[Election-Methods] Why monotonicity?

Steve Eppley SEppley at alumni.caltech.edu
Tue Jan 15 08:22:41 PST 2008

```Hi,

-snip-
> Obviously, I did not mean that monotonicity was sufficient for
> non-manipulability. What I meant was that if a method is non-monotonic, then
> in virtue of its being non-monotonic it has one more way it can be
> manipulated.
-snip-

The strategy of raising a candidate in order to defeat it may
legitimately be counted as one more strategy in the voter's toolbox of
strategies, but I think the (narrow) question here is whether the number
of manipulable scenarios is greater given non-monotonic methods, given
the same set of candidates and same voters' preferences.  To my
knowledge, this has not been demonstrated.

Furthermore, since the assumptions of the same set of candidates and
same voters' preferences are dubious--candidates may adopt different
positions on the issues, and make different decisions about whether to
run, given a different voting method--monotonicity may be unimportant
even if it does reduce the number of manipulable scenarios.

I think all we can say for sure about the desirability of monotonicity
is that, all else being equal, it's better to be monotonic.

-snip-
> Whatever
> you think of range voting, it is a voting system and GST, AT, etc., do not
> apply to it.

(Arrow's theorem can be written to apply to Range Voting and Approval
and all methods.  From the perspective of a math purist, to whom a
"framework" is a non-standard way to express axioms, that's a better way
to write it.  Arrow's theorem is also more powerful when rewritten to
cover any method that chooses a winner, rather than just methods that
return a social ordering of the alternatives.  That's how I present
Arrow's theorem in my webpages at
http://www.alumni.caltech.edu/~seppley, along with a proof.)

I agree the Gibbard-Satterthwaite theorem does not imply Range Voting or
Approval are manipulable.  But they are manipulable nonetheless, so I do
not understand Daniel's point.

Another manipulative ploy with Range Voting is to also nominate inferior
"bogey-men" candidates to dupe sincere voters into giving a higher score
to a candidate that's not as bad. (This is similar to the "inferior
clones" problem that Borda suffers from.)  For example, suppose the
Republicans nominate Dan Quayle in addition to their regular nominee, to
dupe Democrat sincere voters into giving the 0 vote to Quayle instead of
to the Republicans' real candidate.

Range Voting and Approval can also suffer when non-strategically minded
voters vote poorly.  I expect a significant number of voters will give
low scores (or disapproval) to good compromise candidates, due to a
natural, fairly common tendency to overestimate the differences between
favorites and compromises.  I expect the elite political actors
(politicians, party operatives, big donors) will also expect this
behavior and will compensate by severely limiting the number of "good"
candidates nominated to the ballot.  I have observed this with the "Yes
or No" Approval-like method used when voting on public ballot propositions.

Also, don't forget the difficulty that many sincere voters in public
elections will have trying to mathematically analyze the relative merits
of candidates. (Where I work, I've seen adults unable to calculate the
Pacific time of an upcoming event given its Eastern time, and who have
trouble adding single-digit whole numbers to a recent year even though
this operation has been part of their jobs for years.)  Monotonicity is
unimportant compared to voters being unable to figure out meaningful votes.

In my view, these properties of Range Voting are much worse than
non-monotonicity.

--Steve

```