[EM] Draft of CVD analysis about IRV vs. Condorcet Voting

[James Green-Armytage]

This is James Green-Armytage responding to Ken Taylor


>Resloving it with IRV
>would elect C -- basically giving the "insincere" B voters what they ask
>for
>(in fact, B has no chance if IRV is used as the resolution method).

	See below for examples of strategic vulnerability in
Condorcet-completed-by-IRV.
>
>> Yes, but that's just it. No matter what the cycle breaking method is, it
>> will under some circumstances reward those who have strategically
>created
>> the cycle to begin with. Your argument is dependent on this point, and
>> since you are wrong on this point, your argument is wrong.
>
>My *main* argument was that you can never use strategic voting to change
>the
>condorcet winner, as was implied by the original article; at best you can
>create a cycle, and that the strategic incentives depend heavily on the
>actual cycle resolution method used. Please explain to me how your
>assertion
>that there is no perfect resolution method makes this wrong? I believe you
>are misrepresenting my argument by giving my parenthetical statement more
>strength than it was intended to have.

	Well, your overall thesis was that the point CVD was making was "entirely
incorrect." To quote the opening of your letter: "This entire paragraph is
completely incorrect. There is no strategic advantage to ranking (major
candidate) B lower than your real preference for B. Try to come up with an
actual vote distribution (with actual numbers) in which there is such an
advantage and you'll fail."
	You used a few different points to come to the overall conclusion quoted
above, and some of those points are correct. However, your argument is
like a chain with a broken link: only one link needs to be broken for the
chain to fail. 
	One link in the chain is that no single voting bloc acting toward a
common interest can change the result from a sincere Condorcet winner to a
phoney Condorcet winner. That link is, to my knowledge, sturdy.
	The next point is this one: "At best, this
insincere ranking will create a cycle in the result -- and then the
strategic advantage depends on the cycle-breaking method." 
	This is also correct, I think. However, then you come to this point: "The
most popular
cycle-breaking methods espoused by Condorcet enthusasts, such as Schwartz
Sequential Dropping (using *magnitudes* of defeat rather than *margins*)
can
be shown to be immune to such strategies."
	Which we now agree is wrong. My point now is that because SSD(WV) doesn't
eliminate incentive for burying, and because no other Condorcet completion
method eliminates incentive for burying, your whole thesis falls apart
like a broken chain. That argument again is summarized in your phrase
"There is no strategic advantage to ranking (major candidate) B lower than
your real preference for B."
>
>Furthermore, I contend that "under some circumstances reward[ing] those
>who
>have strategically created the cycle to begin with" does not necessarily
>mean there is a strategic incentive to create the cycle. Whether there's
>an
>incentive depends heavily on what those circumstances are, how likely it
>is
>to be in your favor without backfiring, and how well you can predict those
>circumstances ahead of time.

	True. Effective strategy in Condorcet depends on the availability of
information about how other people will vote. In a zero-information
situation, I would like to tentatively say that a fully sincere vote is
always in a given voter's perceived best interest. But a truly
zero-information situation is totally unrealistic for a public election.
Even if poll numbers aren't precice, there will still be a general
perception about who the frontrunners are. 
>
>With SSD, for example, a very small change in the voting numbers could
>result in the B/C defeat being broken instead of the A/B defeat, causing C
>to win. I contend that this is *not* a result B would have wanted, given
>that their true preference was A>C. 

	Right.

>If B voters truly would rather have A
>lose at all costs, then I contend that their true preference is B > C > A,
>as they voted.

	No, it is possible that they actually prefer A to C but are still willing
to engage in dishonest voting and risk getting C elected in order to get a
chance at electing A.
>
>And finally, as IRV is immune to this particular strategy (a claim made
>both
>by you and by the author of the article I was responding to), using IRV
>as a
>completion method would also be immune to this particular strategy. And
>so,
>my argument against the contention that Condorcet falls prey to this
>particular strategy is not ultimately wrong.

	Okay, here's a classic example where Condorcet-completed-by-IRV is
vulnerable:

sincere preferences
45%: A > B > C
6%: B > A > C
21%: B > C > A
28%: C > B > A
	B is a Condorcet winner, but the A>B>C voters can gain an advantage by
truncating (in effect voting A > B = C) Then the result is
45%: A > B = C
6%: B > A > C
21%: B > C > A
28%: C > B > A
	There is no Condorcet winner, so IRV is used, electing A.

	Here's a nearly identical example which doesn't add anything conceptually
but which I'll post anyway:
35%: A > B > C
16%: B > A > C
16%: B > C > A
33%: C > B > A
	Again, although B wins all of her pairwise comparisons with ease, the
A>B>C voters can get A elected if they all truncate.
>
>This stands in stark contrast to a method such as Bourda count, where
>strategic order reversal is almost always going to come out in your favor
>(as long as your opponent doesn't do it, too!). The original article's
>wording seemed to imply that the flaw was just as serious in Condorcet as
>it
>is in Bourda, and I believe I'm correct in stating that it's not.

	I agree with you here. Borda is so strategically vulnerable that it's
almost funny. Yeah, although the CVD draft is making a valid point, they
do use language that pushes it a little over the top, in particular when
they say "All the mathematical elegance of Condorcet Voting is irrelevant
when it can be so obviously gamed through insincere strategic voting."
That's taking it a step too far, I agree. They never mention Borda
specifically, but it does seem like they're putting it in that sort of
range.
>
Sincerely,
James