# [Election-Methods] Why monotonicity?

Steve Eppley SEppley at alumni.caltech.edu
Thu Jan 10 06:42:50 PST 2008

```Hi,

> 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.")

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?
>

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

```