[EM] Can someone point me at an example of the nonmonotonicity of IRV?

[Kathy Dopp]

On 8/10/08, Kristofer Munsterhjelm <km-elmet at broadpark.no> wrote:

> I think what he means is that although the paradox is severe when it
> does happen (similarly to driving off the road), it happens very rarely,

Voters are *not* independent random variables.  So there is no basis
to know whether a particular situation would occur or not during an
election.

> and in general, IRV gives a result that's better than say, Plurality
> applied to ranked ballots.

IRV proponents always compare IRV to whatever method they feel gives a
favorable comparison on a particular issue.  IRV is on the whole much
worse than plurality voting in a lot of ways as well if that is what
you want to compare IRV to - auditability, cost, complexity &
confusion, election administrative burdens, timeliness of election
results, etc. are worse with IRV than with plurality. See my paper
"The 18 Flaws of IRV..."

>
> If it happens too often, though, one could get real paradoxes such as
> one that Ossipoff gave: a candidate being shown to be corrupt (so that
> many rank him lower) leads to that candidate's victory.
>
> There's also the "it smells fishy" that nonmonotonicity - of any kind or
> frequency - evokes. I think that's stronger for nonmonotonicity than for
> things like strategy vulnerability because it's an error that appears in
> the method itself, rather than in the move-countermove "game" brought on
> by strategy,

Yes. The error is out of the control of the individual voters.

> and thus one thinks "if it errs in that way, what more
> fundamental errors may be in there that I don't know of?".

I am amazed that anyone would need "more".

> A less "feelings-based" way of showing the oddities of IRV would be to
> point at Yee pictures: http://rangevoting.org/IEVS/Pictures.html
> The disconnected regions in IRV pictures are a consequence of
> nonmonotonicity - moving towards a candidate leads to another winning.
> Note that a method may be nonmonotonic in general and still be monotonic
> in the subset that 2D Yee-pictures cover.

Thanks for reminding me of these. Even though I have not studied these
pictures enough to understand them myself yet, for completeness for
the reader, I should probably cite them in my paper if they aren't
already in the endnotes.


>Also, that doesn't resolve the
> problem of figuring out how severe a monotonicity failure is, but just
> how frequently they occur in "voting space".

Yes, well since voters are not independent random variables, and due
to the secret ballot, I believe that it is not possible to figure out
how frequently they might occur.

>
> Out of curiosity, what voting system would you recommend? I'm not saying
> "don't say anything if you don't have an alternative", I'm just curious.

I am currently not recommending *any* until I have more time and
inclination to sit down to thoroughly study all the alternatives. I
know that IRV is a really bad method as applied to real life
elections, and I suspect that most other voting methods are superior
to IRV in crucial ways that would make them more practical and
desirable.

> I think that all methods that work by calculating the ranking according
> to a positional function, then eliminating one or more candidates, then
> repeating until a winner is found will suffer from nonmonotonicity. I
> don't know if there's a proof for this somewhere, though.

I do not know about "nonmonotonicity" but range voting does not have
the property that I can possibly help my first choice more by ranking
my first choice below my last choice which is insanity IMO.

Well perhaps there are other voting methods where ranking my first
choice candidate below my last choice candidate helps my first choice
candidate to win more than vice-versa, and I would oppose any method
that did that.  I somehow do not think that most methods that converts
rankings to ratings or use ratings do that, but perhaps I am wrong.

>
> A positional function is one that gives a points for first place, b
> points for second, c for third and so on, and whoever has the highest
> score wins, or in the case of elimination, whoever has the lowest score
> is eliminated.
>
> Less abstractly, these methods are nonmonotonic if I'm right: Coombs
> (whoever gets most last-place votes is eliminated until someone has a
> majority), IRV and Carey's Q method (eliminate loser or those with below
> average plurality scores, respectively), and Baldwin and Nanson (the
> same, but with Borda).
>
> It may be that this can be formally proven or extended to other
> elimination methods. I seem to remember a post on this list saying that
> Schulze-elimination is just Schulze, but I can't find it. If I remember
> correctly, then that means that not all elimination methods are
> nonmonotonic.

Is this the definition of monotonicity:?

Increasing my vote for candidate X, may cause candidate X to lose,
whereas decreasing my vote for X, may cause candidate X to win.

Cheers,

Kathy