[EM] Generalizing "manipulability"

[Juho Laatu]

--- On Thu, 22/1/09, Raph Frank <raphfrk at gmail.com> wrote:

> Anyway maybe a non-manipulable method requires
> 
> 1) a simple method to convert honest preferences into valid
> votes
> 2) this method may not use info about other voters
> 3) If everyone else uses this method, then it is in your
> interests to
> also use this method
> 
> One possible subjective aspect would be what simple means.

One could also drop the requirement of
simplicity (since non-manipulability
doesn't necessarily require that) and
keep it as a separate requirement.
 
> Methods that require some knowledge of polls to work would
> fail this definition.

"Non-manipulability" could also allow
use of this knowledge.

> However, most people have little problems with plurality
> and use the
> standard strategy quite effectively.
> 
> I think the concept of requiring a zero-info strategy to be
> optimal is
> a clean way of saying that voters who have access to more
> information
> should not have an advantage (be able to manipulate).

If there is a simple "non zero-info"
strategy that all can easily use (as
in Plurality) that could still be
classified as "non-manipulable"
(if otherwise ok).

> Perhaps also, the zero info strategy should be reasonably
> easy to understand.

I already noted that simplicity could
be a separate requirement / criterion.

> The criterion could perhaps be relaxed a little by allowing
> publicly
> available information to be used rather than it being
> purely zero-info

Difficult to define what the public
info is. But it would be good to have
criteria that can be met more or less
fully.

> (and that the method is somewhat resistant to inaccuracies
> in that
> info). 

Also level of tolerance against
inaccuracy, risk of backfiring of
the strategy, required level and
difficulty of coordination of the
strategy, frequency of the
vulnerability etc. would be
good parameters.

> Also, perhaps if the partial info strategy was only
> 'slightly'
> less effective than the optimal strategy under perfect
> info, then that
> would be OK too.

Yes. I think too often we ignore the
difference between failing some
criterion in some rare cases and
failing it regularly and in a way
that allows strategic manipulation
of the election.


I try to summarize my comments in the
form of some rough definitions.

A "simple" method requires
1) a 'simple' method to convert honest
preferences into optimal votes

A "zero-info" method requires
2) this method may not use info about
other voters, but still be able to
convert honest preferences into optimal
votes

A "non-manipulable" method requires
3) it is in everyone's interests to use
the default method to convert honest
preferences into optimal votes

(I didn't cover the "if everyone else uses this method" case.)

These definitions allow also e.g. Approval
to be categorized as (close to) "simple",
not "zero-info" and "non-manipulable".

One more definition to point out one
weakness of Approval.

A "decidable" method requires
1) a method to convert honest preferences into an unambiguous optimal vote

The point is that the there should be
no lotteries that may lead also to
unoptimal votes but the best vote
should be found in a deterministic way.
Approval fails this criterion since
picking the correct number of approved
candidates is sometimes tricky (when
there are more than two strong
candidates).

Juho