Approval is not preference (was Re: Arrow and Gibbard-Satterthwaite)

[Saari at aol.com]

Hi, guys.  I haven't been following the thread closely lately, but since you
seem to be taking my name in vain :-) I thought I better respond.

Steve sez:
>It seems to me that Approval *is* a preference order method.
>There are three possible votes on a candidate: Yes, No, and 
>Abstain.   The Yes votes map to "first preference."  The No 
>votes map to "third preference."  Abstentions map to "second 
>preference."

I disagree.  Pure Approval votes contain both more information, and less
information, than preference votes.  Example:

Consider a "true" (nontactical) preference vote with 6 candidates: ABFEDC. It
is impossible to map this data onto a "true" (nontactical) Approval vote -
there is not enough information to determine whether the "true" vote for B is
Yes or Neutral or No.

Similarly, consider a "true" (nontactical) approval vote:
A-Yes
B-Neutral
C-No
D-No
E-No
F-Neutral
It is impossible to map this data onto a "true" (nontactical) preference vote
- there is not enough information to determine if the "true" preference vote
would be ABFCDE or AFBEDC or ABFDCE or ...

Since neither can be derived from the other, it is clear that an Approval
vote is a fundamentally different way to express voter opinion than
preference vote.

(But if the Approval votes allow partial votes as well, i.e. 0.5Yes or 0.8No,
it is now possible to express "true" opinions in a way which allows a
derivation of "true" preferences.  The nice thing here is that this allows
infinitesimal gradations - as much as the voter desires - and it is not
necessary to specify 5 or 7 or N allowed gradations.
However, I think it is very necessary to preserve the notion of "0" or
"neutral", and allow votes on either side, e.g. "For" or "Against" (with
gradations) or "Neither".)

> I didn't want to anger Steve Eppley.
> I wanted to anger Mike Saari.
-I missed who wrote this, but I find it amusing.

>Good luck trying to irritate Saari; he seems quite serene. 
>I'll try, though...  :-)
-Thanks, Steve!  :-)  I've enjoyed our debates.

>Some of his thinking is knuckle-
>headed, such as his attempt to show that voters won't have a 
>rational reason to strategize if his favorite voting method is 
>used.  His example depended on a scenario where all voters but 
>one had their votes conveniently cancel out, letting the one 
>remaining voter vote with no benefit gained from strategizing.  
>Such a scenario is implausible; there's no reason to expect all 
>the other ballots to exactly tie.

I don't believe I depend on this scenario.  My thinking is more along these
lines.  Let's say my "pure" (nontactical) Approval vote is something like:
A-Yes
B-0.8Yes
C-Neutral
D-Neutral
E-0.3No
F-No
We can probably agree that A=Yes, F=No is rational.  But what about B,C,D,E?

Steve claims that my rational (i.e. tactical) vote for B (and C,D,E) will
ALWAYS be either Full Yes or Full No - depending on just which data I have on
the likely outcome.

I claim that any B vote besides 0.8Yes is only rational *IF* I have enough
data on the likely outcome to ensure that any attempt at a tactical vote is
unlikely to backfire. 

Then I claim that, since other voters may or may not follow the same
reasoning (and thus may or may not tactical vote), IT IS IMPOSSIBLE TO
RELIABLY PREDICT THE OUTCOME.  

Therefore any attempt to tactically vote (i.e. any vote besides 0.8Yes on B)
has a significant (non-zero) chance to backfire.

In summary:
The naive (or knuckleheaded) vote for B is 0.8Yes.

The smart or clever vote for B is either Yes or No, but this always has the
risk to backfire.

The extremely-smart, sophisticated, super-rational vote for B is 0.8Yes.  By
foregoing the temptation to tactical vote, I eliminate the risk of backfire.
 And since the outcome can never be reliably predicted, this is the most
rational decision.

Thus I believe that Approval votes (especially with gradations) can yield
good, rational outcomes.

Mike Saari