[EM] Re: IMHO, IRV superior to Approval

[wclark at xoom.org]

Chris Benham wrote:

> This is the bit [Adam Tarr] (and Bill Clark) apparently did't read:

>>> For my demonstration, I am assuming that the voters know nothing
>>> but their own sincere ratings of all the candidates on the ballot,
>>> and that in that situation they all use the best "strategy" of
>>> approving all the candidates they rate above average, and no
>>> others.

Sorry about that.  You're correct, I missed that.

Bill Clark wrote:

>>Is the Blake Cretney definition only meant for rank methods?  A and X
>>don't seem to satisfy the "spirit" of what it means to be a clone, since
>>they basically have nothing in common -- not even whether they're voted
>>the same way by even a single voter.

Chris Benham replied:

> Clones do not have a  "spirit", only a definition.

I disagree.  While we can only MAKE USE of a formal definition (if we wish
to obtain objective results) the whole point of the definition in the
first place is to capture a certain intuitive and informal notion.

In any event, I hadn't actually read Blake Cretney's definition of a
clone, and had simply inferred from previous posts that it went something
like this:

(Def I:) A and X are clones iff they appear adjacent to each other on
every voter's ranking of sincere preferences.

I was complaining that (I) didn't seem to capture the intuitive notion of
"clone" (because adjacent ranking doesn't necessarily imply similar
rating, as your example demonstrated.)

However, I also question whether (I) is relevant to non-rank methods, at
all.  Whether A and X are approved or disapproved -- or even if they're
voted the same or different -- has absolutely no correlation to their
relative positions in a sincere ranking of preferences.  What I'm saying
is that (I) is a worthless definition, when applied to non-rank methods.

...but (I) isn't Blake Cretney's definition.  THAT can be found here (or
by following the link on the Election Methods page at Electorama.com:)

http://condorcet.org/emr/defn.shtml

It states:

(Def II:) A set of alternatives, X[1], X[2], .. X[m] is a clone set
provided that for every alternative Z, where Z is not one of X[1], ..
X[m], the following is true: Every ballot that ranks Z higher than one of
X[1] .. X[m] ranks Z higher than all of them.  Every ballot that ranks Z
lower than one of them, ranks Z lower than all of them.  No ballot ranks Z
equal to any of them.  As well, there must be at least one alternative
outside the set of clones, and at least two alternatives in the set of
clones.

This definition talks only of ballots and not of sincere preference
rankings, so with regards to Approval the definition is equivalent to:

(Def III:) A and X are clones iff they are both voted the same way, and
all other options are voted the opposite way, on ALL ballots.

(II) says that A, X are a clone set provided that for every alternative Z,
if Z is approved and A is not, then X is not.  Also, if Z is disapproved
and A is approved, then so is X.  If A/X are approved, then Z must not be
(and if A/X are disapproved, Z must be approved.)  Since Z can be ANY
alternative to A or X, this implies that EVERY alternative must be voted
the same -- i.e. opposite to A/X.

I'm not sure (III) (or by extension, II) is a very good definition for
"clone" under Approval, either.  I'd argue that this would work best:

(Def IV:) A and X are clones under Approval if they are both voted the
same way (i.e. either both approved or both disapproved) on ALL ballots.

In any case, under II/III or IV, your Approval example no longer seems to
hold.

-wclark

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