[EM] Chris reply

Chris Benham chrisjbenham at optusnet.com.au
Thu Mar 15 08:47:47 PDT 2007

Michael Ossipoff wrote:

> Chris--
> You wrote: 

> 52: AC (offensive order-reversal)
> 100: BA
> 50: C/B 

A>C 152-50, C>B 102-100, B>A 150-52
Approvals: A152, C102, B100
Definite Majority set is {A}, so DMC, ASM, UncAOO elect A.
TACC elects C, WV and AWP elect B.

> You continued:
> Methods that meet Definite Majority (Ranking), interpreting all 
> candidates ranked above bottom or equal-bottom as approved, I believe
> meet your SFC when there are three candidates.
> I reply:
> Yes. That hadn’t occurred to me, and I’m surprised to find it out, but 
> it appears so, at least when the method is DMC. I don’t know if it 
> remains so with more candidates. 

I think all the DM(R) methods do with three candidates. DMC(R) seems to 
be more stubborn in this respect than ASM(R),
which definitely does fail SFC with four candidates.

49: A (sincere is A>B)
24: B>A
27: C>B>A (D is on the ballot, but gets no support)

B is the sincere CW. A>C>B>A, ABC>D. Approvals: A100, B51, C27, D0.
ASM(R) gives the order A>C>B>D. (DMC, AWP, WV elects B).

This could perhaps be fixed by eliminating the candidate bottom in the 
ASM(R) order, and repeating until one remains.
Here D would be eliminated, the 27 C>B>A>D voters would drop their 
approval of A and then the approval gap between
A and B would shrink to smaller (73-51=22) than that between B and C 
(51-27=24) so the new ASM(R) order
would be B>A>C. We eliminate C and then B wins.

> You continued:
> Regarding the above example, I can't see any justification in the 
> actual votes for suggesting that "majority rule" is violated by 
> electing A.
> All three candidates have a majority-strength defeat.
> I reply:
> Correct--they do. But electing A violates majority rule as I defined 
> it on EM:
> Majority rule is violated if we elect a candidate who has a majority 
> pair-wise defeat (PM) against him, and that PM is not in a cycle of 
> P.M.s none of which are weaker than it is.
> In the example, the B>A defeat is not in such a cycle, because the C>B 
> defeat is weaker than the B>A defeat.
> No one challenged that definition of majority rule violation. 

Probably those who noticed said nothing because they were too bemused or 
stunned at your attempt to highjack the
definition of such a popular 'motherhood' term/concept. The criterion 
you suggest might not be ridiculous, but needs
a more modest and original name. Maybe something like "Majority 
Beatpath" (MB)?

Like the "Beatpath Criterion" to me it looks too tailored, but looks at 
least reasonable/interesting for methods that only
collect rankings. For methods that collect both rankings and explicit 
approval information (allowing voters to rank among
unapproved candidates), I'm not impressed with any criterion that can 
insist we elect from outside the Definite Majority

I don't like methods that fail "Independence from Irrelevant Ballots" 
(IIB), and so I tend to economise on criteria/standards
that are vulnerable to that concept.

IIB says "If there is a losing candidate Y with fewer top or equal-top 
preferences than any other candidate and Y appears
above bottom or equal-bottom only on one or more ballots that plump for 
Y, then removing any or all of the Y-plumping
ballots must not change the winner".

So I don't like the idea that it is ok for X to win, but if we remove a 
few ballots that have nothing to say about any of the
remotely competitive candidates than suddenly X isn't allowed to win. Or 
to put it the other way, I don't like the idea that
Y is the winner on the nearly complete set of ballots but then we 
complete the set by adding a few ballots that bullet-vote
for a nobody that all the other ballots ignore and that changes the 
winner to X.

> You continued:
> In general election results IMO need to be justifiable on the 
> assumption that the votes are sincere and not just on some special 
> presumption
> that some of the votes are insincere.
> I reply:
> It isn’t realistic to assume that all votes are sincere. 

I didn't mean that we always should, just that the result can't be 
attacked purely on the presumption that some of the votes are insincere.
When I wrote that I wasn't aware that your "majority rule" referred to a 
specific criterion that referred to actual votes.

> It isn’t realistic to assume that all votes are sincere. If we could 
> assume that, then Plurality would always elect the most favorite 
> candidate, and many-level CR would always give, in some sense, the 
> greatest good for the greatest number.

I don't want to elect the "most favourite" candidate, and I think the 
claim about "many-level CR" is debatable because even if the
voters are trying to be sincere they are likely operating with different 
bench-marks and generally unsynchronised minds. It would
be different if they all agree that well-known figure A is much worse 
than well-known figure B and on what rating each should receive
and to rate the candidates proportionately on that scale.

> Remember that the reason for using a rank method is so that we can get 
> something more than what the Approval method guarantees--as much as I 
> like Approval. For me, as a voter, Approval would be fine. It’s the 
> other progressives who need a good rank method, because they tend to 
> have poor judgment about approving some sleazy crook known as a 
> Democrat lesser-evil. My concern is that they might keep doing the 
> same thing if we had the Approval method. Approval is still definitely 
> worth a try, because they might stop voting for the Democrat when they 
> notice that (say) Nader is outpolling the Republican. But a good rank 
> method homes in on the voter median immediately, instead of after a 
> few elections. And it isn’t proved that the LO2E progressives will 
> have the courage to ever stop voting for the Democrat. Those are the 
> reasons why I’d like a good rank method, as my first choice for our 
> public political elections. 

Without informed strategy Approval guarantees not much. Hopefully a set 
of democratic reforms that include a good rank method will
attract a lot of new voters with more courage and sense than your "LO2E 

Chris Benham

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