[EM] Generalizing "manipulability"

[Kristofer Munsterhjelm]

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, 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 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.