[Election-Methods] Why monotonicity?

[Steve Eppley]

Hi,

Daniel Radetsky wrote:
> On Jan 1, 2008 1:15 PM, Steve Eppley <SEppley at alumni.caltech.edu> wrote:
>
>   
>> Are monotonic methods less manipulable than non-monotonic methods?  I've
>> never heard any evidence of that.
>>     
>
> I'm going to assume that you are not asking something like "For all possible
> voting methods and some reasonable manipulability metric, is the average
> manipulability of the monotonic methods lower than the average
> manipulability of the non-monotonic methods?" For if a method is
> non-monotonic, this means that there is a way to manipulate it. 

I am not aware of any such cause and effect, since monotonic methods too 
are manipulable. (For our purposes we can neglect trivial scenarios: 
dictatorship, fewer than 3 candidates, special cases of voter 
preferences, etc.  The Median Vote method, for example, is feasible only 
if the alternatives are mapped to a single dimension and is 
non-manipulable only if the voters' preferences fall within a particular 
domain sometimes called "single-peakedness.")

I asked about "less manipulable."  Are monotonic methods less 
manipulable?  Right, I did not have averages in mind.  But I don't want 
to ask the question too narrowly, since I can't predict which lines of 
thought might shed light on the issue.

>  If you are
> asking whether given the choice between (say) a monotonic,
> non-clone-independent method and a non-monotonic, clone-independent method,
> all else being equal, then perhaps as you suggest, clone-independence is
> more important. However, I was under the impression that one of the goals of
> studying voting methods was to avoid having to make this choice.
>   

That was a goal decades ago, until it was concluded there is no perfect 
voting method. (Take a look at the Gibbard-Satterthwaite manipulability 
theorem.)

For the particular question of whether methods can be both monotonic and 
independent of clones, the answer is yes. (For instance, MAM, my 
favorite method.)

> In any case, resistance to manipulability is not the only reason to desire a
> particular property for a voting system. Another important quality is
> transparency: does casting a vote do what the voter thinks it does? A voter
> thinks that when he increases his vote for X (whatever "increases" means in
> the system in question), he is helping X win. In a non-monotonic system,
> he's wrong, or at least not guaranteed to be right. This is bad. Right?
>   

Imperfect, not bad.

All else being equal, it's better to be monotonic than non-monotonic.  
But it does not follow that the best method is monotonic (since all else 
is not equal).

All else being equal, it's more transparent to be monotonic than 
non-monotonic.  It does not follow that the most transparent method is 
monotonic.

Regards,
Steve