[EM] Demonstration that Approval doesn't pass our CC

[wclark at xoom.org]

Mike Ossipoff wrote:

> Sincere preferences:

> 40: ABC
> 25: BAC
> 35: CBA

> B is the CW.

> A possible set of sincere Approval ballots:

> 40: A
> 25: B
> 35: C

> The premise of our CC is complied with: There's a CW, and everyone is
> voting sincerely. But the CW doesn't win. So the requirement isn' t met.

You're entirely right.  I wasn't thinking clearly about what "preference"
meant (I had in mind something more like "voting a preference" or
"expressing a preference") and I also misinterpreted this definition:

> [ From http://www.electionmethods.org/evaluation.htm ]

>>A sincere vote is one with no falsified preferences or preferences
>>left unspecified when the election method allows them to be specified
>>(in addition to the preferences already specified).

For some reason, I thought this meant that either your example Approval
ballot wasn't sincere (by the above definition) because there were
preferences (in the common-sense meaning) that couldn't be specified -- or
that the sincere preferences you gave in your example weren't accurate
because only "expressed preferences" mattered.

Basically, I started off trying to extend the notion of "voted higher" as
applied to Approval (which was detailed in the MC section immediately
preceding the CC section on the same page) and then compounded my error by
misinterpreting the definition of "sincere vote."

> Approval doesn't pass our CC.

I completely agree.  Sorry for the confusion on my part.

> But yes, it would pass Blake's CC if he didn't stipulate that his CC
> only applies to rank methods.

I'm unfamiliar with Blake's version, and am curious why he would make that
stipulation if Approval would pass otherwise.  I've tried searching
through the archives (actually, on Google) for 'Blake "Condorcet
Criterion"' (and found a discussion between you and Blake Cretney that on
first glance raises some of the very same issues regarding the meaning of
"preference" as we've raised here) -- but nothing that looks like a
definition of a CC variant.  Would you be so kind as to provide a
reference?

As Alex Small pointed out, I was basically trying to reproduce the result
proven by Brams and Fishburn (though I'm unfamiliar with their results, as
well.)  Here is what Alex had to say about it:

> If all voters only have dichotomous preferences (i.e. each voter's
> SINCERE preferences sort the candidates into two groups, and the voter
> is indifferent among candidates in the same group) then there is always
> a Condorcet Winner, and approval voting always picks that candidate if
> all voters vote sincerely.

If preferences are restricted to those that can be expressed (as I was
unthinkingly assuming) then Approval would indeed meet CC.

However, as was explained on the electionmethods.org website, the whole
point is that Approval doesn't allow you to fully express your
preferences.  Restricting the notion of "preference" would just be
cheating.

-Bill Clark

-- 
Dennis Kucinich for President in 2004
http://kucinich.us/