[EM] Approval Voting and Long-term effects of voting systems

[Kristofer Munsterhjelm]

On 12/06/2016 09:37 PM, Daniel LaLiberte wrote:
> 
> 
> On Sat, Dec 3, 2016 at 9:09 PM, Michael Ossipoff <email9648742 at gmail.com
> <mailto:email9648742 at gmail.com>> wrote:
> 
>     Daniel--
> 
>     Kristofer is repeating the usual Approval-objection, the same one
>     that Robert expressed.
> 
> 
> Thanks Michael.  I recognized some similarities, but Kristofer is
> certainly giving more agreeable, reasonable arguments, and he appears to
> agree regarding the value of Approval Voting.   The contention, if there
> is any, is about when strategizing is required, and whether it matters.

I did actually write a reply to your previous post, but I thought it'd
be a bit cumbersome to continue our discussion in two different threads,
so I was intending on folding it all into one thread once I get a reply
to my other post. But since what I wrote is relevant to Approval, I'll
quote it here:

=====

> IRV is Borda with instant run-off, correct?  Does IRV amplify or
> ameliorate the many problems with Borda?

IRV is Plurality with instant run-off. The analogous method for Borda is
called either Nanson or Baldwin. In Nanson, you do Borda, then eliminate
the candidates with below-average score, then rinse and repeat until you
have a winner. In Baldwin, you eliminate the loser one at a time.

Both Nanson and Baldwin are Condorcet methods, because a Condorcet
winner always has above mean Borda score. But like IRV, neither is
monotone. They're also relatively vulnerable to burial and neither
Nanson nor Baldwin is cloneproof. I'd take the Borda-IRV methods over
plain IRV anyday, but for Condorcet, there are better options.

IRV fixes some of the problems with Plurality. It's kind of an example
of a patch idea:

- Plurality has a problem (vote-splitting where very small parties draw
enough votes to make the aligned major party lose)
- How can we fix that?
- We add a patch where the small parties are eliminated first.
- Then the right major party wins!

It's true, but such patches are usually inadequate because they only
deal with the problem currently present. So IRV works well as long as
there are only two major parties. But when there are three, IRV no
longer knows which is the minor party and behaves erratically (cf
Burlington 2009).

In the past, I've heard some Approval supporters go "well, you know the
parties you absolutely do like and the parties you absolutely don't, so
just approve the former and don't approve the latter". But this is
another kind of patch. It works as long as that's true, but then fails
when it's no longer the case. In a Burlington scenario, both IRV and
Approval would have done well as long as there had been only two major
parties. But when there're three on the line, IRV becomes confused and
the chicken problem appears in Approval.

=====

So I don't find the counter that you can just "approve of the candidates
you like and not approve of the people you don't like" very persuasive.
This assumes that there will always be a clear delineation between the
candidates the voters like and the candidates the voters don't like.

So suppose that there will always be such a clear delineation. Then most
systems (like Condorcet) that support equal rank and reduces to Approval
when everybody equal-ranks will work: just equal rank the acceptables
and don't rank the rest. In particular, because such a preference type
is singlepeaked, there is automatically a Condorcet winner.

On the other hand, suppose that there won't always be such a clear
delineation. Then Approval will start running into trouble and/or put a
burden on the voters when you get into a fuzzy territory. In a
Burlington scenario, Approval could misjudge -- like IRV, except it
would misjudge in favor of a centrist rather than in favor of an
extremist, to the extent that the voters are risk averse and approve
more candidates than they would under optimal strategy.

So my point is that in "easy to call" elections where all the voters
have a sharp delineation between who they like and not, most reasonable
methods get it right. The difference is that ranked methods don't force
you to vote as if that were the case when there *is* no such sharp
delineation. On the other hand, in the scenarios where it's unclear what
society's preference is, like when there are multiple real contenders,
methods like Condorcet can have trouble. That's right, but so will
Approval.

The trouble manifests differently: in a Condorcet method, it permits
strategic voting if the voters know what they're doing. In Approval, it
increases the burden for honest voters (and the risk of a wrong result
if the honest voters don't pay attention).

A RangeVoting page on IRV says something like this:

'Q: Do you support IRV over Condorcet since Condorcet has problems with
strategy?
'A: Condorcet has problems with strategy. But IRV has problems without
strategy! So no sale!'

and I would say something similar:

'Q: Do you support Approval over Condorcet since Condorcet has problems
with strategy?
A: Condorcet has problems with strategy. But Approval burdens the voters
even without strategy! So no sale!'

And if Approval doesn't burden the honest voters, then neither do the
ranked methods.

Again, this kind of loops back to my concept of "manual DSV". Approval
can't do the impossible even though it seems to to do so, because
[Approval + whatever you do in your head to quantize the ballot] could
be considered just another voting method. If you do a fair comparison
between Approval and other methods by explicitly stating an algorithm
that does the quantization step for you, then the resulting quantized
Approval method is susceptible to strategy like every other.

> I don't think Approval goes wrong so badly, after it stabilizes around
> the median.  With most candidates who have a chance of winning being
> close to the median, it can't go far wrong when someone slightly farther
> away from the median wins occasionally.  

> I think this stability around the median is far better than having third
> parties occasionally win due to the weakness of major parties, or other
> destabilizing situations and asymmetries of power. 

Consider a method like, say, MAM. This method passes the Smith
criterion, which means that it'll elect from the set of candidates where
all of them would win a one-on-one runoff with any of the candidates
outside the set. Another way of saying this is that it'll be uncertain
of whom to elect (in the absence of strategy) only among those who are
close to the median anyway. So it picks someone close to the median
without the honest voters having to accommodate the restrictions of the
system.

Now, you could say that Approval is more resistant to strategy. It is,
because you have to play the strategy game no matter whether you're a
honest voter or not. If the voters can absorb the noise they need to
absorb in order to get Approval to behave nicely, then they can absorb
the noise that would result from strategy campaigns as well -- as long
as those strategy campaigns don't poison the polls, etc.