Michael Ossipoff mikeo2106 at msn.com
Tue Mar 13 16:22:24 PDT 2007

```Chris--

You wrote:

Mike,
Does this compromising "one C voter" have to unapprove C?

No.

Referring to this example,

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

You continued:

A>C>B>A. Approvals: A152, C102, B100. A>C 152-50, C>B 102-100, B>A 150-52
DMC and ASM elect A.

You continued:

Here if one C|B changes to B|C

It doesn’t matter if it’s B/C or BC, because, as I said, the approval votes
don’t come into play, because there’s already an unbeaten candidate, B, who
therefore wins.

You continued:

then DMC just becomes indecisive with B and C on the same approval score and
pairwise tied.

Pairwise tied, yes. Indecisive, no. B wins because B is the only unbeaten
candidate. According to DMC’s rules, B wins.

If the C voters vote BC, approving both, then, as you said, they make a
pair-wise tie between B and C. B beats A and pair-ties C. B wins as the only
unbeaten candidate. The Approval scores don’t come into play, because there
already is an unbeaten candidate. At least that’s how I understood the rules
of DMC: If no one is unbeaten, repeatedly eliminate the least-approved
candidate till someone is unbeaten.

If I’ve misunderstood DMC’s rules, tell me the correct DMC rules.

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.

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 don’t know if that could sometimes cause the letter of my criteria to
violate the intent of my criteria, when rankings are counted in that way. If
so, then a stronger definition of voting X over Y could be useful.

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.

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.

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.

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. And IRV voters would happily let their last choice win
instead of the CW, when IRV decides to do that.
(One IRVist, when backed into a corner, actually told me that a voter
doesn’t want his second choice to win instead of his last choice, if the
second choice is favorite to fewer voters).

We can write demonstration examples in which some ballots are insincere, to
demonstrate how that effects the outcome.

You continued:

In the example, given that a concept of approval is being used, I can't see
how any post-election complaint
that the most approved candidate should have been defeated by the least
approved would be taken seriously.

Perhaps you’re trying to give the concept of Approval a bad name.

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.

I’m making a _pre_-election complaint about any rank method that doesn’t
deliver the guarantee that justifies rank-balloting. I’d like voters to feel
free to rank freely, without regard to strategy, under the plausible
conditions for which that can be guaranteed. SFC describes such conditions.
There are methods that comply. If you’re considering a rank method that
doesn’t, then it doesn’t significantly improve on Approval, and then I’d
recommend just proposing Approval instead. Approval is at least as good, and
a lot more briefly-defined.

Mike Ossipoff

```