[EM] Re: Condorcet's strategy problem, ICA

[Kevin Venzke]

Rob,

--- Rob Lanphier <robla at robla.net> a écrit :
> I think implicit approval punishes honest voters.  You're asking that
> voters opt out of races between candidates that they don't approve of,
> even though they could very well have an opinion.

I'm not asking them to do so. I haven't attempted to map "sincere approval"
to an ICA concept. It seems to be the case that in ICA, one should approve
*lower* than one would under ordinary Approval. I suppose we would expect
that, since ICA nearly satisfies Condorcet, and so provides better protection
to higher-ranked candidates than Approval does.

I would rather punish "honest voters" (i.e., people who want to rank even
among candidates they don't like) than open the method up to lots of strategy.

> If the approval question is actually tied to something substantive (e.g.
> term length), does that help remove the incentive to bury?

I don't see how. The problem with explicit approval (relative to other 
Condorcet methods) is that the turkey candidate (under which a frontrunner is 
buried) can never be elected on approval. He can only be elected as the CW, 
when both sides try to use him. So if you believe that the turkey candidate won't 
be the Condorcet winner, you are better off or the same by attempting burying
strategy.

> ...and C would win, and there's no way that B voters could truncate
> their way to victory.  So, at least in a head-to-head race, WV methods
> behave in a relatively predictable way.  Your approval example doesn't
> require a third candidate to produce a peculiar result.

In the two candidate-case, it requires that enough voters rank both
candidates *equal top*, that neither candidate can beat the other if the
equal-top voters were to count for the other side.

These two candidates aren't going to be Bush and Kerry. They're going to
be rather similar candidates.

> I can't say I'm thrilled with how WV handles this problem, but accept
> that the result is never going to be perfect when there is no Condorcet
> winner.

Of course, I feel there are negative consequences when we respect even
*weak* Condorcet winners. I suggest we throw those out, and try to satisfy
additional criteria instead.

> I'd be willing to concede that both this:
> 40 A>B
> 35 A=B
> 25 B
> 
> ...and this:
> 49 A>B=C
> 24 B>C=A
> 27 C>B>A
> 
> ...constitute cases where no candidate can claim majority support, and
> thus, there's really no "good" answer.

In my opinion, in the second case, it's quite clear that B is the "good"
answer. This commits us to truncation incentive when, changing B to B>C,
C becomes the winner. But as I said before, we don't have any great methods
that completely lack truncation incentive, so we might as well not pretend
we can get away from it.

I agree that it would be preferable to elect A in the former scenario, and
also that A's claim to the win is not very strong.

> I'll have to do some more thinking on this.  It appears as though ICA is
> a variant of CDTT//Approval.  Am I getting that right, and if so, can
> you explain the difference and why it's different?  If this was
> discussed before, just let me know the rough timeframe and I'll try to
> dig up the reference.

Some differences:

1. ICA attempts to respect all wins, while CDTT only respects majority-strength
wins.
2. ICA uses an "eliminate all of a certain type of candidate unless that would
leave no one" method. CDTT uses beatpaths.
3. Because CDTT uses beatpaths, it can't satisfy FBC, but it can be clone-independent.
(With beatpaths, there is no way I can see to treat equal-top rankings in a
way that is guaranteed to be as advantageous as a strict ranking. For the same
reason, I can't think of a way to modify IRV to satisfy FBC.)

CDTT reduces truncation incentive. But Approval has significant truncation
incentive, so I think it would be a bit odd to mix them. (You can use CDTT
to force minimal defense compliance, but Approval already satisfies a form of
that.)

Closer to CDTT//Approval is MDDA. MDDA is just like ICA except only majority-
strength wins are counted, and there is no need to treat equal-top rankings
in a special way.

Another method is what I call "MAMPO": If no candidate is majority-approved,
elect the most approved candidate. Otherwise elect the majority-approved
candidate with the lowest MMPO score.

I like ICA presently because it is the most sensitive to the ranking data,
although it is harder to explain.

Kevin Venzke



	

	
		
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