[EM] eliminate the plurality loser until there is a Condorcet winner

[James Green-Armytage]

Quick question for everyone: Do you happen to know when the method  
described in the subject line (eliminate the plurality loser until  
there is a Condorcet winner) was first proposed?

The rest of this message is a reply to Chris Benham.


Hi Chris,

You wrote:

> Smith,Hare (which Woodall called "CNTT,AV") meets those criteria and has a
> simpler algorithm:
>
>> Begiinining with their most preferred candidate, voters strictly rank
>> however many candidates they wish.
>> Before each (and any) elimination, check for a candidate X that pairwise
>> beats all  (so far uneliminated)
>> candidates. Until such an X appears, one-at-a-time eliminate the candidate
>> that is voted favourite
>> (among uneliminated candidates) on the fewest ballots. As soon as an X
>> appears, elect X.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-November/026954.html

I see that you assert this equivalence also at
http://rangevoting.org/SmithIRV.html

I accepted this for months, but today I was sitting around at a strip  
mall waiting for my car to be fixed, when I finally realized that  
these methods are not equivalent.
For example...
4 voters: A>B>C>D
5 voters: B>D>A>C
6 voters: C>D>A>B

The Smith set includes all candidates.
The Hare elimination order is D, A, C, B.
Therefore Woodall's CNTT,AV method elects B (as does Smith//IRV).

However, once D is eliminated, A is a Condorcet winner.
Therefore, the method you describe elects A (as does Tideman's  
Alternative Smith method).

Assuming that I'm right about this, it seems that you have defined a  
new method, distinct from Woodall's CNTT,AV.

I'm working on an essay about these different Smith/Hare hybrids: For  
convenience in writing, I refer to them as Tideman (a.k.a. Alternative  
Smith) Smith-Hare (a.k.a. Smith//IRV), and Woodall (a.k.a. CNTT,AV).  
Now I see that I should probably add this fourth method into the mix  
as well. Should I refer to it as the Benham method? I feel like this  
method has been mentioned on the list a few times over the years, but  
I don't really remember when it first arose. It doesn't really matter  
much what I call it, as the name is only intended to serve as a  
place-holder, but since I'm using person-names for the other methods,  
I'd prefer to continue with that.

Anyway, it seems to be a good method, sharing most of the properties  
of the other Smith/Hare hybrids, and probably having the simplest  
definition. I'm pretty sure that it's Smith efficient, and I'd be  
quite surprised if it were any more vulnerable to strategic  
manipulation than the other methods, though I will verify that. At  
first glance, it seems to be like CNTT,AV in that it fails local IIA  
but passes mono-add-plump and mono-append, but I'd appreciate it if  
you would think about this and let me know whether you agree. The  
local IIA failure is easily shown by example, but the others will  
require a formal proof, which I haven't constructed yet. Of course I'd  
be happy to send you a draft of the essay if you like, although it's  
still in a sort of skeletal form.

my best,
James