[EM] Generalizing "manipulability"

[Juho Laatu]

--- On Fri, 23/1/09, Kristofer Munsterhjelm <km-elmet at broadpark.no> wrote:

> Juho Laatu wrote:
> > 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).
> 
> Since all ranked methods are vulnerable to strategy, what
> constitutes an optimal vote depends on the votes of
> everybody else. Thus no such method can be either of the
> above

I refer to our discussion on the
possibility to meet some criteria
partially. I think we too often use
black and white criteria (or use the
criteria in a b&w way). I'd use all
four criteria that I listed also as
"partially met" criteria.

One can thus define an ideal and then
check how close each method gets.

> , and any simple method (by the definition) must also
> be non-manipulable, since to discover the optimal vote
> otherwise, you'd have to know the votes of potentially
> everybody else.

The definitions that I gave are not
necessarily good/optimal/useful. One
could e.g. remove word "optimal" from
the definition of the "non-manipulable"
definition.

One should maybe have a separate term
for optimal vote at the time of voting
and optimal vote at the time of counting
the votes.

One should also have separate terms for
a method with a default vote creation
method defined and for one without.
These correspond to "election method as
part of the society" (with default rules
of behaviour) and "vote tabulation method"
(that doesn't take position on how and
where the ballots came from).

You are welcome to propose better
definitions. I don't have a perfect set
available right now.

> 
> The definitions you gave could be used for zero info
> strategy. For instance:
> 
> Simple zero-info: The optimal zero-information strategy is
> simple to determine.
> 
> Dominant zero-info: If everybody uses zero info strategy,
> and the method doesn't output a tie, no single voter
> could gain by changing his vote to something else.
> 
> And there's also the usual zero-info strategy
> criterion:
> 
> No zero-info strategy: The optimal zero information
> strategy is a sincere vote.
> 
> 
> "No zero-info strategy" implies "simple
> zero-info". Dominant zero-info is vaguely similar to
> SDSC, though the latter deals with counterstrategies.
> Dominant zero-info may also be too strong: consider a
> situation where the voters produce a "tie minus one
> vote" (where a certain ballot can produce a tie); then,
> if the final voter prefers a candidate that would be ranked
> lower to one that would be ranked higher, he can construct a
> vote that leads to the two being tied.

This last note sounds quite a lot like
"one-man-one-vote" (=one voter can not
change the end result much).

I need to think more what kind of useful
definition sets we might have, and which
ones could be used as an (few ideal
targets based) "coordinate system" to
describe and classify the methods.
That would (in theory) mean few core
criteria and their refinements and
estimated levels of compliance (instead
of just a large set of black and white
criteria). I'm not sure if it is possible
to achieve anything useful though but one
can always try.

Juho