[Election-Methods] Why monotonicity?

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


Daniel Radetsky wrote:
> 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.

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.

> 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 


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