[EM] The responsiveness of Condorcet / Monotonicity

Adam Tarr atarr at purdue.edu
Tue Jul 15 15:07:50 PDT 2003

David Gamble wrote:

>Monotonicity is undoubtedly a desirable feature of an electoral method. I 
>do however feel that no method can be perfect and that other features are 
>more important ( proportional representation of parties, proportional 
>representation of opinion,

I'm re-stating others here, but anyway...

I'd agree that proportionality in parties or opinion is more important than 
whether or not there is a bizarre result here or there.  But this is 
meaningless when considering a single winner, where there is no 
"proportionality" to be had.  In that case, you just want the candidate 
that best represents everyone in the district.  (That may constitute a sort 
of "degenerate case" of proportionality, I suppose.)

>[and] maximum freedom of  voter choice regarding the individuals who 
>represent you, etc).

Does a voting system that has been shown to support a two-party duopoly 
really provide this?  We can debate until the cows come home about how much 
choice approval/Concorcet/etc. will provide, but from what I can see 
there's no reason to be satisfied with IRV in that regard.

>As to the non-monotonicity of IRV and STV let me give an alternative 
>definition of non-monotonicity
>" Non-monotonicity -something that occurs more frequently in theoretical 
>examples than real elections "

This is true, since monotonicity violations can only really occur when 
there are more than two viable candidates.  While this is a desirable 
situation (because it increases voter choice) but it is vanishingly rare in 
places where IRV is used.

That said, the lack of frequent monotonicity violations doesn't get IRV off 
the hook in my mind.  The fact that a method violates monotonicity means 
that it is strongly vulnerable to strategic manipulation.  Sure enough, IRV 
has all sorts of situations where it makes sense to move your compromise up 
on the ballot, and it can be extremely hard for the voter to figure out 
when to do this and when not to.

I consider monotonicity one of the two most important "academic" criteria, 
among those that are violated by any reasonable methods.  The other one is 
idependence from clones.  Clone-independence means that the election can 
effectively merge multiple candidates that always appear next to each other 
on the ballot.  Adding or removing a candidate that always appears just 
after a given candidate on every ballot will not change the result.

If a method fails clone-independence, then it will either have a bad 
"spoiler" problem (like plurality does), or will have the bizarre effect of 
making parties want to run as many candidates as possible (like Borda 
does).  IRV actually passes clone-independence, which is one point in its 

Again, like monotonicity, it's not the failure of the precise definition of 
clone-independence that I have a problem with.  It's that failing to 
satisfy that criteria is a red flag that other problems exist.

As a side note, only a few methods discussed here actually pass both 
clone-independence AND monotonicity.  Beatpath, ranked pairs, approval, 
cardinal rankings, median ranking, and extended MCA (Bucklin with equal 
rankings allowed) all satisfy both.  These are the only methods I know of 
that I'd work to get adopted for single-winner reform.

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