[EM] Some brief campaign argument

[Richard Moore]

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.

LAYTON Craig wrote:

  This is my post on why you shouldn't vote for Approval in the upcomming
  election.  I apologise for the negativity in advance - I didn't have enough
  space to throw in arguments in support of Ranked Pairs or BeatPath (or SSD).
  There seem to be three main reasons for believing Approval is the best
  electoral method - 1) a sincere vote is always the best strategic vote; 2)
  approval elections will elect a higher SU winner than any other method/s in
  a real world scenario.

Better let an Approval advocate state the case for Approval. Craig has it wrong.

1. The best strategic vote is always a sincere vote, but the converse stated by
Craig
doesn't follow from that.
2. I don't claim that Approval will always select a higher SU winner, real-world

or otherwise. There may be cases where Condorcet will outperform the Approval
SU. There will probably be a lot more cases where Approval will give the better
SU. 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".

These two reasons do not reflect my central reason for supporting Approval,
although the second reason is related. Since this message is a rebuttal I'll
only
briefly state my central theme before continuing to answer Craig's points:
Unlike
ranked methods, Approval measures intensity of preference and not just order
of preference.

  (There may be a further reason, that approval is the most mathmatically
  consistent method, but on its own, I don't find this argument persuasive.
  Please let me know if you do, and why.)
  1) Approval is unique in that a sincere vote is always the best strategic
  vote.  However, this is because you are only allowed to express a single
  layer of preferences - if you're preference is A>B>C, you can only express
  the preference A>B or B>C (in addition to A>C).  If you choose to express
  A>B, the system forces you to express B=C, even though this may be far from
  your sincere preference.  It is only a severe restriction on the preferences
  you can express that gives Approval this property, so I don't see it as an
  advantage.

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.

All systems have constraints. In Condorcet systems, if I vote A>B>C, it doesn't
convey whether I like A a lot more than B whom I like a little more than C,
or vice versa. That is a constraint that we will have to live with if we adopt
Condorcet.

(Hybrid systems like Dyadic Approval may provide something of a
best-of-both-worlds resolution, but I haven't yet seen enough analysis of
Dyadic Approval to fully support it).

  2) Issues of Social Utility are perhaps more complex than game theorists
  would have us believe.  If everybody uses sophisticated strategy and/or if
  everybody uses an above mean (zero info) strategy then it is true that
  Approval would do slightly better on average in electing the highest SU
  winner.  Arguments that voters will use highly sophisticated strategies are,
  I feel, a little optimistic.

If they are "optimistic", then do you mean voters will be less likely to
incorporate
polling information in their decisions (that would require a more sophisticated
strategy), in which case they are more likely to vote as if they had zero
information? But if it is true that zero info improves the chances of electing
the
highest SU winner, then doesn't the system actually perform better (under this
metric) in such cases?

    Of course, it is a little irrelevant - zero
  info strategy is the most intuitive, and most likely type of voting,

I do wish that were the case, but even I don't claim the zero-info strategy
will be the most likely one. I would expect more to see voters vote for all
candidates above the midpoint utility, or at and above some specific
ranking (such as top 3), or at and above their favorite of the front runners.
I don't think any of these variations will drive the result to a significantly
lower SU.

  and will still result in a higher SU candidate than Condorcet.  Right?
  Maybe, but I suspect not.  In a country with plurality voting, approval
  might not change voting habits at all and the vast majority might continue
  to vote for just one candidate.  This is by no means fanciful - I consider
  it likely among voters who don't understand the system very well (and
  perhaps even those who do).

Unless there are only a few candidates, I find this statement unwarranted.
Even with three candidates, it seems not unlikely that there would be
a bullet "disapproval" voter for every bullet approval voter. There are
always voters intent on keeping their most-feared candidate out of
office.

  Okay, it's a learning curve and over time, voting habits will change.  When
  the voters finally cotton on to what's happening, will they vote for above
  mean candidates?  There are still many things that might happen.  Approval
  leaves the way open for "vote for everyone except X" type campaigns, where
  the result of the election may bear no resemblance to the highest SU winner
  whatsoever.  In fact, any elections where the voters vote for too many or
  too few will result in a decidedly non-utility maximising outcome.  On the
  whole, I find no evidence to suggest that Approval will, on average, find
  the SU winner more often than a Condorcet system.  The examples that "prove"
  approval will, are based on unreasonable assumptions.

How candidates and parties campaign and how voters respond is external
to the method itself. But suppose the type of negative campaigning you
describe does become common. Do you really think voters always respond
favorably (from the campaigner's pov) to a negative campaign? I think such
campaigns will be sometimes rewarded, sometimes punished, and always
risky. Of course the risk won't prevent them from being attempted. I just
doubt that Approval will be led to far astray by this tactic.

Richard