thought, then I apologize for my
mis-statements.
I'm going to re-work my examples, this time taking into account the D
alternative and the local quota, R. Obviously I have to do that before
I make any more statements about what would happen in my examples.
But at the end of your post, you said something to the effect that,
when D is taken into account, where A>B>>C is (correctly, in my
opinion) interpreted as A>B>D>C, then the defection works perfectly,
and elects B every time, just as I said it would in my examples.
Likewise for the 3rd example too.
> So either our system doesn't work like you think it does, or you
> need to fix your examples.
I'll re-work my examples with D and R. But didn't you agree with me,
about B winning, in your concluding statements in your post?
>
>> In the example-tables below, the number on the left,on each line, is
>> the number of voters who have the preferences stated on that line, or
>> who vote the rankings stated on that line. "A>B>C" indicates
>> preference for A over B, and for B over C. ...or a ranking of A over
>> B, and B over C. ">>" indicates a much stronger preference.
>
> Note that we always have a default option too, let's call that D.
> This can be used to indicate if you think an option is acceptable
> or not, and the majority of the voters need to say they find that
> option acceptable or not. I'm going to assume that with the ">>"
> you mean that the other option is not acceptable.
Yes, I agree with that interpretation.
> But if you then look at the result, assuming a simple 1:1 majority
> requirement, you see that:
> A>D: 99, D>A: 101, A is dropped because it didn't reach majority
> B>D: 101, D>B: 99, B is kept
> C>D: 99, D>C: 101: C is dropped
>
> So suddenly B wins, because it's the only one that reaches
> majority requirements.
Yes, and so, even though I mistakenly disregarded D, and the
requirements that go with it it remains true that B wins, and that the
B voters' defection has successfully stolen the election from A.
>
>> 2 defecting B voters have stolen the election from 99 co-operative A voters.
>>
>> ----------------------------
>>
:
> 33: A>B>D>C
> 32: B>A>D>C
> 34: C>D>(A=B)
>
34: C
>
> And:
> 33: A>B>D>C
> 32: B>D>(A=C)
> 34: C>D>(A=B)
>
> A>D: 33, D>A: 66, A is dropped
> B>D: 65, D>B: 34, B is kept
> C>D: 34, D>C: 65, C is dropped
>
> B is the winner again
Again, the B voters' defection succeeds in electing B.
>
> 26: A>B>D>C
> 25: B>D>(A=C)
> 49: C>D>(A=B)
>
> A>D: 26, D>A: 74, A is dropped
> B>D: 51, D>B: 49: B is kept
> C>D: 49, D<C: 51: C is dropped
>
> B is again the winner
We don't reallly disagree, then. We agree that, with the present
system, the B voters' defection, in those examples, will elect B,
stealing the election from A.
Then that's why I propose that Schwartz Woodall would be a better
voting system for Debian, because Schwarz Woodall doesn't have a
chicken dilemma. That means that the Mutual Majority Criterion is
fully in force. It means that a mutual majority truly have no need to
do other than rank sincerely, to ensure that one of their
mutual-majority-preferred options will win. ...and they can achieve
that even while freely choosing among their MM-preferred options, by
ranking them sincerely.
In CSSD, the chicken dilemma can spoil and disband a mutual majority.
I recommend Schwartz Woodall for Debian voting.
>
> So there clearly is a problem because of the majority requirement,
> and by marking something not acceptable even when it is, it could
> results in an other option winning that what should have won.
>
> Can you make your suggestions again, taking the above into
> account?
My best recommendation is Schwartz Woodall. Let me re-write its definition here:
Do IRV till only one member of the initial Schwartz set remains
un-eliminated. Elect hir.
[end of Schwartz Woodall definition]
Definition of IRV:
Repeatedly, delete from the rankings the candidate who currently tops
the fewest rankings.
(In ordinary pure IRV, of course the winner would be the last
remaining un-deleted candidate)
[end of IRV definition]
I'm going to look at some examples, this time taking D and R into
account, to find out if the provisions about D and R could spoil any
of Schwartz Woodall's good properties. Voss acknowledged that those D
provisions can spoil some of CSSD's desirable properties. So it's
worth checking if those D provisions would do any harm to Schwartz
Woodall's desirable properties.
I'll post what I find out.
By the way, I'd like to parenthetically add here that, though we all
recommended winning-votes, as opposed to margins, as the way to
compare the magnitude of pairwise defeats, I now prefer margins to
winning votes.
Winning votes says that X>Y is stronger than A>B if:
...V(X,Y) > V(A,B)
Margins says that X>Y is stronger than A>B if:
V(X,Y)-V(Y,X) > V(A,B) - V(B,A)
...where V(X,Y) is the number of voters ranking X over Y.
Here's why I now prefer margins to winning-votes:
We all formerly preferred winning-votes to margins because
winning-votes is a litle more resistant to Condorcet offensive
stratgegy against a CW. A majority's wishes are somewhat better
protected against offensive order-reversal or truncation against a
Condorcet winner (CW).
But note that, if that majority is a _mutual_ majority, then the
winner must come from their mutual majority preferred set if the
members of that mutual majority rank sincerely. Condorcet offensive
strategy can't cheat them out of that.
...but the chicken dilemma can.
The chicken dilemma can disrupt and disband a mutua majority. The
chicken dilemma can make Mutual Majority Criterion compliance
meaningless. It can make Condorcet Criterion compliance meaningless.
Because Condorcet offensive strategy can't take the win from a
sincere-voting mutual majority, but the chicken dilemma can spoil a
mutual majority, therefore I say that the chicken dilemma is worse
than Condorcet offensive strategy.
Though winning-votes is a little better about Condorcet Offensive
strategy, margins is considerably more resistant to the chicken
dilemma.
Let me state some numerical facts in that regard:
In the A, B, C chicken dilemma example, in order for B's defection to
succeed in margins CSSD:
(where A, B, and C stand for the numerical size of the A, B, and C factions)
C must not be as much as twice B.
A must not be as much as 3/2 times B.
C must exceed A by an amount at least as great as the difference
between A and B.
-----------------------------------
Yes, Margins CSSD still has the chicken dilemma, but not in the
all-out, wide-open way that Winning-Votes CSSD does.
Margins CSSD gives B defectors more to reconsider about before
defecting, as compared to Winning-Votes CSSD.
Now, Margins CSSD fails the Plurality Criterion, as I've previously
mentioned. I'll re-define it below:
Y shouldn't win if, for some X, more voters vote X at top than vote Y
above bottom.
[end of Plurality Criterion definition]
Maybe Plurality-Criterion failure would bring enough criticism
vulnerability to disquailfy Margins CSSD from consideration as a
public proposal for official government elections. That's ok, because
i don't think that CSSD qualifies for governement elections under
current conditions anyway, because it fails FBC (It can give incentive
to bury one's favorite, for voters who have been seriously deceived by
disinformational media that claim that only the Democrat or
Republican can win).
But, other than its criticism vulnerability as a proposal for
government elections, I don't find Plurality-Criterion-failure to be a
problem.
It doesn't bring any practical strategy problem. It's purely an
"embarrassment criterion", without strategic importance.
So it seems to me that, for Debian, Margins CSSD would be better than
Winning-Votes CSSD, in spite of its failing the Plurality Criterion.
--------------------------------------------------
But Schwartz Woodall would be a lot better than _either_ CSSD version,
because Schwartz Woodall doesn't have the chicken dilemma at all.
Yes, Schwartz Woodall fails Mono-Raise (often referred to as the
Monotonicity Criterion)
(I prefer the name "Mono-Raise",because Mono-Raise is only one of
several monotonicity criteria)
But lest we take too seriously Schwartz Woodall's failure of
Mono-Raise, I poinit out that CSSD, in both versions, fails several
other monotoniity criteria:
Participation, Mono-Add-Top, and Mono-Add-Unique Top.
Let me define those criteria here:
Participation:
Say X wins the election. Now we add a new ballot that votes X over Y.
The addition of that new ballot shouldn't change the winner from X to
Y.
[end of Participation definition]
All Condorcet methods, including CSSD and Schwartz Woodall, fail Participation.
Mono-Add-Top:
A ballot vote a candidate at top if it doesn't vote anyone over hir,
and votes hir over someone.
Say X wins the election. Now we add a ballot that votes X at top. The
addition of that new ballot shouldn't cause X to lose.
[end of Mono-Add-Top definition]
All Condorcet methods, including CSSD and Schwartz Woodall, fail Mono-Add-Top.
Mono-Add-Unique Top:
Say X wins the election. Now we add a ballot that votes X over all of
the other candidates. The addition of that new ballot shouldn't make X
lose.
[end of Mono-Add-Unique-Top definition]
All Condorcet methods, including CSSD and Schwartz Woodall, fail
Mono-Add-Unique-Top.
So lets not take too seriously the criticism of Schwartz Woodall
failing Mono-Raise, when all Condorcet methods, including CSSD, fail
several monotonicity criteria.
------------------------------------------------------
Comparing Schwartz Woodall to Margins CSSD:
Schwartz Woodall's failure of Mono-Raise is probably less of an
embarrassment than Margins CSSD's failure of the Plurality Critrerion.
In any case, Mono-Raise is nothing but an embarrassment criterion,
with no practical strategic importance.
In contradistinction, the chicken dilemma is a strategy problem. And
it's an unnecessary strategy problem, because methods like Schwartz
Woodall can avoid it.
So I claim that Schwartz Woodall would be the best voting system for Debian.
Michael Ossipoff
>
>
> Kurt
>
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