[EM] IRV vs Condorcet vs Range/Score

[Chris Benham]

>CB: Not necessarily, no. I have in mind something like
>(with sincere ratings):
>
>49: A(99)  > C(2)  > B(1)
>48: B(99)  > C(2)  > A(1)
>03: C(99) > A(98) > B(1)
>
>C is the CW, but A is a much more stable, much higher SU,
>arguably as fair or fairer winner.
>

Aaron Armitage wrote:
Any strategically informed voter will give approval-like ratings, and will
approve the top two frontrunner he likes better, as well as any candidates
he prefers to that frontrunner, which means that the stated ratings will
look like that regardless of the real ones and a range election will tend
to produce that result regardless of how much utility voters attach to
each candidate. And, of course, IRV produces the same result.

What you're suggesting, then, is a case where the sincere ratings just
happen to match the stated ratings that would be produced by strategic
voting, and that in this special case the strategic voting under range or
approval will look legitimate in elected A over C despite the existence of
a majority coalition for C over A. But range and approal must assume that
this is always the case, when it almost never is.

CB: I explicitly specified that the ratings are sincere. You seem to be assuming
that I am promoting Range or Approval as better than all the Condorcet methods
when I am not. I just gave the example to show that the sincere CW isn't necessarily
the most stable or only justifiable winner. (Maybe I am in the wrong thread.)

Since all Condorcet methods fail Later-no-Harm, in practice in a Condorcet election
the A and C supporters would most likely truncate making A the voted CW. If only
the A supporters truncate then the candidates are in a cycle that would most likely
be resolved in favour of  A.

In response to my question "what do you mean by 'Smith/IRV'?" Aaron replied:

"...we would first check to see who is in the Smith set.
If there's only one, he is the Condorcet winner and is elected. If not, we
eliminate all non-Smith candidates and the lowest Smith set member. Then
repeat until a winner emerges."

I assume that "eliminate" means "eliminate at once and drop from the ballots", so
the first Smith-set member to be eliminated is the one with the fewest initial first
preferences.  I think that is a method suggested by N.Tideman in his book. Is
that right?

In any case that method and "Smith//IRV" (eliminate and drop from the ballots all
non-members of the Smith set and then apply IRV)  both fail  Mono-Append and
Mono-add-Plump, unlike Smith,IRV.

Chris Benham


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