[Election-Methods] voting research

[Jonathan Lundell]

On Aug 3, 2008, at 4:13 AM, Warren Smith wrote:

>> 1. USUALLY it is EASY to find a BETTER-than-honesty
>> strategy in IRV.  This is not just me ranting.
>> It is in fact a published theorem.
>
> Please post a citation of this published source others can find it.
> Thanks in advance.
>
> --see this:
> http://RangeVoting.org/ConitzerSmanipEasy.pdf

I'm confused by the definition of manipulability in this paper, and  
I'd appreciate someone straightening me out. In the abstract, the  
authors write:

> …the Gibbard-Satterthwaite theorem shows that when

> there are three or more candidates, all reasonable voting rules
> are manipulable (in the sense that there exist situations in
> which a voter would benefit from reporting its preferences in-
> sincerely).

So far so good--that's what I understand manipulation to mean in this  
context. But later on, in the paper's formal definition of  
manipulability, for purpose of proving their theorem, the authors write:

> The computational problem of manipulation has been defined
> in various ways, but typical definitions are special cases of
> the following general problem: given the nonmanipulators’
> votes, can the manipulator(s) cast their votes in such a way
> that one candidate from a given set of preferred candidates
> wins? In this paper, we study a more difficult manipulation
> problem: we require that the manipulator(s) find the set of
> all the candidates that they can make win (as well as votes
> that will bring this about). This stronger requirement makes
> our impossibility result stronger: we will show that even this
> more powerful type of manipulation cannot be prevented.
>
> Definition 1 [you'll have to go to the paper for the formal  
> definition; the format is incompatible with my mailer]
>
> An instance is manipulable if the manipulators can make
> more than one candidate win.

Problem one is that I don't see a definition of "instance". I take it  
to be a particular set of (nonmanipulator) ballots, but I'm not  
entirely sure that's the intent.

Problem two is that it seems that an instance in which the  
nonmanipulators end up with a tie between some number of candidates  
 >1, then the that instance is by definition manipulable by a single  
manipulator who simply casts a vote for any one of the candidates,  
causing that candidate to win. And that isn't manipulation.

Where am I going off the rails?