[EM] simpler proof of "no conflict theorem" now trivial

[Abd ul-Rahman Lomax]

At 07:58 PM 8/16/2006, David Cary wrote:
>"The Condorcet criterion for a voting system is that it chooses the
>Condorcet winner when one exists."
>
>"The Condorcet candidate or Condorcet winner of an election is the
>candidate who, when compared in turn with each of the other
>candidates, is preferred over the other candidate."
>
>The ambiguity is about exactly how candidates are compared with each
>other and what preferences are to be used.

I'll say my assertion that Approval and Plurality satisfy the 
Condorcet Criterion was ... provocative. Here is the basis for it.

Practical election methods and their ballots are limited in the 
number of ranks which may be expressed. For example, does a write-in 
candidate have a prayer of success in a "fully ranked" method; 
"fully-ranked" implies that all candidates are compared; but the 
printed ballots would not have the write-in candidate on them; the 
number of potential write-in candidates is, of course, enormous, and, 
quite possibly, one or more of them would be well-known and liked 
sufficiently to be the true "Condorcet Winner."

Practically, then, the number of expressible ranks, usable in the 
method, is limited, the only real question is *how* limited. 
Plurality takes this to the extreme, not even allowing equal ranking. 
Approval fixes that, leaving two usable ranks. Approval Plus uses three.

Does Range Voting satisfy the Condorcet Criterion? The definition 
above, I'd suggest, does not really allow us to answer this 
definitively. As Mr. Cary pointed out, "how the candidates are 
compared" is unspecified. Range Voting compares them using average 
rating (which is a kind of ranking with equal ranking allowed), 
whereas standard ranked methods make no distinction between a minor 
difference in rank and a major one, i.e., strength of preference is 
not considered. I'd argue that Range is a more rational method of 
comparing candidates than binary or trinary ranking, if we assume 
that voters vote sincerely, and there is evidence that they would, by 
and large.

Asset Voting, on the other hand, could quite easily choose a winner 
who is not on the ballot (if the rules permit, which I would submit 
would be quite a good idea).

By the way, the argument is sometimes raised against Asset Voting 
that "I wouldn't want anyone to choose a candidate on my behalf; how 
could I know that I'd approve of this?"

My essential argument on this, I think, bears repeating: if I would 
trust candidate X in the office, most political offices, including 
that of representative, are largely about skill in delegating 
authority to staff. I voted for Kerry in 2004, but, when we needed 
assistance in facilitating an orphan petition to CIS (today's version 
of the INS), we contacted both our senators, Kerry and Kennedy. 
Kerry's office was quite unhelpful. Kennedy's office got the job 
done. What we had been told would take 90 days (leaving a child 
waiting in an orphanage in Ethiopia for an otherwise unnecessary 90 
days) took *one day* with the intervention of Senator Kennedy. Was it 
actually the Senator? Probably not. It was good, effective staff. And 
thus I come to the conclusion that I'd greatly prefer Kennedy to 
Kerry.... though I doubt I'll ever get the chance.

The skill needed for good performance in office, then, is the same 
skill as is needed to be able to delegate authority. And the ultimate 
delegation of authority is the choice of the office-holder. If I 
trust Candidate X to actually fill the office, I ought to trust him 
or her to make the choice of who fills the office. That's what Asset 
Voting does.