[EM] Some brief campaign argument (Approval)

[LAYTON Craig]

Thanks to Richard, Martin & Anthony for their comments.

>Like Don Davison and Craig Carey, Craig has attempted to find points
>against approval. Although he has done a somewhat better job of it,
>I still think there are problems with his arguments.

Oh, no! Don Davison and Craig Carey?!

As I said, I don't intend to repeat these arguments often - I was just
taking the election as a chance to campaign for my favourite group of
methods by pointing out the flaws with its major rival.

I would like to emphasise that I don't think Approval is a terrible method.
I actually think it is very good for non-political elections, and certainly
better than Plurality, IRV, Cardinal Ratings, Borda &c. for political
elections (except in the case of two very strong candidates and a bunch of
frivolous candidates, where IRV might be marginally better, but IRV does so
much worse in any other situation that I don't believe it is a good
proposal).

I'll respond to a couple of comments here;

Richard wrote:

>I don't find collapsing of preferences under Approval to be a disadvantage
to
>the
>method. It forces voters to express the preferences that matter most to
them.

While I do think that this is a disadvantage, that wasn't my point.  My
argument was based on a criteria type approach to approval, where approval
passes all these strategy criteria by virtue of never having to
order-reverse.  I was pointing out that this was a non-argument, because the
only reason it is true is that the preferences you can express are
constrained.  With more detail, any system will fail these tests.

>I do have a conjecture in mind to the effect that the worst-case SU result
>from Approval (all voters voting optimum strategy) will always be better
than
>the worst-case SU result from fully-ranked methods. A slightly more
probably
>conjecture is that worst-case SU from Approval will be better than
worst-case SU
>from fully-ranked methods if all voters vote optimum zero-information
strategy.
>I don't claim to be able to prove these statements, hence the label
>"conjecture".

Martin also wrote some interesting things about SU.  It seems to be the crux
of the matter.  What I'm actually arguing is that SU predictions or
measurements of how Approval will do are innacurate.  Rob LeGrand's analysis
of the different Condorcet methods (given sincere voting) were interesting,
and have quite a bit of relevance (particularly noting that margins does
much better than defeat support, despite Mike's prior claims to the
contrary).  Although this, too, is somewhat of an approximation, the
assumptions made probably don't advantage one method over another.

It is worth noting that there is no way of ensuring a consistently high SU
result.  There are bad SU scenarios in any method - in Approval (with all
voters using zero info above mean strategy);

Sincere Utilities (out of 100);
20% A-60; B-40; C-40; D-0   Approval vote ABC
20% A-100; D-40; C-20; B-5  Approval vote A
60% D-6; B-3; C-2; A-0      Approval vote DB

B wins in Approval, followed by D then A, then C.  B is the worst SU
candidate, and D is the second worst.  A (who comes third in Approval) has
an SU rating which is nearly as high as all of the other candidates
combined.  Obviously the worst case scenario is pretty much the same for any
election method.

This is also one of my criticisms of CR.  Even when it is "sincere", the
utilities are generally weighted to give one candidate 100 and one candidate
0, which may bear no resemblance to actual utility values, but I won't go
into the problems with this.

Basically, I think that SU arguments are important, but that an election
method should be justified by some other means.

Martin wrote;

>*shrug* Approval fails the Condorcet criterion. Yep - that's kind of the
point:
>in order to elect the best SU winner, you have to fail a number of
criterion
>which people who don't care about SU seem to like. The Condorcet Criterion
is
>just one of them - the best SU candidate and the Condorcet Winner may well
be
>seperate people. In this situation the best SU candidate will have a higher
SU
>than the Condorcet Winner, but will lose to it in a pairwise comparison. If
you
>think that in this case we should elect the Condorcet winner over the
candidate
>with the higher SU, then Approval isn't for you, full stop. I'd like to
know why
>you think that, though.

I do place some faith in the Condorcet criterion, but that wasn't the point
of the example.  The point was that your vote was wasted, because you (as
part of a large group of people fooled by the polls) picked the wrong
preference to express.

>That's just wrong. Remember, for an instrumental voter, their vote is only
>relevant if they break or make a tie. That's it: everything else is
irrelevant.

You are right, of course.  But imagine you are playing in a soccer match and
your team loses 3-1.  During the match, you score your team's only goal, but
you also score an own-goal for your opponents.  You haven't caused your team
to lose by scoring the own-goal, but that doesn't stop you feeling bad about
it.  In Condorcet, you almost never score an own-goal, and I see that as
being utility positive (you are happier with your role in the contest, even
if you don't win).  The example I gave was like a team losing because a
number of the players scored own goals.  There was no instrumental player to
blaim, but if none of them had done it, then they would have won.

>How is that simpler than Approval 101? Not only do I have to decide which 
>candidates I like (which is easy), I have to decide which ones I like
>best. Sometimes that's easy, too, but not always. If I like Candidate X's
>fiscal policy but like Candidate Y's social policy, which one do I rank
first?

I have, in the past, posted some examples that show just how tough approval
can be in deciding how to vote, even when you know all of your expected SU
scores and you have detailed polling information, there can still be three
or four different ways to vote, all seemingly sensible and in line with the
information available to you.  I haven't got my old examples, but I can
think up some more if anyone wants.